2-1 Aero Question Bank

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY

Department of Aeronautical Engineering

QUESTION BANK FOR 2 year – 1 semester

INDEX

S.NO Subject

1 INTRODUCTION TO AEROSPACE ENGINEERING

2 MECHANICS OF FLUIDS

3 THERMODYNAMICS

4 MATHEMATICS-II

5 MECHANICS OF SOLIDS

6 ENVIRONMENTAL SCIENCE

Code No: A109212101 R09 Set No. 2

II B.Tech I Semester Examinations,December 2011INTRODUCTION OF AEROSPACE ENGINEERING

Aeronautical EngineeringTime: 3 hours Max Marks: 75

Answer any FIVE QuestionsAll Questions carry equal marks

? ? ? ? ?

1. Write short notes on the following:

(a) Coefficient of lift

(b) Coefficient of drag

(c) Reynold’s number [5×3]

2. What are meant by ‘design’ and ‘Design skill’? [15]

3. List out and discuss in detail the advanced spacesuit considerations. [15]

4. All spacecraft will eventually come down and re-enter atmosphere - yes or no?Justify. [15]

5. Enumerate the various aerodynamics related experiments conducted by Sir GeorgeCayley. [15]

6. Compare the way aircraft and helicopters fly. [15]

7. With the help of a neat sketch, explain the working of an omni-directional antennacreating uplink and downlink of data with the satellite. [15]

8. Explain the findings of Isaac Newton that led to Newtonian Physics. How doesEinstein’s general theory of relativity superseed the concepts of Isaac Newton?

[15]

? ? ? ? ?

1

Code No: A109212101 R09 Set No. 4




? ? ? ? ?

1. Write short notes on the following with regard to propulsion and station keepingpractices:

(a) Initial spin-up

(b) Station keeping (N-S, and E-W)

(c) Angular momentum management [3×5]

2. Explain the working principle of a rocket engine. Describe the different componentsof a rocket. [15]

3. Write a detailed note on Computer Aided Design / drafting (CAD). [15]

4. Write detailed notes on

(a) longitudinal static stability of an aircraft,

(b) Stall Speed. [8+7]

5. (a) Write short notes on Galactic cosmic rays.

(b) Explain Solar cosmic rays. [7+8]

6. Write in detail on human performance in low-gravity environments. [15]

7. Over the ages the development of civilization was not Steady - Justify. [15]

8. (a) Provide a detailed note on the development of balloons during the 18th centurythat flew in air and created history in lifting a human being off the ground fora sustained period of time.

(b) Discuss the factors basically employed in the design of flapping wing of or-nithopters, which were subsequently modified by Sir George Cayley and theconcepts in the design of an airplane that paved way to the development ofcurrent modern aircraft. [7+8]

? ? ? ? ?

2

Code No: A109212101 R09 Set No. 1




? ? ? ? ?

1. Bring out the salient features that are involved in the design of a spacesuit. Whatdo the terms EMU and HUT mean? [15]

2. (a) Differentiate between lighter-and heavier-than-air flights.

(b) Illustrate the developments that took place during 18th and 19th centuries inthe area of heavier-than-air flight. [7+8]

3. (a) What do you understand by the Van Allen belts?

(b) Write about the structure of Magnetosphere. [7+8]

4. Write short notes on

(a) Elements of a satellite.

(b) Power systems of a satellite.

(c) Mechanisms of a satellite. [5+5+5]

5. Explain in detail the design process. [15]

6. Describe the aircraft and rocket and engines. [15]

7. Discuss longitudinal and lateral stabilities of an aircraft. [15]

8. Discuss the development of technology from the days of ‘wheel’. [15]

? ? ? ? ?

3

Code No: A109212101 R09 Set No. 3




? ? ? ? ?

1. Write a detailed note on the near Earth radiative environment. [15]

2. Discuss the various sources of drag that opposes an aircraft’s motion through air.[15]

3. Explain developments in Engineering that took place during the Hellenistic period,and Middle ages. [15]

4. (a) Explain the need for insulating and plating the satellite components. Cite afew examples.

(b) Discuss communication and telemetry systems of a satallite. [7+8]

5. Compare Mercury and Gemini Missions. [15]

6. Discuss in detail the NASA plans of a comprehensive space program to place aspace station with permanent human presence in low earth orbit and other relevanttechnical aspects. [15]

7. Compare steady and accelerated flights of an aircraft, mentioning the governingequations. [15]

8. ‘Safety is the most important aspect of aircraft design’ - Justify. [15]

? ? ? ? ?

4

Code No: A109212101 R09 Set No. 2

II B.Tech I Semester Examinations,November 2010INTRODUCTION OF AEROSPACE ENGINEERING



? ? ? ? ?

1. (a) Write a detailed note on microgravity. What is the magnitude of microgravityin terms of gravitational force of acceleration of Earth?

(b) Assuming 6370 km as the radius of the earth estimate the distance above thesurface of the earth where the microgravity effects or near-weightless conditioncould be felt. [8+7]

2. With the help of neat sketches, explain the design of an airfoil as wing that provideslift to an aircraft. [15]

3. With fundamental concepts explain how to draw straight lines, parallel lines, per-pendicular lines, and angles. [15]

4. (a) With the help of a neat sketch explain the attempts made by Sir GeorgeCayley to design and test a full sized airplane. Also discuss the features of‘Boy-carrier’.

(b) Discuss the features incorporated by Sir George Cayley in his design of gov-ernable Parachutes, during 19th century. [7+8]

5. Obtain the equations for endurance and range of a Jet aircraft. [15]

6. Discuss Indian Science and Technology. [15]

7. Present a detailed report on an oceanographic mission as a case study. [15]

8. Explain the physiological effects of extravehicular activity on human body. Whatwere the methods currently in practice to prevent such effects? [15]

? ? ? ? ?

1

Code No: A109212101 R09 Set No. 4




? ? ? ? ?

1. (a) “Lilienthal was the first human to be photographed in an airplane as a pilot”and got his research work published as articles. Elaborate.

(b) Present a detailed note on the work of German researcher Lilienthal withregard to glider experiments. [7+8]

2. Explain developments in Engineering that took place during the stone age, bronzeage, and iron age. [15]


(a) Projection in drawing

(b) T-square drawing instrument

(c) Triangle drawing instrument [3×5]

4. Describe the aircraft and rocket and engines. [15]

5. Compare the way aircraft and helicopters fly. [15]

6. Describe

(a) Satellite structures.

(b) Satellite propulsion.

(c) Power systems. [5+5+5]

7. Write a detailed note on Martian environment. [15]

8. Describe

(a) US space suit design.

(b) USSR (Russian) space suit design.

(c) Your judgement on superiority of one over the other. [15]

? ? ? ? ?

2

Code No: A109212101 R09 Set No. 1




? ? ? ? ?

1. (a) Discuss the motivation for the United States to develop a space program.

(b) Write about the major contribution of the European Space Agency (ESA) inthe U.S. space program. [8+7]

2. Write short notes on the following

(a) Solar winds

(b) Solar flares

(c) Solar activity [3×5]

3. Explain developments in Engineering that took place during the Hellenistic period,and Middle ages. [15]

4. Write detailed notes on

(a) longitudinal static stability of an aircraft,

(b) Stall Speed. [8+7]


(a) Lift curve for symmetrical and cambered airfoils

(b) The effect of Reynold’s number on lift curve

(c) The effect of Reynold’s number on drag curve [5+5+5]

6. Write notes on design of

(a) Mission

(b) Performance

(c) Safety requirements of lighter than air aircraft [5+5+5]

7. Describe manned flights to the moon. How are they different from human flight tolow earth orbit? Explain with stress on magnitudes of design and risk factor. [15]

8. Present a detailed report on a space-based telecommunication system as a casestudy. [15]

? ? ? ? ?

3

Code No: A109212101 R09 Set No. 3




? ? ? ? ?

1. Describe the various components of a rocket and explain its working principle. [15]

2. (a) Write a short note on ‘maximum lift-to-drag ratio’.

(b) What do you understand by “Endurance”, and “Range” of an aircraft? [8+7]

3. Write short notes on the following with regard to propulsion and station keepingpractices:

(a) Satellite orbit change

(b) Attitude control

(c) Satellite End-of-life (EOL) disposal [3×5]

4. How did the development of Electricity give rise to the industrial revolution in thelate 1700s? [15]

5. Mention a few aspects relating LTA (Lighter than air) vehicle design so that thevehicle becomes controllable. [15]

6. Discuss in detail the NASA plans of a comprehensive space program to place aspace station with permanent human presence in low earth orbit and other relevanttechnical aspects. [15]

7. (a) Discuss the reasons for choosing a white colored thermal micrometeorite ma-terial as the outer garment for a space suit.

(b) Describe two solutions in practice to overcome the space debris problem. [8+7]

8. What are the major problems associated with human extravehicular activity inspace? Compare the currently available measures to counteract these problems.

[15]

? ? ? ? ?

4

Code No: R07A12101 R07 Set No. 2

I B.Tech Examinations,December/January -2011/2012INTRODUCTION TO AEROSPACE ENGINEERING



? ? ? ? ?

1. Explain the operation of Thermal Protection System. [16]

2. (a) At what part of a wing does a shock wave is formed first.

(b) What is the buffer boundary of an aircraft? [8+8]

3. What are the components that come under secondary flying control and explaintheir functions? [16]

4. (a) What is the purpose of drag and anti-drag wires?

(b) State and explain Stalling. [10+6]

5. For a given wing-body combination, the aerodynamic center lies 0.05 chord lengthahead of the centre of gravity. The moment coefficient about the aerodynamiccentre is - 0.016. If the lift coefficient is 0.45, calculate the moment coefficientabout the center of gravity. [16]

6. Compare the advantages and disadvantages of turbo jet engine aircraft and turbo-prop aircraft. [16]

7. (a) Discuss in detail about control tabs and your evaluation.

(b) What is the role of a tail plane during horizontal flight? [8+8]

8. (a) Define Sweep back angle?

(b) What is the effect of swept wing on critical Mach number? [8+8]

? ? ? ? ?

1





? ? ? ? ?













? ? ? ? ?

2





? ? ? ? ?













? ? ? ? ?

3





? ? ? ? ?













? ? ? ? ?

4

Code No:A109212102 SET-1R09

B.Tech II Year - I Semester Examinations, December 2011

MECHANICS OF FLUIDS (AERONAUTICAL ENGINEERING)

Time: 3 hours Max. Marks: 75 Answer any five questions

All questions carry equal marks ---

1.a) Define specific weight, specific volume, specific gravity, viscosity, Surface

tension and capillarity. b) A “U”-tube manometer is being used to measure the pressure difference between

two points on a horizontal pipe. The fluid in the pipe has a relative density of 0.8 and the manometric fluid has a density 13600 kg/m3. The two readings on the manometer differ by 0.5m. What is the pressure difference measured by the manometer? [15]

2.a) Derive one dimensional continuity equation and clearly state its assumptions

while deriving it. b) A fluid flows through a horizontal conical pipe where inlet discharge varying

linearly from 0.3 m3/s to 0.6 m3/s over two seconds. The pipe having an inlet diameter of 200mm and outlet diameter of 400 mm and a length of 2m. The velocity over any cross section may be considered to be uniform. Determine the convective and local acceleration at a section where the diameter is 300mm. [15]

3.a) What is the difference between pitot tube and pitot static tube?

b) Water flows at a rate of 0.5m3/s rising through a 50 cm, contracting pipe bend. The diameter at the bend entrance is 700mm and at the exit is 500mm. If the pressure at the entrance to the bend is 200 kN/m2, determine the magnitude and direction of the force exerted by the fluid on the bend. (The exit of the bend is 0.4m higher than the entrance and the bend has a volume of 0.2 m3) . [15]

4.a) Explain about major and minor energy losses in the pipe.

b) Determine the rate of flow of water through a pipe of diameter 20 cm and the length 50m when one end of the pipe is connected to a tank and the other end of the pipe is open to the atmosphere. The pipe is horizontal and the height of water in the tank is 4m above the center of the pipe. Consider all minor losses and the friction coefficient for the pipe material is 0.009. [15]

5.a) Derive an expression for velocity distribution for laminar flow through a circular

pipe. Show that the Darcy friction coefficient is equal to 16/Re where Re is the Reynolds number.

b) Water at 600 flows between two large flat plates. The lower plate moves to the left at a speed of 0.3m/s. the plate spacing is 3mm and the flow is laminar. Determine the pressure gradient required to produce zero net flow at a cross-section. Take dynamic visocity of water at 600 is 4.7 × 10-4 pa.s. [15]

6.a) Define and explain about the following: i) Displacement thickness ii) Momentum thickness.

b) Discuss the phenomenon of separation for flow over curved surfaces and the prevention of separation. [15] 7.a) Derive for speed of sound in a compressible fluid. b) Air at rest (p=101 kPa, T=288 K) in a chamber. It is expanded isentropically.

What is the Mach number when the velocity becomes 200 m/s? What is the velocity when the speed becomes sonic? Also find out the maximum attainable speed. [15]

8. Write short notes on the following: a) Kinetic energy Correction factor b) Laminar sub-layer c) Micromanometers. [15]

********






1.a) Differentiate between absolute & gauge pressure, simple manometer &

differential manometer, piezometer & pressure gauge. b) A sphere of 1219 mm diameter floats half submerged in salt water ( ρ =1025

kg/m3). What minimum mass of concrete ( ρ = 1025 kg/m3) has to be used as an anchor to submerge the sphere completely.

c) Derive an expression for center of pressure of an arbitrary body submerged vertically in a static fluid. [15]

2.a) State and prove Bernoulli’s theorem with a neat sketch and mention its

limitations. b) In a two-dimensional incompressible flow, the fluid velocity components are

given by u = x- 4y and v = -y-4x. Show that the velocity potential exists and determine its form. Find also the stream function. [15]

3.a) Differentiate between distorted and non-distorted models.

b) A vertical venturimeter carries a liquid of specific gravity 0.8 and has inlet and throat diameter of 150mm and 75mm respectively. The pressure connection at the throat is 150mm above that at the inlet. If the actual rate of flow is 40 lit/s and the coefficient of discharge is 0.96, calculate i) the pressure difference between the inlet and throat ii) the difference in levels of mercury in a vertical U-tube manometer connected between these points. [15]

4.a) Derive the Darcy-Weisbach equation. b) A pipe line, 50 cm diameter and 4500m long, connects two reservoirs A and B

whose constant difference of water level is 12m. A branch pipe, 1250m long and taken from a point distant 1500m from reservoir A, leads to reservoir C whose water level is 15m below that of reservoir A, find the discharges to the reservoir B and C. Assume Darcy’s friction coefficient of 0.03 for all pipes. [15]

5.a) Show that in case of a Couette flow, the shear stress at the horizontal mid-plane

of the channel is independent of the pressure gradient imposed on the flow. b) Water flows between two very large, horizontal, parallel flat plates 20mm apart. If

the average velocity of water is 0.15 m/s. What is the shear stress (a) at the lower plate and at 5mm above the lower plate. Assume dynamic viscosity of water is 1.1 × 10-3 pa-s. [15]

6. Describe with the aid of diagrams the following: i) Boundary layer separation

ii) Magnus effect. [15] 7.a) Derive for speed of sound in a compressible fluid.

b) One problem creating high mach number flows is condensation of the oxygen component in air when the temperature reaches 50 K. if the temperature of a reservoir is 300 K and the flow is isentropic, at what Mach number will condensation of oxygen take place? [15]

8. Write short notes on the following: a) Momentum Correction factor b) Laminar sub-layer c) Hydrostatic force on curved surfaces. [15]

********






1.a) Explain stable, unstable and neutral equilibrium of floating body. b) If 30 cm diameter circular plate is placed over a fixed bottom plate with a 2.5mm

gap between the two plates filled with glycerin. Determine the torque required to rotate the circular plate slowly at 2 rpm. Assume the velocity distribution in the gap is linear and the shear stress on the edge of the rotating plate is negligible.[15]

2.a) What do you understand by convective and local accelerations? Find out the

expression for total acceleration if the flow is passing through a diffuser. b) A three dimensional flow field is represented by the velocity components as

find out the third velocity component if the flow field exists. [15]

22 2 ;u x xy and= + 2 4 2w z xz yz= − −

3.a) Derive the Bernoulli’s equation of motion through the derivation of Euler’s

equation of motion and clearly state the assumptions involved in it. b) A pipeline carrying oil of specific gravity 0.8, changes in diameter from 300mm

at a position A to 500 mm diameter of a position B, which is 5m at a higher level. If the pressures at A and B are 200 kPa and 152 kPa respectively and discharge is 150 liter/sec. Determine the loss of head and direction of flow. [15]

4.a) Explain about the concept and types of Physical similarity b) A sphere advancing at 1.5 m/s in a stationary mass of water experiences a drag of 4.5 N. Find the flow velocity required for dynamic similarity of another sphere

twice the diameter, placed in a wind tunnel. Calculate the drag at this speed if the kinematic viscosity of air is 13 times that of water and its density is 1.25 kg/m3.

[15] 5.a) What is flow separation? What causes it? What is the effect of flow separation on the drag coefficient?

b) Water having dynamic viscosity 0.018 poise is flowing over a smooth thin plate of 5m × 3m at a velocity of 1 m/s parallel to 5 m side. The boundary layer changes from laminar to turbulent at Reynold’s number 5 × 105. Find i) boundary layer thickness where laminar flow ends. ii) the total drag-force on one side of the plate and the boundary layer thickness at the trailing edge of the plate. [15]

6.a) What is the physical significance of the Reynolds number? How is it defined for i) flow in a circular pipe of inner diameter D.

ii) flow in a rectangular duct of cross section a × b. b) Water is discharged from one tank to another with 30 m difference of water levels

through a pipe 1200 m long. The diameter for the first 600 m length of the pipe is 400 mm and 250 mm for the remaining 600 m long. Find the discharge in lit/s through the pipe. Assume the coefficient of friction as 0.008 for both the pipes.

[15] 7.a) Write down general Euler’s equation of motion and then find out Bernoulli’s equation for isothermal process.

b) Find the pressure on the nose of an aircraft flying with 800km/hr through still air and Mach number when atmospheric air pressure and temperature are 68.7 kN/m2 and -10C. Take ρ = 1.295 kg/m3 for the air. [15]

8. Write a short notes on the following:

a) Magnus effect b) Hydrodynamically smooth and rough boundaries

c) Meta center and meta-centric height. [15]

********






1.a) Explain the terms

i) stable equilibrium ii) unstable equilibrium iii) neutral equilibrium of floating bodies.

b) Each gate of lock is 6m high and is supported by two hinges placed on the top and bottom of the gate. When the gates are closed, they make an angle of 1200. The width of the lock is 5m. if the water levels are 4m and 2m on the upstream and downstream sides respectively, find the magnitude of the forces on the hinges due to water pressure. [15]

2.a) What is free vortex? Give some examples of its occurrence. Show how the

velocity and pressure vary with radius in a free vortex flow. b) Derive an expression for continuity equation in three dimension for cylindrical

coordinate which is applicable for steady and incompressible flow. [15]

3.a) State Bernoulli’s theorem and write down all the assumptions made in its derivations.

b) At a point in the pipeline where the diameter is 200mm, the velocity of water is 4m/s and the pressure is 343 kN/m2. At a point 15m downstream the diameter gradually reduces to 100mm. Find the pressure at this point, if the pipe is i) horizontal ii) vertical with flow downward iii) vertical with flow upward. [15]

4.a) Differentiate between Fundamental and Derived dimensions. b) Using the Buckingham’s π theorem, show that the velocity U through a circular

orifice is given by 0.5(2 ) ( / , / )U gH D H UHφ ρ µ= where H is the head causing the flow, D is the diameter of the orifice, µ is the

coefficient of dynamic viscosity, ρ is the density of fluid flowing through the orifice and g is the acceleration due to gravity. [15]

5.a) Prove that for a steady laminar flow between two fixed parallel plates, and for

laminar flow, is equal to 1.5 times of the average velocity of flow. b) What are the velocities involved in a turbulent flow. Explain? c) Derive the expression for loss of head due to sudden contraction. [15]

6.a) Define stagnation points. How the position of the stagnation point for a rotating cylinder in a uniform flow is determined? What is the condition for single stagnation point?

b) A flat plate 1.5m × 1.5m moves at 50km/hr in stationary air of density 1.15 kg/m3. if the co-efficient of drag and lift are 0.15 and 0.75 respectively. Find i) the lift force. ii) the drag force iii) the resultant force iv) the power required to keep the plate in motion. [15]

7.a) Write down general Euler’s equation of motion and then find out Bernoulli’s equation for adiabatic process. b) Air is flowing through a pipe with a velocity of 285 m/s where its pressure and

temperature are 0.6 bar (absolute) and 300K. The pipe along the flow changes in diameter and its pressure at that section was found to be 0.9 bar. Assuming the flow is adiabatic, find the velocity at this section. Assume any other data if necessary. [15]

8. Write a short notes on the following a) boundary layer separation b) Hydrodynamically smooth and rough boundaries c) Meta center and meta-centric height. [15]

********

Code No: A109212102 R09 Set No. 2

II B.Tech I Semester Examinations,November 2010MECHANICS OF FLUIDSAeronautical Engineering

Time: 3 hours Max Marks: 75Answer any FIVE Questions

All Questions carry equal marks? ? ? ? ?

1. (a) Describe a formula developed by Darcy for loss of head due to friction for theflow through a pipe.

(b) A pipe carrying water increased in diameter from 40 cm to 100 cm suddenly.The pressure difference in small and bigger sections is measured by using Hg-U-tube which connected to upstream and downstream of the enlarged sectionimmediately. The difference in pressure is equal to 6 cm of Hg. Find out thedischarge through the pipe. Take specific gravity of Hg = 13.6. [4+11]

2. (a) Define coefficient of drag and lift and state the factors on which these coef-ficients depend.

(b) A truck having a projected area of 6.5 m2 travelling at 70 km/h has a totalresistance of 2000 N. Of this 20 percent is due to rolling friction and 10 percentdue to surface friction. The rest is due to form drag. Make calculations forthe coefficients of form drag. Take ρ = 1.22 kg/m3 for air. [8+7]

3. 2.57 kg of gas for which the ratio of specific heats is 1.35 occupies a volume of 0.15m3 at 10 bar and 500 K. The gas undergoes expansion to 0.6 m3 and process ofexpansion may follow any one of the following cases:

(a) Constant pressure,

(b) Constant temperature,

(c) Adiabatic

(d) Polytropic law pV1.32 = const.

For these cases determine:

(a) Final temperature,

(b) Work done and

(c) Heat interchange. [15]

4. A vessel cylindrical in shape and closed at the top and bottom is 200 mm in diameterand 0.15 m in height. The vessel is completely filled with water. If it is rotatedabout its vertical axis with a speed of 200 rpm, what is the total pressure forceexerted by water on the top and bottom of the vessel? [15]

5. A horizontal circular tube of radius ‘a’ has a fixed coaxial cylindrical core of radiusb. τa and τb are the shear stresses along the tube and core surfaces when a viscous

1

Code No: A109212102 R09 Set No. 2

liquid is flowing through the annulus. The flow is laminar and the rate of variationof pressure along the length of the passage is

(−∂p

∂l

)Show that:

aτ a − b.τb = 12(a2 − b2)

(∂p∂l

). [15]

6. Explain the terms geometric similarity, kinematic similarity and dynamic similarityand discuss the difficulties faced in satisfying these three similarity laws in modelingstudies. [15]

7. (a) A solid cone of radius R, height h and relative density 0.70 floats in fresh waterwith its axis vertical and vertex downwards. Determine the minimum valueof R/h.

(b) Define and explain the terms metacentre and metacentric height. [10+5]

8. (a) Under what conditions a stream line coincides with a streak line.

(b) A stream function is given by the expression Ψ = 2x2 + y3. Find the compo-nents of velocity, as well as the resultant velocity a point (3,1). [8+7]

? ? ? ? ?

2

Code No: A109212102 R09 Set No. 4




1. (a) Show that in a laminar steady flow the pressure gradient in the direction ofmotion is equal to the shear gradient normal to the direction of motion.

(b) A pipe 200 mm in diameter, 20 km long conveys oil of density 900 kg/m3 andviscosity 0.08 Ns/m2 at 10 litres/second. Find the power required to maintainthe flow. [8+7]

2. A pipe converges uniformly from 0.5 m diameter to 0.25 m over 2.5 m length. Therate of flow changes uniformly from 25 l/s to 50 l/s in 40 seconds. Find the totalacceleration at the middle of the pipe at 20th second. [15]

3. (a) Discuss the basic components of total drag.

(b) A kite of dimensions 0.7 m × 0.7 m and weighing 6 N assumes an angle of 80

to the horizontal and the string attached to the kite makes an angle of 450 tothe horizontal. The pull on the string is 25 N when the wind is blowing at aspeed of 40 km/hr. Find the lift and drag forces and the corresponding liftand drag coefficients. The density of air is given as 1.2 kg./m3. [4+11]

4. A 600mm diameter pipeline carries water under a head of 30m with a velocity of3m/s. This water main is fitted with a horizontal bend which turns the axis ofthe pipeline through 75 (i.e. the internal angle at the bend is 105 ). Calculate theresultant force on the bend and its angle to the horizontal. [15]

5. (a) Explain with a neat sketch the working of a Bourdon Gauge.

(b) Define the term metacentric height and explain its significance in stability offloating bodies. [8+7]

6. (a) How is a shock wave produced in a compressible fluid? What do you mean bythe term “Shock strength”?

(b) A gas with a velocity of 300 m/s is flowing through a horizontal pipe at asection where pressure is 60 kN/m2 (abs.) and temperature 40 0C. The pipechanges in diameter and at this section the pressure is 90 kN/m2. If the flowof gas is adiabatic find the velocity of gas at this section. Take R = 287 J/kgKand γ = 1.4. [5+10]

7. (a) Find an expression for the ratio of the outlet area of the nozzle to the area ofthe pipe for maximum transmission of power.

3

0 0

Code No: A109212102 R09 Set No. 4

(b) A fire engine supplies water to a hose pipe, 75 m long and 0.075 m in diameter,at a pressure of 294 kN/m2 (gauge). The discharge end of the hosepipe has anozzle of diameter ‘d’ fixed to it. Taking friction factor as 0.032, determine thediameter ‘d’ of the nozzle, so that the momentum of the issuing jet may be amaximum. [5+10]

8. (a) What do you mean by model testing? What are pre requisites for modeltesting?

(b) Properties of a structure can be calculated by analytical method and by modelanalysis, which is more suitable? Why? [8+7]

? ? ? ? ?

4

Code No: A109212102 R09 Set No. 1




1. The velocity distribution in a circular pipe is given by µUo

=(yR

)1/nwhere u is the

velocity at a distance y from the well of the pipe, Uo is the centerline velocity, R isthe radius of the pipe and n an exponent. Calculate the energy correction factor.

[15]

2. (a) Establish a relation for the average and maximum velocity for one-dimensionalviscous flow of fluid between two fixed parallel plates.

(b) An oil of viscosity 0.02 Pa-s flows between two stationary parallel plates whichare kept at a distance of 10 mm apart. The plates are 1 m wide and thecenterline flow velocity is stated to be 2.5 m/s. Make calculations for theaverage flow velocity, flow rate of oil, pressure gradient and the wall shearstress. [5+10]

3. (a) i. What is stagnation point of an object immersed in fluid?

ii. What is stagnation pressure?

(b) In case of isentropic flow of a compressible fluid through a variable duct, showthatAAc

= 1M

[1+ 1

2(γ−1)M2

12(γ+1)

] γ+12(γ−1)

where γ is the ratio of specific heats, M is the Mach number at a section whosearea is A and Ac is the critical area of flow. [8+7]

4. An oil of specific gravity 0.9 and viscosity 0.03 poise is to be transported at therate of 3000 l/s through a 1.5 m diameter pipe. Tests were conducted on a 15 cmdiameter pipe using water. If the viscosity of water is 0.01 poise find velocity offlow in the model and the rate of flow in the model. [15]

5. (a) Define the terms stream line, streak line and path line.

(b) Show that the stream function and velocity potential intersect orthogonally.[8+7]

6. (a) Two vertical parallel glass plates at distance ‘t’ apart are partially submerged ina liquid of specific weight γ and surface tension σ. Show that the capillary riseis given byh = 2σCosθ

tγ

Make necessary assumptions. (b) Derive the expression for the total pressure and centre of pressure for a sub-

merged inclined plane surface. [8+7]

7. (a) Develop a formula to determine the equivalent diameter of a compound pipe.

5

Code No: A109212102 R09 Set No. 1

(b) A compound pipe line made of 900 m long, 45 cm diameter, 450 m long and37.5 cm diameter and 300 m long and 30 cm diameter is to be replaced by asingle uniform diameter pipe line having the length equal to compound pipeline and the flow remains same. Find the diameter required for uniform pipeline. Take f is same for all pipe lines and neglect minor losses in both cases.

[4+11]

8. (a) The velocity distribution for the boundary layer along a flat plate is prescribed

by a power law uU

=(yδ

)0.22. Find the displacement thickness δ*, momen-

tum thickness θ and energy thickness δ** where δ is the nominal thickness ofboundary layer. U is the free stream velocity.

(b) Atmospheric air at 250C flows parallel to a flat at a velocity of 3m/s. Use theexact Blasius solutions to estimate the boundary layer thickness and the localskin friction coefficient at x=1 m from the leading edge of the plate. Howthese values would compare with the corresponding values obtained from theapproximate Von-Karman integral techniques assuming cubic velocity profile.

[9+6]

? ? ? ? ?

6

Code No: A109212102 R09 Set No. 3




1. (a) Differentiate between

i. solid and fluid and

ii. ideal fluid and real fluid.

(b) Determine the bulk modulus of elasticity of a liquid, if the pressure of theliquid is increased from 7 MN/m2 to 13 MN/m2 and consequently the volumeof the liquid decreases by 0.15%. [8+7]

2. (a) Define the terms: Major energy losses and minor energy losses in pipe.

(b) Water flows through a pipe of diameter 300 mm with a velocity of 5 m/s. Ifthe coefficient of friction is given by f = 0.015+ 0.08

Re0.3where Re is the Reynolds

number, find the head lost due to friction for a length of 10 m. Take kinematicviscosity of water as 0.01 stoke. [5+10]

3. (a) Describe Reynolds experiments to demonstrate the laminar and turbulent fluidflows. How is the type of flow related to Reynold number?

(b) Determine the nature of flow when an oil of specific gravity 0.85 and kinematicviscosity 1.8 × 10−5 m2/s flows in a 10 cm diameter pipe at 0.5 liter per second.

[8+7]

4. The outlet pipe from a pump is a bend of 45 rising in the vertical plane (i.e.and internal angle of 135 ). The bend is 150mm diameter at its inlet and 300mmdiameter at its outlet. The pipe axis at the inlet is horizontal and at the outletit is 1m higher. By neglecting friction, calculate the force and its direction if theinlet pressure is 100kN/m2 and the flow of water through the pipe is 0.3m3/s. Thevolume of the pipe is 0.075m3.

[15]

5. With a neat sketch, explain the different types of deformations that a fluid particleundergoes and derive the condition for the flow to be irrotational. [15]

6. (a) Explain the concept of stagnation properties.

(b) A supersonic plane flies at 2000 km/hr at an altitude of 9 km above sea levelin standard atmosphere. If the pressure and density of air at this altitude arestated to be 30 kN/m2 absolute and 0.45 kg/m3, make calculations for thepressure, temperature and density at the stagnation point on the nose of theplane. Take R = 287 J/kg K and γ = 1.4. [8+7]

7

0 0

Code No: A109212102 R09 Set No. 3

7. (a) Set up Navier-Stokes’s equations and make suitable assumptions to prove thatfor a two dimensional steady flow, the pressure gradient in the direction offlow (dp/dx) is equal to shear gradient (dτ/dy) in the direction normal to thedirection of fluid motion.

(b) Examine whether or not the following velocity profiles satisfy the essentialboundary conditions for velocity distribution in the laminar boundary layeron a flat plate:

i. uU

= 1 +(yδ

)− 2

(yδ

)2ii. u

U= sin(πy/2δ)

Where δ is boundary thickness and U is free stream velocity. [8+7]

8. 215 liters of gasoline (Specific gravity=0.82) flows per second upwards in an inclinedventurimeter fitted to a 300 mm diameter pipe. The venturimeter is inclined at 60 0 to thevertical & its 150 mm diameter throat is 1.2 m from the entrance along its length. Pressuregages inserted at entrance and throat show pressures of 0.141 N/mm2 and 0.077N/mm2 respectively. Calculate Cd of the venturimeter. If instead of pressure gagesthe entrance and the throat of the venturimeter are connected to the two limbs of aU-tube mercury manometer, find its reading in mm of differential mercury column.

[15]

? ? ? ? ?

8

Code No: A109210305 R09 Set No. 2

II B.Tech I Semester Examinations,December 2011THERMODYNAMICS

Common to Mechanical Engineering, Aeronautical Engineering, AutomobileEngineering, Mining Machinery



1. A steam turbine receives steam at 20 bar and superheated by 800C. The exhaustpressure is 0.10 bar and expansion takes place isentropically. Calculate

(a) heat supplied, assuming that the feed pump supplies water to the boiler at 20bar,

(b) heat rejected

(c) turbine work,

(d) net work,

(e) thermal efficiency, and

(f) theoretical steam consumption. [15]

2. (a) Describe diesel gas power cycle with the help of P-V and T-S diagrams. Derivean expression for its air standard efficiency

(b) A diesel engine has a clearance volume of 220 cm3 and a bore and stroke of15cm and 20cm respectively. The inlet conditions are 100KN/m2 and 200C.The maximum temperature of the engine is 14000C. Calculate

i. Ideal thermal efficiency of cycle and

ii. m.e.p. [7+8]

3. (a) What is critical point? What process is possible below the critical point?

(b) Steam initially at 1.5 Mpa, 3000C expands reversibly and adibatically in asteam turbine to 400C. Determine the ideal work output of the turbine per kgof steam. [7+8]

4. (a) Explain “internal energy”, “heat and work”

(b) To a closed system 100 KJ of work is supplied. If the intial volume is 0.5 m3

and pressure of a system changes as P = (8 - 4V), where P is in bar and V isin m3, determine the final volume and pressure of the system. [5+10]

5. (a) Prove that at adiabatic saturation: tdb = twb = t∗.

(b) A mixture of ideal air and water vapour at a dbt of 220C and a total pressure of730 mm Hg abs. has a temperature of adiabatic saturation of 150C. Calculate:

i. the specific humidity in gms per kg of dry air.

ii. the partial pressure of water vapour

1

Code No: A109210305 R09 Set No. 2

iii. the relative humidity, and

iv. enthalpy of the mixture per kg of dry air. [7+8]

6. 0.2 m3 of air at 3 bar and 1200C is contained ia a system. A reversible adiabaticexpansion takes place till the pressure falls to 1.5 bar. The gas is then heated atconstant pressure till enthalpy increases by 75 kJ. Calculate the work done andthe index of expansion, if the above processes are replaced by a single reversiblepolytropic process giving the same work between the same initial ans final states.

[15]

7. (a) What is a PMM 2?

(b) A heat pump operates between two identical bodies of specific heat C and T1.The operation of the pump cools down one of the bodies to T2. Show that forthe operation of pump the minimum work input is given by

Wmin = C[T 21

T2+ T2 − 2T1

]. [5+10]

8. (a) Show that energy of an isolated system remains unchanged?

(b) A system comprises a stone of mass 20 kg and a drum containing 1000 kg ofwater. Initially the stone is 50 m above the water and the stone and water areat the same temperature. The stone is then made to fall into water. Determinechange in internal energy, kinetic energy, potential energy heat transfer, andwork transfer for the changes of state given below?

i. The stone is to just enter water.

ii. The stone just comes to rest in drum, and

iii. The heat transferred to surroundings is such that water and stone remainin the same temperature. Assume g = 9.81 m/s2. [5+10]

? ? ? ? ?

2

Code No: A109210305 R09 Set No. 4





1. One kg of air at 270C is heated reversibly at constant pressure until the volume isdoubled and then heated reversibly at constant volume until the pressure is doubled.For a total path find work, heat transfer and change in entropy. [15]

2. Draw T-S diagram of water and show dew point temperature, dry bulb temperatureand critical temperature. [15]

3. (a) State the limitations of first Law of Thermodynamics.

(b) A reversible heat engine operates between 875K and 310K and deliver a re-versible refrigerator operating between 310K and 255K. The engine receives2000 KJ of heat and the net work out put from the arrangement equals to 350KJ. Calculate the cooling effect of refrigerator. [5+10]

4. Steam at 0.8 Mpa, 2500C and flowing at the rate of 1 kg /s passes into a pipecarrying wet steam at 0.8 Mpa, 0.9 dry.After adiabatic mixing the flow rate is2.5 kg/s. Determine the condition of steam after mixing. The mixture in nowexpanded in a frictionless nozzle isentropically to a pressure of 0.4 Mpa. Determinethe velocity of the steam leaving the nozzle. Neglect the velocity of steam in thepipe line. [15]

5. Steam at a pressure of 15 bar and 2500C is delivered to the throttle of an engine.The steam expands to 2 bar when release occurs. The steam exhaust takes placeat 1.1 bar. A performance test gave the result of the specific steam consumptionof 12 kg/kwh and a mechanical efficiency of 80 % .Determine

(a) Ideal work or the modified Rankine engine work per kg

(b) efficiency of the modified rankine engine or ideal thermal efficiency

(c) indicated and brake work per kg

(d) brake thermal efficiency

(e) relative efficiency on the basis of indicated work and brake work. [15]

6. (a) Derive enery equation for a closed system undergoing

i. Isochoric process

ii. Isothermal process

iii. Polytropic process between state 1 to state 2.

3

Code No: A109210305 R09 Set No. 4

(b) When a closed system executes a certain non- How process the work and heatInteractions per degree rise in temp. at each temp attained are given bydWdT

= (4 − 0.08T )KJ/K dQdT

= 1.00KJ/K Calculate for the Increase (or) de-crease in the Internal energy of the system if it is to operate between thetemperature limits of 2000C and 5000 C. [7+8]

7. (a) Describe Ericcson cycle with the help of p-V diagram and draw it on T-sdiagram. Deduce an expression for its air standard efficiency

(b) An air standard dual cycle has a compression ratio of 18, and compressionbegins at 1 bar 500C.The maximum pressure is 60 bar. The heat transferredto air at constant pressure is equal to that at constant volume. Estimate

i. pressures and temperatures at cardinal points of the cycle

ii. cycle efficiency

iii. m.e.p of cycle. Cv=0.718 kj/kg k, Cp=1.005 kj/kg k. [7+8]

8. A system of volume V contains a mass m of gas at pressure P and temperatureT. The macroscopic properties of the system obey the following relationship (P+a/ V 2)(V-b)=mRT, where a, b, R are constants obtain an expression for the dis-placement work done by the system during a constant temperature expansion fromvolume V1 to V2. Calculate the work done by a system which contains 10 Kg ofthis gas expanding from 1m3 to 8 m3 at a temperature of 300 K. Use the valuesa = 15.7 × 10Nm4,b = 1.07 ×10−2m3 and R = 0.278 Kj/kg-k. [15]

? ? ? ? ?

4

Code No: A109210305 R09 Set No. 1





1. An air-standard Otto cycle has a compression ratio of 6. The temperature at thestart of compression process is 250C and the pressure is 1 bar. If the maximumtemperature of the cycle is 11500C, calculate

(a) the heat supplied per kg of air,

(b) net work done per kg of air, and

(c) thermal efficiency of cycle. Assume γ = 1.4, Cv = 0.718, kJ/kg.K for air. [15]

2. (a) State the conditions for a process to be reversible

(b) A mass of gas is compressed in a quasi-static process form 75 kpa,0.1 m3 to0.45 Mpa,0.03 m3. Assuming that the pressure and volume are related byPV n=constant, find net work done by gas system. [7+8]

3. A steam power cycle operates between the pressure limits of 18 bar and 1.2 bar.The isentropic efficiency (internal efficiency) of steam turbine is 85% and that offeed pump is 80%. Calculate

(a) the of net work

(b) the specific steam consumptions. [15]

4. (a) Derive the expressions for the first law applied to

i. a cycle

ii. a process

(b) Air expands in a reversible adiabatic manner through a horizontal nozzle from800 kPa and 3500C to an exit pressure of 100 kPa. Determine the exit velocityand the mass flow rate, if the exit area is 5 cm2. Neglect the inlet velocity.Assume for air, γ = 1.4 Cp = 1.005 kJ/kg.K and R = 0.287 kJ/kg.K. [7+8]

5. (a) State and explain steam Calorimetry.

(b) The following data were obtained in a test on a combined separating andthrottling calorimeter: Pressure of steam sample =12 bar, pressure of steamat exit = 1 bar, temperature of steam at the exit =1500C, discharge formseparating calorimeter =0.5 kg/min, discharge from throttling calorimeter =10kg /min. Determine the dryness fraction of the sample steam. [7+8]

6. (a) Prove that PV V = constant for an adiabatic process

5

Code No: A109210305 R09 Set No. 1

(b) A container of 3 m3 capacity contains 10 kf of CO2 at 270C. Estimate thepressure exerted by CO2 by using

i. Perfect gas equation

ii. van der waals equation. [15]

7. A rigid tank of 1m3 volume contains a mixture of molar composition 30% CH4,25%C2

H6 and 45% air at 1 bar and 300K. It is necessary to change the composition suchthat the final mixture contains 60 mole percent methane and tank is always heldat 300K. Determine the mass of methane to be added into tank and final pressureof the gas mixture. [15]

8. An engine working on Carnot cycle absorbs Q1 units of heat from a source at T1

and rejects Q2 units of heat to a sink at T2. Te temperature of the working fluid isθ1 and θ2, where θ1 < T1 and θ2 > T2,If θ1 = T1-KQ1 and θ2 = T2+kQ2

where k is constant, then show that efficiency of the engine is given by:η = 1 − T2

T1−2kQ1. [15]

? ? ? ? ?

6

Code No: A109210305 R09 Set No. 3





1. (a) Discuss the advantages and disadvantages of vapour absorption refrigerationsystem over the vapour compression system.

(b) A Bell-Coleman refrigeration cycle works between 1 bar and 6 bar. The adia-batic efficiency of compression is 85% and expansion is 90%. Find the C.O.Pof the system and its tonnage when the air flow rate is 1kg/sec. The ambienttemperature is 270C and refrigerator temperature is 00C. [7+8]

2. (a) Make an energy analysis of the following devices

i. Centrifugal pumps

ii. Heat Exchanger

(b) At the inlet of a nozzle, the enthalpy of the passing fluid is 3210 KJ/kg andvelocity is 60 m/s. At the discharge end, the enthalpy is 2760 kJ/kg. Thenozzle is horizontal and there is negligible heat loss from it. Find(a) velocity at exit, and(b) mass flow rate if inlet area is 0.1 m2 and specific volume at inlet is 0.185m3/kg. [7+8]

3. (a) How throttling helps in estimating the dryness fraction of steam.

(b) A vessel of volume 1 m3 capacity contains steam at 20 bar and 0.85 drynessfraction Steam is blown off until the pressure drops to 10 bar. The valve isthen closed. Determine mass of steam blown off. Assume process as throttling.

[8+7]

4. (a) Determine an expression for the work done in a closed isothermal process?

(b) Gas from a bottle of compressed helium is used to inflate an inelastic flexibleballoon, originally folded completely flat to a volume of 0.65 m3. If the barom-eter reads 760 mm Hg, what is the amount of work done upon the atmosphereby the balloon? Sketch the system before and after the process. [7+8]

5. (a) What do you understand by exergy and anergy?

(b) A reversible heat engine working between two thermal reservoirs at 875 K and315 K drives a reversible refrigerator which operates between the same 315 Kreservoir and a reservoir at 260 K. The engine is supplied 2000 kJ of heat andthe network output from the composite system is 350 kJ. Calculate he heattransfer to the refrigerator and the net heat interaction with the reservoir at315 K temperature. [7+8]

7

Code No: A109210305 R09 Set No. 3

6. (a) Draw the variation of thermal efficiency against compression ratio of an Ottocycle.

(b) An air standard diesel cycle has a compression ratio of 17. The pressure atthe beginning of compression stroke is 1 bar and the temperature is 230C. Themaximum temperature is 14300C. Determine the thermal efficiency and themean effective pressure for this cycle. Take γ = 1.4. [5+10]

7. (a) State Dalton’s law of partial pressures.

(b) Atmospheric air at 300C and a relative humidity of 65% is cooled at a constantpressure of 100 kN/m2 to 200C. Calculate

i. the final relative humidity and

ii. the change in specific humidity. [7+8]

8. The following is the equation which connects u,p and v for several gases u = x+ypvwhere x and y are constants. Prove that for a reversible adiabatic process pvγ =constant where γ = (y+1)/y. [15]

? ? ? ? ?

8

Code No: R05222103 R05 Set No. 2

II B.Tech II Semester Examinations,April/May 2012THERMODYNAMICS



? ? ? ? ?

1. (a) Explain with a neat diagram P-V-T surface?

(b) Steam at 10 bar and 2000C enters at convergent divergent nozzle with a ve-locity of 60 m/sec. and with a velocity of 650 m/sec .Assuming that there isno heat loss, determine the quality of the steam leaving the nozzle. [7+9]

2. In an ammonia vapour compression system, the pressure in the evaporator is 2bar. Ammonia at exit is 0.85 dry and at entry its dryness fraction is 0.19. Duringcompression, the work done per kg of ammonia is 150kJ. Calculate the C.O.Pand volume of vapour entering the compressor per minute, if the rate of ammoniacirculation is 4.5kg/min. The latent heat and specific volume at 2 bar are 1325kJ/kgand 0.58m3/kg respectively. [16]

3. (a) Define the terms state, path, process and cycle with suitable diagrams.

(b) A mass of 1.5 kg of air is compressed in a quasi-static process from 0.1MPato 0.7 MPa for which pv = constant. The initial density of air is 1.16 kg/m3.Find the work done by the piston to compress the air. [8+8]

4. (a) Write short notes on

i. Mole fraction

ii. Volumetric analysis

iii. Dry bulb temperature

(b) An air water vapour mixture has a relative humidity of 60 % at l atmosphereand 300C. Determine per 100m3 of the mixture

i. Mass of water vapour

ii. Mass of dry air [6+10]

5. A piston and cylinder machine contains a fluid system, which passes through acomplete cycle of four processes. During a cycle, the sum of all heat transfer is -150KJ and the system completes 100 cycles per minute. Complete the following tableand calculate the net rate of work output. [16]

Process Q (KJ/Min) W (KJ/min) δ U(KJ/min)1-2 0 2150 —–2-3 20,000 0 —–3-4 -2,000 —– -36,0004-1 —– —– —–

1


6. (a) Write down the Vander Waal’s equation of state. How does it differ from theideal gas equation of state?

(b) A mass of air is initially at 2600C and 700 kPa and occupies 0.028m3. Theair is expanded at constant pressure to 0.084m3. A polytropic process with n= 1.5 is then carried out, followed by a constant temperature process, whichcompletes a cycle. All the processes are reversible

i. Sketch the cycle in the P-V &T-S planes

ii. Find heat received & rejected in the cycle

iii. Find η of the cycle. [7+9]

7. (a) What is perpetual motion machine of second kind? Why such a machinecannot be constructed in actual practice?

(b) Two Carnot heat engines operate so that the exhaust of one is the intake ofthe other; the highest and lowest temperature limits are 1200 K and 400 K.Determine the intermediate temperature if

i. both the engines give the same work output

ii. both the engines have the same thermal efficiency. [6+10]

8. (a) What is a cycle? What is the difference between an ideal and actual cycle.

(b) Derive an expression for efficiency of Brayton cycle in terms of pressure ratio.[8+8]

? ? ? ? ?

2





? ? ? ? ?




(b) A mass of air is initially at 2600C and 700 kPa and occupies 0.028m 3. Theair is expanded at constant pressure to 0.084m3. A polytropic process with n= 1.5 is then carried out, followed by a constant temperature process, whichcompletes a cycle. All the processes are reversible










i. Mole fraction




3










? ? ? ? ?

4





? ? ? ? ?







i. Mole fraction









5




(b) A mass of air is initially at 2600C and 700 kPa and occupies 0.028m 3. Theair is expanded at constant pressure to 0.084m3. A polytropic process with n= 1.5 is then carried out, followed by a constant temperature process, whichcompletes a cycle. All the processes are reversible








? ? ? ? ?

6





? ? ? ? ?














7



i. Mole fraction







(b) A mass of air is initially at 2600C and 700 kPa and occupies 0.028m3. Theair is expanded at constant pressure to 0.084m3. A polytropic process with n= 1.5 is then carried out, followed by a constant temperature process, whichcompletes a cycle. All the processes are reversible




? ? ? ? ?

8

Code No: A109210101 R09 Set No. 2

II B.Tech I Semester Examinations,December 2011MATHEMATICS-II

Common to CE, CHEM, AE, BT, MMTTime: 3 hours Max Marks: 75


? ? ? ? ?

1. (a) Obtain the Fourier series for the functionf(x) = x - x2 in 0 < x < 4

(b) Find the half range cosine series for f(x) = π - x in (0, π) [15]

2. (a) Form the partial differential equation fromz = f( y - x) + x g( y - x) + x2 h(y - x)

(b) Solve the partial differential equationx2

p+ y2

q= z [15]

3. (a) Reduce the quadratic form to canonical form by Lagrange’s reduction 2x21 +

7x22 + 5x2

3 − 8x1x2 − 10x2x3 + 4x1x3 and hence find rank signature of thequadratic form.

(b) Find the rank and signature of the quadratic form x2−4y2 +6z2 +2xy−4xz+2w2 − 6zw. [15]

4. Find the Fourier cosine Transform of e−ax cos ax and e−ax sin ax [15]

5. (a) Solve the system of equations, x+y+z+t =4; x-z+2t=2; y+z -3t = -1; x+2y-z+t =3.

(b) Investigate for what values of a and b equations x+2y+3z=4, x+3y+4z =5,x+3y+az = b, have

i. no solution

ii. unique solution

iii. infinite solution. [15]

6. Find the characteristic equation of the matrix A =

1 3 74 2 31 2 1

and show that the

equation is satisfied by A and hence find A−1. [15]

7. (a) Express the matrix

1 + i 2 5− 5i2i 2 + i 4 + 2i

1 + i −4 7

as the sum of Hermitian matrix

and skew-Hermitian matrix.

(b) Prove that every Hermitian matrix can be written as A+iB, Where A is realand symmetric and B is real and skew - symmetric. [15]

1

Code No: A109210101 R09 Set No. 2

8. The temperature u is maintained at 00 C along three edges of a square plate oflength 100 cm and the fourth edge is maintained at 1000 C until steady stateconditions prevail. Find the temperature u(x,y). Hence show that the temperature

at the centre of the plate is 200π

[1

Coshπ2− 1

3Cosh 3π2

+ 15Cosh 5π

2

− .................]

[15]

? ? ? ? ?

2

Code No: A109210101 R09 Set No. 4




? ? ? ? ?

1. (a) Obtain the Fourier series for the functionf(x) = πx, 0 < x < 1

= π(2− x), 1 < x < 2

(b) Find the half range cosine series for f(x) = ex in (0,1) [15]

2. (a) Form the partial differential equation fromF (x2 + y, x2 + y2 + z2) = 0

(b) Solve the partial differential equationpx2 + q

y2[15]

3. (a) Find the rank, index, and signature of the sylvester’s canonical form

1 0 0 00 1 0 00 0 1 00 0 0 −1

.

(b) Determine the nature, index and signature of the Quadratic form x21 + 5x2

2 +x2

3+2x1x2+2x2x3+6x3x1. [15]

4. (a) Verify that the matrix A = 12

[1 + i 1− i1− i 1 + i

]has eigen values with unit mod-

ulus.

(b) Prove that the matrix 12

[1 + i −1 + i1 + i 1− i

]is a unitary matrix. [15]

5. Show that

2 −1 1−1 2 −11 −1 2

satisfies its characteristic equation. Hence find A−1.

[15]

6. Solve the partial differential equation ∂u∂t

= a2 ∂2u∂x2 with the conditions

(a) u→ 0, ast→∞(b) ∂u

∂x= 0 when x = 0 and L, t > 0

(c) u = x( L - x ), when t = 0 and x = 0 and L [15]

7. (a) For what value of K the matrix

4 4 −3 11 1 −1 0k 2 2 29 9 k 3

has rank 3.

3

Code No: A109210101 R09 Set No. 4

(b) Find the rank of the matrix A =

2 3 −1 −11 −1 −2 −33 1 3 −26 3 0 −7

by reducing it into

echelon form. [15]

8. Find the Fourier sine Transform of xa2+x3 and Find the Fourier cosine Transform of

1a2+x2 [15]

? ? ? ? ?

4

Code No: A109210101 R09 Set No. 1




? ? ? ? ?

1. (a) Form the partial differential equation fromz = xy + f(x2 + y2)

(b) Solve the partial differential equationp2

z2= 1 - pq [15]

2. (a) Find the Fourier Transform off(x) = x, |x| < a

= 0, |x| > a

(b) Find the Fourier cosine transform of 2e−3x + 3e−2x [15]

3. (a) Obtain the Fourier series for the function x + x2 in (0, 2 )

(b) Find the half range cosine series for f(x) = x in [0, π2]

= π - x in [π2, π] [15]

4. (a) Define the rank of the matrix and find the rank of the following matrix2 1 3 54 2 1 38 4 7 138 4 −3 −1

.

(b) Determine the rank of the matrix A =

1 1 −3 22 −1 2 −33 −2 1 −4−4 1 −3 1

[15]

5. Find the rank, index, signature of the quadratic form 10x2 + 2y2 + 5z2 − 4xy +6yz − 10xz by reducing it to canonical form. [15]

6. Diagonalize the matrix A =

−1 2 −21 2 1−1 −1 0

. [15]

7. A rod of length 10 cms has its ends A and B kept at 300 C and 800 respectively,until steady state conditions prevail. If the temperature at A and B are suddenlychanged to 400 C and 600 C and the temperatures there after maintained., , findthe temperature at a distance x from A and at time t. [15]

8. (a) Prove that every square matrix is uniquely expressed as the sum of a Hermitianmatrix and a skew-Hermitian matrix.

5

(b) Reduce the matrix into Echelon form and hence find its rank. ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

− 0211121041435

[15]

Code No: A109210101 R09 Set No. 1

(b) Find the Eigen vectors of the Hermitian matrix A =

[a b+ ic

b− ic k

]. [15]

? ? ? ? ?

6

Code No: A109210101 R09 Set No. 3




? ? ? ? ?

1. (a) Obtain the Fourier series for the functionF(x) = π2 − x2 in [-π, π]

(b) Find the half range cosine series for f(x) = 1 in (0, 3)= - 1 in (3, 6) [15]

2. (a) Express the functionf(x) = 1 for |x| ≤ 1

= 0 for |x| > 1

as a Fourier integral. Hence evaluate∞∫0

sinλ cosλxλ

dλ

(b) Find the finite Fourier sine and cosine transforms of f(x) = eax in (0, 1) [15]

3. (a) Form the partial differential equation fromz = f( y - 3x) + g( y + 5x)

(b) Solve the partial differential equationq = px+ q2 [15]

4. (a) Find the rank of the matrix

1 2 32 −1 03 1 2

by reducing it to normal form.

(b) Determine the rank of the matrix A =

−2 −1 −3 −11 2 3 −11 0 1 10 1 1 −1

by reducing it

to normal form. [15]

5. Reduce the quadratic form x2 + 4y2 + z2 + 4xy + 6yz + 2zx to canonical form bylinear transformation. [15]

6. A string is stretched and fastened to two points L apart. Motion is started bydisplacing the string in the form y = K x(L - x2) from which it is released at timet = 0. Find the displacement of the string at any point x at any time t. [15]

7. Find the characteristic polynomial of the matrix A =

3 1 1−1 5 −11 −1 5

verify Cay-

ley - Hamilton theorem and hence find A−1. [15]

7

(b) Determine the non-singular matrices P and Q such that the normal form of A is

PAQ where A = . [15] ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−− 110321211

Code No: A109210101 R09 Set No. 3

8. (a) Prove that the matrix 1√3

[1 1 + i

1− i −1

]is unitary and determine the eigen

values and eigen vectors.

(b) Prove that the characteristic roots of a Hermitian matrix are real. [15]

? ? ? ? ?

8



Common to CE, ME, CHEM, MECT, MEP, AE, AME, MMTTime: 3 hours Max Marks: 80


? ? ? ? ?

1. (a) Find the Fourier sine transform of e−|x| and hence evaluate∞∫0

x sinnxdx1+x2 . Find

also Fourier cosine transform of f(x)

(b) Find Finite Fourier sine and cosine transform of πx− x2 in [0, π]. [8+8]

2. Reduce the quadtratic form 2x2 + 2y2 + 2z2 - 2xy + 2xz - 2yz to the canonicalform. [16]

3. (a) Solve the difference equation, using Z - transforms yk+2 - 4yk+1 + 4yk = 0where y0 = 1, y1 = 0

(b) If Z(un) =2z2+5z+14(z−1)4

, find u2 and u3. [8+8]

4. If A =

1 2 −12 1 −22 −2 1

verify cayley Hamilton theorem. Find A4 and A−1 using

cayley Hamilton theorem. [16]

5. (a) Expand L2

-x in −L < x < L.

(b) Find the Fourier half range Cosine Series of

f(x) =

{x, 0 < x < π

2

0, π2< x < π

[10+6]

6. (a) Find the rank of the matrix A =

2 −2 0 64 2 0 21 −1 0 31 −2 1 2

by reducing it to the

normal form.

(b) Find whether the following equations are consistent, if so solve them.x1 + 2x2 + 3x3 = 16x1 + x2 - 3x3 = -9x1 - 2x2 + 2x3 = 8. [8+8]

7. (a) Form the partial differential equation by eliminating the arbitrary functionfrom φ

(yx, x2 + y2 + z2

)= 0

(b) Solve the partial differential equation x2

p+ y2

q= z.

(c) Solve the partial differential equation x(y2 + z)p - y (x2+z) q = z(x2 - y2).[5+6+5]

1


8. Solve the boundary value problem uxx+uyy= 0; 0 < x < a, y > 0 If the temperaturealong the short edge y = 0 is u (x, 0) = c sin( πx/a) while all other edges are keptat 0o C . Find the steady state temperature at any point (x,y) of the plate. [16]

? ? ? ? ?

2





? ? ? ? ?


(yx, x2 + y2 + z2

)= 0


p+ y2

q= z.







4. If A =

1 2 −12 1 −22 −2 1




2 −2 0 64 2 0 21 −1 0 31 −2 1 2


normal form.




(b) If Z(un) =2z2+5z+14(z−1)4

, find u2 and u3. [8+8]

8. (a) Expand L2

-x in −L < x < L.

3



f(x) =

{x, 0 < x < π

2

0, π2< x < π

[10+6]

? ? ? ? ?

4





? ? ? ? ?


2. If A =

1 2 −12 1 −22 −2 1




(yx, x2 + y2 + z2

)= 0


p+ y2

q= z.


4. (a) Expand L2

-x in −L < x < L.


f(x) =

{x, 0 < x < π

2

0, π2< x < π

[10+6]



2 −2 0 64 2 0 21 −1 0 31 −2 1 2


normal form.



(b) If Z(un) =2z2+5z+14(z−1)4

, find u2 and u3. [8+8]

5






? ? ? ? ?

6





? ? ? ? ?

1. If A =

1 2 −12 1 −22 −2 1










2 −2 0 64 2 0 21 −1 0 31 −2 1 2


normal form.


6. (a) Expand L2

-x in −L < x < L.


f(x) =

{x, 0 < x < π

2

0, π2< x < π

[10+6]


(b) If Z(un) =2z2+5z+14(z−1)4

, find u2 and u3. [8+8]


(yx, x2 + y2 + z2

)= 0

7



p+ y2

q= z.


? ? ? ? ?

8

SET - 1R09CODE NO: A109210304

II B.TECH - I SEMESTER EXAMINATIONS – MAY, 2011 MECHANICS OF SOLIDS

(COMMON TO ME, MCT, MMT, AE, AME) Time: 3hours Max. Marks: 75

Answer any FIVE questions All Questions Carry Equal Marks

- - - 1.a) What is ductility of a material? Is ductility a desirable property of constructional

material? Explain with reasons. b) A rope comprising three 3.0 mm diameter wires clamped together at the ends lifts a

load of 15.0 kN. The lengths of the wires are 10.0 m, 10.01 m and 10.02 m. Compute the stresses in each wire. What is the maximum load the rope can lift, if the working stress is limited to 800.0 MPa and the deformation of the rope to 40.0 mm? Assume E = 210.0 GPa. [8+7]

2.a) Develop Bending moment and Shear force for the Figure 1 given below indicating the

maximum and minimum values.

Figure 1

b) Develop Bending moment and Shear force for the Figure 2 given below indicating the maximum and minimum values. [8+7]

Figure 2

3. A cantilever beam, 60 mm wide by 200 mm high and 6 m long, carries a load that

varies uniformly from zero at the free end to 1000 N/m at the wall. a) Compute the magnitude and location of the maximum flexural stress. b) Determine the type and magnitude of the stress in a fiber 40 mm from the top of the beam at a section 3 m from the free end. [8+7]

4. Develop the shear stress distribution diagrams for the sections shown for the

following Figure 3 when subjected to a transverse S.F. of 200.0 kN. What are the maximum shear stresses? [15]

Figure 3

5. Analyze the truss indicated in Figure 4 by method of sections. [15]

Figure 4

6. Compute the maximum deflections and support rotations in the beams of the

following Figure 5 using a) The methods of integration b) The method of moment area. [15]

Figure 5

7. A cylinder boiler of diameter 1.7 m, 4.5 m length and 10 mm thickness with flat ends

is provided with six tie rods of 40 m diameter. If the tie rods are stressed initially to 82.0 MPa, determine the stresses in the tie rods and the cylinder under a pressure of 1.8 MPa. Assume the same material for the boiler and tie rods. [15]

8. A compound cylinder comprises an inner tube of diameters 100.0 mm and 140.0 mm,

and an outer tube of diameters 140.0 mm and 180.0 mm. determine the diametral interference required so that the final maximum stress in the tube does not exceed 120.0 MPa under an internal pressure of 45.0 MPa. Neglect the effects of longitudinal stresses. Assume E = 120.0 GPa. [15]

********

SET - 2R09CODE NO: A109210304




- - - 1.a) Explain the concept of factor of safety and its significance in the design of machine

components? What is working stress of a material? b) A prismatic member of length l and unit weight w is suspended freely from its end.

Determine the elongation of the member under gravity. [8+7] 2.a) Develop Bending moment and Shear force for the Figure 1 given below indicating the


Figure 1


Figure 2

3. A flat steel bar, 25 mm wide by 6 mm thick and 1 m long, bent by couples applied at

the ends so that the midpoint deflection is 20 mm. Compute the maximum stress in the bar and the magnitude the couples. Use E = 200 GN/m2. [15]

4. Develop the shear stress distribution diagrams for the sections shown for the

following Figure 3 when subjected to a transverse S.F. of 200.0 kN. What are the maximum shear stresses? [15]

Figure 3

5.a) Explain the advantages of trusses, indicating various truss configurations and their economical span ranges.

b) What is degree of indeterminacy in trusses? Explain with examples. [8+7] 6. Compute the maximum deflections and support rotations in the beams of the

following Figure 4 using a) The methods of integration b) The method of moment area. [15]

Figure 4

7. A mild steel pipeline of 550.0 mm diameter and 5 mm thickness is subjected to an

internal water pressure of 1.1MPa. The pipeline is subjected to a torque of 70.0 kNm as well. Determine the design stresses in the pipeline. [15]

8. Design a cylinder of 800.0 mm inner diameter to sustain an internal pressure of 5.0

MPa. Assume E = 30.0 GPa and a safe stress of 15.0 MPa. [15]

********

SET - 3R09CODE NO: A109210304




- - - 1.a) Describe the effects of temperature changes when a body is

i) Free to deform and ii) Restrained.

b) A concrete column is reinforced with steel bars comprising 6 percent of the gross area of column section. What is the fraction of the compressive load sustained by steel bars, if the ratio of Young’s modulii of steel and concrete is 12.5? [8+7]

2.a) Develop Bending moment and Shear force for the Figure 1 given below indicating the


Figure 1


Figure 2

3. In a laboratory test of a beam loaded by end couples, the fibers at layer AB in as

shown in Figure 3 are found to increase 30 × 10-3 mm while those at CD decrease 90 × 10-3 mm in the 200 mm gauge length. Using E = 100 GPa, determine the flexural stress in the top and bottom fibers. [15]

Figure 3

4. Show that the maximum shearing stress in a beam having a thin-walled tubular

section of net area A is 2VA

τ = . [15]

5. Analyze the truss indicated in Figure 4 by method of sections. [15]

Figure 4

6.a) Determine the maximum deflection δ in a simply supported beam of length L

carrying a concentrated load of P at 1/4 of the span from left hand side. b) Determine the maximum deflection δ in a simply supported beam of length L

carrying a uniformly distributed load from center of the beam to left hand support. [8+7]

7. A cast iron pipe of 200.0 mm diameter and 6 mm thickness carries water at a head of

27.0 m. Determine the maximum allowable spacing of supports, if the yield strength of the material is 180.0 MPa. Use a factor of safety of 1.8. [15]

8. The outer diameter of a cylinder is 1.8 times its inner diameter. Assuming E = 0.25,

determine the ratio of external and internal pressures applied separately, so that in both the cases a) The largest stresses have the same numerical values and b) The largest strains have the same numerical values. [15]

********

SET - 4R09CODE NO: A109210304


(COMMON TO ME, MCT, MMT, AE , AME) Time: 3hours Max. Marks: 75


- - - 1.a) State the principle of superposition, and explain its significance.

b) A weight of 500 N falls on the collar of a 20 mm diameter steel bar from a height of 100.0 mm. Investigate whether the bar can withstand the load. Assume a yield stress of 275.0 MPa, a fracture strain of 24.5 percent and E = 195.0 GPa for steel. [8+7]

2.a) The following Figure 1 indicates the Shear Force diagram. Develop the loading and

Bending Moment diagram for the beam.

Figure 1

b) The following Figure 2 indicates the Shear Force diagram. Develop the loading and Bending Moment diagram for the beam. [8+7]

Figure 2

3. Determine the moment capacity of a timber beam of section 50.0 × 120.0 mm with an

allowable stress of 8.5 MPa and E = 16.0 GPa. Determine the size of 2.0 mm thick steel flitches required to double its moment capacity when the flitches are attached a) at top and bottom b) to the sides (ES = 200.0 GPa). [15]

4. A plywood beam is built up of 6-mm strips separated by blocks as shown in Figure 3.

What shearing force V will cause a maximum shearing stress of 1.4 MPa? [15]

Figure 3

5. Analyze the truss indicated in the Figure 4 by method of joints. [15]

Figure 4

6.a) Determine the maximum deflectionδ in a simply supported beam of length L

carrying a concentrated load of P at 1/4 of the span from right hand side and also carrying a uniformly distributed load for the entire span.

b) Determine the maximum deflection δ in a simply supported beam of length L carrying a uniformly distributed load from center of the beam to right hand support. [8+7]

7. A concrete pipe of radius 1.1m and 110.0 mm wall thickness is pre-stressed by a wire

5.0 mm diameter to withstand a working pressure of 1.0MPa. Determine the minimum initial stress required in the wire so that the pipe is not subjected to tensile stresses under the applied pressure. Assume EC = 30.0 GPa, and ES = 200.0GPa. [15]

8. A cast iron hub of 300.0 mm external diameter and 70.0 mm thickness is pressed on

to a steel shaft of 125.0 mm diameter. Determine the radial stress required at the interface so that the shaft can transmit 4.0 MW at 740 rpm. Compute the necessary diametral interference and the stresses in the shaft and the hub. If the shaft is subjected to a compressive force of 300.0 kN, find the change in the stresses. Assume a frictional coefficient of 0.29, Poisson’s ratio of 0.22, and Young’s modulii of steel and cast iron to be 210.0 GPa and 180.0 GPa, respectively. [15]

********

Code No: 07A32101 R07 Set No. 2

II B.Tech I Semester Examinations,December 2011FOUNDATION OF SOLID MECHANICS



? ? ? ? ?

1. A cantilever of length 2 m carries a uniformly varying load of zero intensity at thefree end, and 45 kN/m at the fixed end. If E = 2 × 105 N/mm2 and I = 108 mm4,find the slope and deflection of the free end. [16]

2. A cast iron pipe has 300 mm bore and 10 mm metal thickness, and is supportedat two points 8 m apart. Find the maximum stress in the metal when it is runningfull. Take unit weight of cast iron as 70 kN/m3 and that of water as 9.81 kN/m3.

[16]

3. A cylinder of thickness 2 cm has to withstand maximum internal pressure of 2.5N/mm2. If the ultimate tensile stress in the material of the cylinder is 350 N/mm2,factor of safety 3.0 and joint efficiency 85%, determine the diameter of the cylinder.

[16]

4. For the steel bar shown in figure 4. determine the longitudinal force P and stress pat all cross-sections. Determine also the vertical displacement ∆ of all cross-sectionsof the bar Take E=2 × 105 N/mm2. Also, locate the section of zero displacement.

[16]

Figure 4

5. Draw the S.F. and bending moment diagrams, indicating principal values, for anoverhanging beam shown in Figure 5. [16]

1


Figure 5

6. A cast iron bracket has a cross-section of I-shape with unequal flanges as shownin Figure 6. If the section is subjected to a S.F. of 100 kN, draw the shear stressdistribution over the depth of the section giving salient values. [16]

Figure 6

7. Find the size of the fillet weld required to connect the bracket plate to the columnas shown in figure 7. The stress in the weld is not to exceed 100 MPa. [16]

Figure 7

8. Locate the shear centre of the section shown in Figure 8. [16]

2


Figure 8

? ? ? ? ?

3





? ? ? ? ?


Figure 1


4


Figure 2


[16]



[16]

5


Figure 5


[16]


Figure 7


6


Figure 8

? ? ? ? ?

7





? ? ? ? ?


Figure 1


Figure 2

3. A cylinder of thickness 2 cm has to withstand maximum internal pressure of 2.5N/mm2. If the ultimate tensile stress in the material of the cylinder is 350 N/mm2,

8


factor of safety 3.0 and joint efficiency 85%, determine the diameter of the cylinder.[16]


[16]

Figure 5


[16]


Figure 1



9

4

6

6

8


Figure 2

? ? ? ? ?

10

8





? ? ? ? ?


Figure 1


Figure 2

3. A cast iron pipe has 300 mm bore and 10 mm metal thickness, and is supportedat two points 8 m apart. Find the maximum stress in the metal when it is running

11


full. Take unit weight of cast iron as 70 kN/m3 and that of water as 9.81 kN/m3.[16]


Figure 4


[16]

Figure 5


[16]


12


Figure 7


? ? ? ? ?

13

Code No: A109210301 R09 Set No. 2

II B.Tech I Semester Examinations,December 2011ENVIRONMENTAL STUDIES

Common to ME, CHEM, MEP, AE, ETM, ECETime: 3 hours Max Marks: 75


? ? ? ? ?

1. Give the guidelines for sustainable development? [15]

2. How GIS and remote sensing methods are useful in EIA? [15]

3. What is phosphorus cycle with diagram? [15]

4. Can companies and government department be also prosecuted under the air act?[15]

5. Explain the importance of biodiversity? [15]

6. Explain that changes likely to occur in annual temperature and precipitation as aresult of global warming? [15]

7. Explain about ecologically sound, economically viable engineering alternatives tolarge dams? [15]

8. Write the impacts of fertilizers on soil? [15]

? ? ? ? ?

1

Code No: A109210301 R09 Set No. 4




? ? ? ? ?

1. Write about biomedical waste management and handling rules? [15]

2. Explain about draft and final environmental impact statements? [15]

3. Explain about hydrological cycle, with diagram? [15]

4. Explain about productive use of biodiversity? [15]

5. Explain about pyramid of numbers with examples? [15]

6. Write the concepts of sustainable development? [15]

7. What are the adjustments to be considered for potential global warming? [15]

8. Explain about the collection of municipal solid waste? [15]

? ? ? ? ?

2

Code No: A109210301 R09 Set No. 1




? ? ? ? ?

1. What is green house effect? [15]

2. Explain the living and non-living natural resources? [15]

3. Explain about the in-situ conservation of biodiversity? [15]

4. (a) How is environment defined under Indian law?

(b) What is the reason that every person should know the law? [15]

5. Explain about salient features of matrices methods for carrying out EIA? [15]

6. How crazy consumerism can overcome exploitation of resources? [15]

7. Write about the E-waste management? [15]

8. What is biosphere? [15]

? ? ? ? ?

3

Code No: A109210301 R09 Set No. 3




? ? ? ? ?

1. Write about the pollutants? [15]

2. Write about subsurface mining? [15]

3. How to carryout the impact assessment study on vegetation and wild life? [15]

4. Write different types of ecosystems with diagrams? [15]

5. What are the threats to sustainability? [15]

6. Explain about the aesthetic value of biodiversity? [15]

7. What are the current requirement that should be met before declaring an area into a wide life sanctuary or a national park under the forest acts? [15]

8. How human activity has resulted in increased emissions of green house gases? [15]

? ? ? ? ?

4

Documents

2-1 Aero Question Bank