GUJARAT TECHNOLOGICAL UNIVERSITY - …mytoolbag.in/media/GTUPAPERS/1/2/CIVIL/S3/FM.pdfTotal pressure and center of pressure, pressure diagram, ... Analyze forces on floating and immersed

GUJARAT TECHNOLOGICAL UNIVERSITY

CIVIL ENGINEERING (06) FUILD MECHANICS

SUBJECT CODE: 2130602

B.E. 3rd

Semester

Type of course: APPLIED PHYSICS

Prerequisite: System of units, Laws of motion, Basic idea of force, Concept of centroid

Rationale:

1. To develop a basic understanding about the properties of fluids, their behavior under static and

dynamic conditions.

2. To enable the students to apply the basic principles of Fluid Mechanics to solve real life problems

Teaching and Examination Scheme:

Teaching Scheme Credits Examination Marks Total

Marks L T P C Theory Marks Practical Marks

ESE

(E)

PA (M) PA (V) PA

(I) PA ALA ESE OEP

3 0 2 5 70 20 10 20 10 20 150

Contents:

Sr

No

Contents Teaching

Hrs

Weightage

(%)

1 Module 1:Properties of Fluids Mass density, specific weight, specific gravity, specific volume, vapour

pressure, compressibility, elasticity, surface tension, capillarity; Newton’s

law of viscosity, classification of fluids, dynamic viscosity, kinematic

viscosity, variation of viscosity with temperature; Basic concept

applicable to fluid mechanics.

4 10

2 Module 2: Fluid Statics

Measurement of Pressure:

Pressure variation in static fluid, PASCAL’s law, Units and scale of

pressure measurement- Atmospheric pressure, Absolute pressure, Gauge

pressure, and Vacuum pressure, Hydrostatic paradox, Piezometer, U-

Tube manometer, Single column manometer, U-tube differential

manometer, Inverted U-tube differential manometer, micromanometers,

Mechanical pressure gauges.

Hydrostatic force on plane and curved surface :

Total pressure and center of pressure, pressure diagram, Total pressure on

plane surfaces and curved surfaces depth of center of pressure, Practical

applications of Total pressure and Center of pressure.

Buoyancy and Flotation:

Buoyant force, Buoyancy and Center of Buoyancy, Archimedes

Principle, Metacentre and Metacentric height, Equilibrium of floating and

12 25

submerged bodies, Metacentric height evaluation –theorectical and

experimental method, Oscillation of floating body

Fluids in Relative Equilibrium:

Static fluid subjected to uniform linear acceleration, Liquid containers

subjected to constant horizontal acceleration,Liquid containers subjected

to constant vertical acceleration, Liquid containers subjected to constant

rotation.

3 Module 3:Fluid Kinematics

Fluid flow methods of analysis of fluid motion, Streamlines, Path lines,

Streak lines and Stream tubes. Types of fluid flow-Steady and unsteady

flow, Uniform and non-uniform flow, Laminar and turbulent flow,

Reynolds number, Reynolds experiment, Rotational and Irrotational flow,

Subcritical, critical and Supercritical flow, Compressible and

Incompressible flow, One, Two and three dimensional flow, Circulation

and vorticity, Velocity potential and stream function, flow net, Source,

Sink and Doublet.

6 10

4 Module 4: Fluid Dynamics

Euler’s equation, Bernoulli’s equation, Energy correction factor

3 10

5 Module 5: Flow Measuring Devices

Measurement of discharge- Venturimeter, Orificemeter, Nozzlemeter,

Rotometer. Measurement of velocity-Pitot tube. Orifice- classification.

Flow through reservoir opening i.e. orifice, trajectory of free jet,

hydraulic coefficients, Experimental determination of hydraulic

coefficients, Small and large orifice, Time of emptying a tank with

orifice. Mouthpiece- classification, External cylindrical mouthpiece,

Convergent –divergent mouthpiece, Borda’s mouthpiece. Notches and

weirs-discharge over rectangular notch and triangular notch. Velocity of

approach, End Contractions. Cippoletti notch. Time of emptying a tank

with notch or weir, Ventilation of weir, Sutro weir.

8 25

6 Module 6: Flow Immersed Past Bodies

Drag and lift, Types of drag, Drag on sphere, cylinder, flat plate and

Airfoil, Karman vortex street, Effect of drag, Development of lift,

Magnus effect, Circulation and lift characteristics of airfoils.

4 10

7 Module 7 Compressible Flow

Basic equations, Mach number, Mach cone, Area-velocity relationship,

Propagation of sound wave, Stagnation properties.

5 10

Reference Books:

1. Engineering Fluid mechanics, K.L. Kumar, 8th Edition S. Chand & Company Ltd.

2. Hydraulics and Fluid Mechanics, P.M. Modi and S.M. Seth, Standard Book House

3. Theory and Applications of Fluid Mechanics, K. Subramanya, Tata McGraw Hill.

4. Fluid Mechanics, A.K. Jain, 4th edition, Khanna Publishers.

Course Outcomes:

After successful completion of the course the students shall be able to:

1. Describe types of fluid and determine their properties

2. Measure pressure and calculate hydrostatic pressures and forces on flat/curved surfaces

3. Analyze forces on floating and immersed bodies and understand fluids in relative equilibrium

4. Know the basics of fluid kinematics and dynamicsand understand and apply the Bernoulli

principle.

5. Calibrate fluid flow measuring devices like venturimeter, orificemeter, notches, orifice,

mouthpieces.

6. Understand the concept of drag and lift on various objects.

7. Know the basics of compressible fluid flow.

List of Practicals:

Students will have to perform following experiments in laboratory and prepare the laboratory manual.

The students will have to solve atleast five examples and related theory from each topic as an

assignment/tutorial.

Measurement of viscosity (Verification of Stokes law)

Study of pressure measurement devices

Hydrostatic force and center of pressure on flat/curved surfaces

Stability of Floating body

Study Characteristics of Laminar and Turbulent flows (Reynolds experiment)

Verification of Bernoulli Theorem

Determine Hydraulic coefficients of a small circular orifice.

Calibration of flow measuring devices (Venturimeter, Orificemeter)

Calibration of Rectangular and V notch.

Drag on immersed objects.

Design based/open ended problem

1. Measurement of capacity of storage tanks

2. Measurement of viscosity of different fluids

3. Measurement of pressure and discharge in pipe flow

4. Comparison of time of emptying a tank computed theoretically and actually observed (Using

mouth pieces, orifices).

5. For the college building/ department determine the pressure head,peizometric head from a water

tank at a point of interest in flow system.

6. Measurement of pressure in aninflated tube.

7. Prepare working model for falling sphere viscometer, stability of floating bodies

8. Prepare working models of different types of gates for storing water/liquid in a tank/reservoir.

9. Prepare working models of different types of notches, weirs, and orifice.

10. Estimate the time to empty the water /liquid tank of different shapes with orifice.

11. Estimate drag force on objects (like advertisement display board,) or design of a parachute etc.

12. Any other related problem framed by college faculty.

Major Equipments:

1. Viscometer

2. Piezometers, Manometers, pressure gauges

3. Centre of pressure

4. Floating body

5. Reynolds experimental setup

6. Hydraulic bench with modular attachments for various experiments

7. Open channel with flow and depth measurement setup etc.

List of Open Source Software/learning website:

www.nptel.iitm.ac.in/courses/

Active learning Assignments (AL) : Preparation of power-point slides, which include videos,

animations, pictures, graphics for better understanding theory and practical work – The faculty will

allocate chapters/ parts of chapters to groups of students so that the entire syllabus to be covered. The

power-point slides should be put up on the web-site of the College/ Institute, along with the names of the

students of the group, the name of the faculty, Department and College on the first slide. The best three

works should submit to GTU.

1

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III (NEW) - EXAMINATION – SUMMER 2017

Subject Code: 2130602 Date: 05/06/2017 Subject Name: Fluid Mechanics Time: 10:30 AM to 01:00 PM Total Marks: 70 Instructions:

1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks.

Q.1 Short Questions 14

1 What is a Newtonian fluid? [1]

2 Distinguish clearly between an ideal fluid and real fluid. [1]

3 Define dynamic viscosity of fluid. [1]

4 Explain the capillary action of rise and fall of liquid columns. [1]

5 Explain the term Buoyancy and Archimedes principle. [1]

6 A spherical sea mine of diameter 0.9 m is weighing 2300 N. It is chained to the bottom

of a harbor. What external force must the chain provide to keep the sea mine floating to

the surface? Take mass density of sea water ρ = 1025 kg/m3.

[1]

7 Calculate the height of capillary rise of water in a glass tube of diameter 1 mm. The air-

water surface tension at room temperature is 0.073 N/m. The contact angle for air-water-

glass system is taken as 0O.

[1]

8 How is the atmospheric pressure measured? [1]

9 What is the difference between gauge and absolute pressure? [1]

10 Why mercury is preferred as an indicating liquid in a U tube manometer? [1]

11 Distinguish between a laminar and turbulent flow. [1]

12 How is the metacentric height calculated experimentally? [1]

13 Write the working principle of a Pitot tube. [1]

14 What do you understand by stagnation pressure? [1]

Q.2 [1]

(a) Explain with a neat sketch a U-tube differential manometer. When do we use an inverted

U-tube manometer?

[3]

(b) The underground oil storage tank as shown in Figure 1 has developed a leak such that

water has entered the tank. The depth of oil is 2.0 m and water depth is 0.5 m. For the

dimension given, determine the hydrostatic pressure at the (i) water –oil interface and (ii)

at the base of the tank. Take specific gravity of oil = 0.87.

[4]

(c) A circular annular area of 2.0 m outer diameter and 1.0 m inner diameter is immersed [7]

2

vertically in water with the centre of area at 3.5 m below the water surface. Find (i) the

force exerted on one side of the area, and (ii) location of the centre of pressure.

OR

(c) An open cylindrical tank of 0.9 m in diameter and 2 m high contains water up to 1.5 m

depth. If the cylinder rotates about its vertical axis what maximum angular velocity can

be attained without spilling any water?

[7]

Q.3

(a) Explain free and forced vortex with suitable examples. [3]

(b) Explain the use of flow net for a two dimensional flow. [4]

(c) Sketch the jet trajectory from a small circular orifice located on the side wall of a liquid

container. Show the vena contracta. What do you understand by coefficient of

contraction? Give typical values of Cc for small circular orifice.

[7]

OR

Q.3

(a) What is the difference between Euler equation and Bernoulli’s equation? [3]

(b) Explain the components of a venturimeter with a neat proportionate sketch. [4]

(c) A pitot tube is inserted in a pipe of 30 cm diameter. The static pressure of the tube is 10

cm of mercury, vacuum. The stagnation pressure at the centre of the pipe recorded by the

pitot tube is 1.1 N/cm2. Calculate the rate of flow of water through the pipe if mean

velocity of flow is 0.85 times centre line velocity. Take coefficient of pitot tube = 0.98.

[7]

Q.4

(a) Verify whether the given stream function ψ = y2 – x2 represent irrotational flow. [3]

(b) Write the Bernoulli’s equation for ideal fluid and real fluid. Also list the applications

where Bernoulli’s equation is used.

[4]

(c) Estimate the discharge over a 90o triangular notch having head over crest as 45 cm. The

coefficient of discharge Cd = 0.62. If the head over crest becomes 55 cm calculate the

percentage increase in discharge.

[7]

OR

Q.4

(a) What is the difference between a mouthpiece and an orifice? [3]

(b) Explain the terms Total drag, Frictional drag, pressure drag with suitable examples. [4]

3

(c) A car has frontal projected area of 1.5 m2 and travels at 55 km/h. Calculate the power

required to overcome wind resistance if coefficient of drag is 0.35. If the drag coefficient

is reduced by streamlining to 0.25 what speed of the car is possible? Take ρair = 1.2

kg/m3

[7]

Q.5

(a) Distinguish between subsonic and supersonic flow. [3]

(b) Explain with neat sketches the Convergent-Divergent mouthpiece and the Borda’s

mouthpiece

[4]

(c) Define Mach number. A supersonic plane in its flight has a Mach angle of 400 and is

flying in air with -20 0C. Calculate the speed of plane. Assume k = 1.4 and R = 287

J/Kg.K

[7]

OR

Q.5

(a) Calculate the discharge for flow passing through a trapezoidal notch having base width

of 0.75 m and side slope of 1:1. Take the head over crest of notch = 50 cm. The

coefficient of discharge Cd= 0.63.

[3]

(b) Explain with neat sketches the contracted rectangular notch and Cippoleti notch. [4]

(c) Derive the equation for time (T) required to empty a rectangular tank filled with liquid.

The tank has an orifice at its bottom. The initial depth of water in the tank is H1.

[7]

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III(New) • EXAMINATION – WINTER 2016

Subject Code:2130602 Date:06/01/2017

Subject Name:Fluid Mechanics

Time: 10:30 AM to 01:00 PM Total Marks: 70 Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

MARKS


1. ___________ cannot retain any unsupported shape and volume.

(a) Liquid, (b) gas, (c) fluid, (d) solid.

2. The cohesive forces are more in case of

(a) Liquid fluid, (b) gaseous fluid, (c) equal in both, (d) none of the above.

3. The value of normal atmospheric pressure is

(a) 1.01325 bar, (b) 10.33 m of water, (c) 760 mm of mercury,

(d) All the above.

4. The numerical value of 1 bar = __________ in terms of Pa.

(a) 1 Pa, (b) 1.1352 Pa, (c) 105 Pa, (d) 100 Pa.

5. Which of the following is a cause/s of dam failure

(a) due to overturning, (c) due to sliding,

(b) due to tension/compression, (d) All of the above.

6. For ___________ flow, path line, streamline and streak line are identical.

(a) Steady, (b) uniform, (c) laminar, (d) one dimensional.

7. The equation of continuity holds good when the flow

(a) is steady, (c) velocity is uniform at all the cross sections,

(b) is one dimensional, (d) all of the above.

8. The rate of change of linear momentum equals

(a) Force, (b) torque, (c) energy, (d) work done.

9.The length of divergent portion of venturimeter in comparison to convergent portion

is

(a)More, (b) same, (c) less, (d) less or more.

10.Total energy line is obtained by adding __________ head to hydraulic gradient

(a) Pressure head, (c) datum head,

(b) Kinetic head, (d) friction head.

11.For pipes, laminar flow occurs when Reynold’s number is

(a) Less than 2000, (c) more than 4000

(b) Between 2000 and 4000, (d) less than 4000.

12.Which of the following is dimensionless?

(a) Force, (b) power, (c) efficiency, (d) torque.

13.A fluid flow taking place continuously round a curved path about a fix axis of

rotation , is known as

(a) Rotational flow,(b) vortex flow, (c) radial flow, (d) circular flow.

2

14._________ is the ability of fluid to change its volume under pressure

(a) Vapour pressure, (c) compressibility,

(b) Surface tension, (d) capillary.

Q.2 (a) Explain Compressibility and Bulk modulus. 3

(b) Obtain an expression for Capillary rise of liquid. 4

(c) State the Pascal’s law and prove it. 7

OR

(c) Write a short note on 7

(i) U-tube Manometer, (ii) Diaphragm pressure gauge.

Q.3 (a) Define the terms metacentre, metacentric height and absolute pressure. 3

(b) Derive the expression for total pressure for a vertical plate submerged in the 4

Liquid.

(c) A solid cylinder of diameter 4 m has a height of 4 m. Find the metacentric 7

height of the cylinder if the specific gravity of the material of cylinder is 0.7

and it is floating in water with its axis vertical. State whether the equilibrium

is stable or unstable.

OR

Q.3 (a) Explain Buoyancy and Centre of Buoyancy. 3

(b) Explain equilibrium in floating bodies. 4

(c) Derive an equation for time period of oscillation of floating body. 7

Q.4 (a) Define following terms 3

i) Path line, ii) streamline, iii) streak line

(b) Explain Reynold’s experiment with neat sketch. 4

(c) Derive Euler’s equation of motion along streamline. 7

OR

Q.4 (a) How volumetric flow rate can be measured by pitot tube? 3

(b) Write a short note on the hydraulic co-efficient. 4

(c) Derive an expression for the discharge through a venturimeter. 7

Q.5 (a) Explain characteristics of laminar flow and turbulent flow. 3

(b) Explain hydraulic gradient and total energy line. 4

(c) Derive Darcy-Weisbach formula for head loss due to friction in pipe flow. 7

OR

Q.5 (a) Classify various types of notches. 3

(b) Briefly discuss about drag force and lift force. 4

(c) Define Mach number. Give classification and explanation of the type flow 7

based on Mach number.

*************

1



BE - SEMESTER–III(New) EXAMINATION – SUMMER 2016


Subject Name:Fluid Mechanics Time:10:30 AM to 01:00 PM Total Marks: 70 Instructions:


2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks.

MARKS


1 What do you meant by ideal fluid?

2 Define Newtonion fluid.

3 What do you meant by TEL and HGL

4 Define Path line.

5 What is pressure head?

6 Define coefficient of discharge (Cd)

7 What is sonic flow?

8 Define term “Total pressure.”

9 What is compound pipe?

10 Define rotational flow.

11 What is stagnation point?

12 Define Mach Number.

13 Define steady flow.

14 What is buoyant force?

Q.2 (a) Explain the terms Dynamic Viscosity and Kinematics Viscosity. 03

(b) Explain piezometer. 04

(c) What is Euler’s equation of motion? How will you obtain

Bernoulli’s equation from it?

07

OR

(c) A circular tank of diameter 5 m contains water up to a height of 4.5

m. the tank is provided with an orifice of diameter 0.5 m at the

bottom. Find the time taken by water (i) to fall from 4.5 m to 1.5 m

(ii) for completely emptying of tank. Take Cd= 0.62

07

Q.3 (a) The weight of 5 m3 of certain oil is 45 KN. Calculate its specific

weight, mass density and specific gravity. 03

(b) Distinguish between laminar flow and turbulent flow in pipes. 04

(c) Derive darcy-weisbach equation for friction loss in the pipe. 07

OR

Q.3 (a) State Pascal’s law and give some examples where this principle is

applied.

03

(b) Discuss relative merits and demerits of venturimeter with respect to

orifice meter.

04

(c) Derive an expression for the depth of center of pressure for inclined

plane surface submerged in the liquid.

07

Q.4 (a) Explain surface tension. 03

(b) A projectile is traveling in air having pressure and temperature as 9

N/cm2 and -50C. If the mach angle is 350, find the velocity of 04

2

projectile. Take k=1.4 and R=287 J/kg0K

(c) Explain the procedure of measuring vaccum pressure with the help

of U-tube manometer.

07

OR

Q.4 (a) An open tank contains 2 m of water covered with 1 m of oil

(specific gravity 0.85). Find the pressure of the interface and the

bottom of the tank.

03

(b) What are the advantages of triangular notch over a rectangular

notch?

04

(c) A solid wooden cylinder of 3 m diameter and 2 m height floating in

water with its axis vertical. Find the metacentric height of cylinder.

Specific gravity of wood = 0.6

07

Q.5 (a) What is weir? How it different from a notch. 03

(b) What are the advantages of providing mouth piece? 04

(c) A 200 m long pipe is laid on a slop of 1 in 50. It has 1 m diameter

at the high end and reduces to half of its diameter at lower end.

Water is flowing at a rate of 60 liter/sec. If the pressure at the high

end is 35.72 KN/m2. Find pressure at the low end. Neglect losses.

07

OR

Q.5 (a) Explain term metacentre and metacentric height. 03

(b) Explain characteristics of airfoil. 04

(c) Water is flowing in a rectangular channel of 1.2 m width and 0.08

m depth. Find the discharge if the crest length is 50 cm, if the head

of water over the crest of weir is 18 cm and water from channel

flows over weir. Take Cd= 0.62. Neglect end contraction. Take

velocity of approach in to consideration.

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III (New) EXAMINATION – WINTER 2015


Subject Name: Fluid Mechanics

Time: 2:30pm to 5:00pm Total Marks: 70 Instructions:




MARKS


1 Define surface tension.

2 What is Magnus effect?

3 State Newton’s law of viscosity.

4 Define specific gravity.

5 Define metacentric height.

6 Define stream line.

7 State Bernoulli’s theorem.

8 Define drag and lift.

9 Define elasticity.

10 State Archimede’s principle.

11 Define total pressure and center of pressure.

12 Define circulation.

13 Define co-efficient of discharge.

14 What is the value of atmospheric pressure head in terms

of water column?

of water column

Q.2 (a) What is hydrostatic paradox? Explain with figure. 03

(b) A 150mm diameter shaft rotates at 1500rpm in a 200 mm

long journal bearing with 150.5 mm internal diameter.

The uniform annular space between the shaft and the

bearing is filled with oil of dynamic viscosity 0.8 Poise.

Calculate the power dissipated as heat.

04

(c) Explain construction and working of vertical and inclined

single column manometer with equation. 07

OR

(c) Explain construction and working of Bourdon tube

pressure gauge. 07

Q.3 (a) Derive generalized equation of total pressure on inclined

plane surface. 03

(b) An isosceles triangle of base 3m and altitude 6m, is

immersed vertically in water, with its axis of symmetry

horizontal. If the head of water on it is 9m, Determine (i)

total pressure on plate ,(ii) The position of center of

pressure.

04

(c) State and define different types of fluid flow. 07

OR

Q.3 (a) A rectangular pantoon is 5m long, 3m wide and 1.2m

high. The depth of immersion is 0.8m in sea water. If the

center of gravity is 0.6m above the bottom of pantoon,

03

2

determine the metacentric height. Take density of sea

water as 1025 kg per meter cube.

(b) Derive expression for rate of flow through venturimeter 04

(c) Derive the equation of pressure at the bottom of the

container when liquid in it is subjected to uniform

acceleration in vertically upward and downward

direction.

07

Q.4 (a) What is Pitot tube? Derive equation of velocity for flow

of fluid through it. 03

(b) A stream function for a two dimensional flow is given by

ψ = 2xy, calculate the velocity at point P (2,3). Find the

velocity potential function ϕ.

04

(c) Derive Bernoulli’s equation from Euler’s equation of

motion. State assumptions also. 07

OR

Q.4 (a) Explain possibilities of dam failure in short. 03

(b) Derive the equation of discharge over a rectangular

notch. 04

(c) Prove that velocity of sound wave is square root of the

ratio of change of pressure to the change of density of the

fluid

07

Q.5 (a) Explain working of rotameter with figure. 03

(b) Define Mach number and various flow on its basis 04

(c) An aero plane weighing 40 kN is flying in a horizontal

direction at 360 km/hr. The plane spans 15m and has a

wing surface area of 35 m2. Determine the lift coefficient

and the power required to drive the plane. Assume drag

coefficient =0.3 and for air ρ = 1.20 kg/m3. Also work out

the theoretical value of the boundary layer circulation.

07

OR

Q.5 (a) Define various parts of an aerofoil. 03

(b) A reservoir discharges through a sluice 0.915m wide by

1.22m deep. The top of the opening is 0.65m below the

water level in the reservoir and the downstream water

level is below the bottom of the opening. Calculate (i) the

discharge through the opening if Cd= 0.6 and (ii) % error

if the opening is treated as a small orifice.

04

(c) Derive equation of discharge through a convergent-

divergent mouthpiece. 07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER– III (NEW) EXAMINATION – SUMMER 2015

Subject Code: 2130602 Date:04/06/2015


Time: 02.30pm-05.00pm Total Marks: 70 Instructions:




Q.1 (a) Define the terms: (1) kinematic viscosity (2) surface tension (3) specific gravity

(4) specific weight (5) Ideal fluid (6) capillarity (7) Newtonian fluid

07

(b) A square plate of size 1m x 1m and weighing 500 N slides down an inclined

plane with a uniform velocity of 2 m/s. The plane makes an angle of 300 to the

horizontal and has oil film of 1.5 mm thickness. Find the dynamic viscosity of

oil.

07

Q.2 (a) State Pascal’s law of pressure and prove it. 07

(b) Absolute pressure at a point is 30 kPa. Convert this pressure in terms of gauge

pressure. Also calculate the corresponding height in terms of oil of specific

gravity 0.9 for both of the above values. Take atmospheric pressure = 101.39

07

OR

(b) Write a short note on (1) piezometer & (2) inverted U-tube differential

manometer with neat sketches.

07

Q.3 (a) Rectangular lamina of size 3m x 5m is immersed vertically in water such that 5m

side is parallel and lies below 1m to the free water surface. Determine the total

hydrostatic force and centre of pressure.

07

(b) Discuss the equilibrium conditions for floating and submerged bodies with

proper sketches.

07

OR

Q.3 (a) Briefly discuss about (1) uniform and non-uniform flow (2) velocity potential

function & (3) uses of flow net.

07

(b) Tapering pipe has diameters of 40 cm and 25 cm at two different sections. Oil of

specific gravity 0.85 flows through it. If the velocity of flow at 25 cm section is

3 m/s and pressure is 200 kPa, determine the pressure at the other end. Assume

pipe is laid horizontal and losses are negligible between two sections.

07

Q.4 (a) Open cylindrical tank of 15 cm diameter and 35 cm deep contains water upto the

brim. Tank is rotated at 400 rpm about its vertical axis. Determine the volume of

water left in the tank.

07

(b) Give derivation of Bernoulli’s equation from Euler’s equation of motion.

Enumerate assumptions made in derivation and explain the meaning of each term

of Bernoulli’s equation.

07

OR

Q.4 (a) Derive the equation for determining the discharge from Borda’s mouthpiece

running full.

07

(b) Briefly discuss about drag force and lift force. Explain the types of drag. 07

Q.5 (a) Define various hydraulic coefficients. How to determine coefficient of velocity

experimentally?

07

2

(b) A tank has two identical orifices in one of its vertical side. The upper and lower

orifices are 3m and 5 m below the water surface respectively. Determine the

point of intersection of two jets if coefficient of velocity is 0.92 for both the

orifices.

07

OR

Q.5 (a) Classify various types of notches. Derive the equation for discharge through a

rectangular notch.

07

(b) Define Mach number. Give classification and explanation of the type of flow

based on Mach number.

07

*************

1/2


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III • EXAMINATION – WINTER • 2014

Subject Code: 2130602 Date: 30-12-2014


Time: 02.30 pm - 05.00 pm Total Marks: 70 Instructions:




Q.1 (a) Write statements of the following:

(i). Hydrostatic law

(ii). Pascal’s law

(iii). Bernoulli’s theorem

(iv). Newton’s law of viscosity

(v). Archimedes principle for the buoyant force

05

(b) 1) Define the following terms:

Metacentric height, Kinematic viscosity, Surface tension,

Velocity potential function and Reynolds number. 2) Differentiate between the following in brief:

(i). Rotational flow and Irrotational flow

(ii). Laminar flow and Turbulent flow

(iii). Compressible flow and Incompressible flow

(iv). Uniform flow and Non-uniform flow

05

04

Q.2 (a) Derive expressions for total force and centre of pressure on a vertical

plane surface submerged in static liquid.

07

(b) A dam section is shown in Fig. 1. Calculate, (i) total force exerted by

static water on the dam section, (ii) inclination of the force with

horizontal and, (iii) depth at which this force acts. Take length of the

dam section (perpendicular to the section given in Fig.1) equal to 1 m.

07

OR

(b) Derive theoretical equation for the metacentric height of a floating

body.

07

Q.3 (a) Derive Bernoulli’s equation for incompressible fluid flow. State

assumptions made in the derivation.

07

(b) For a fluid flow, velocity components in x and y directions are u = 2xy

and v = x2 – y

2 + 4 respectively. Show that the components represent a

possible case of fluid flow. Derive stream function and the flow rate

between the stream lines corresponding to points (1, 0) and (1, 1).

07

OR

Q.3 (a) Derive equation for rate of flow through the venturimeter. 07

(b) A sharp-edged orifice of 125 mm diameter is fixed on vertical side of a

tank under a constant head of 9 m. The orifice is discharging water at a

rate of 105 liters/sec. A point on the jet has horizontal and vertical

coordinates of 4.25 m and 0.55 m respectively, which are measured

from the vena contracta. Calculate coefficient of velocity, coefficient of

discharge and coefficient of contraction. Also estimate area of the jet at

the vena contracta.

07

2/2

Q.4 (a) Derive equation for discharge over a rectangular weir. Also explain

significance of velocity of approach.

07

(b) 1) Calculate capillary effect in a glass tube of 3 mm diameter when

immersed in (i) water and, (ii) mercury (specific gravity = 13.6) at

temperature of 20o C. The surface tension of water and mercury

at temperature of 20o C are 0.074 N/m and 0.52 N/m. The contact

angles water and mercury are 0o and 130

o respectively. Take

specific weight of water at 20o C as equal to 9.8 KN/m

3.

2) Define compressibility of a fluid. When the pressure of liquid is

increased to 7.5x103 KN/m

2 from 4x10

3 KN/m

2, its volume is

found to reduce by 0.075 percent. Calculate the bulk modulus of

elasticity of the liquid.

04

03

OR

Q.4 (a) Differentiate between a stream lined body and a bluff body. Prove that

the coefficient of drag for the drag on sphere is given by CD = 24/Re,

when Re (Reynolds’ number) ≤ 0.2.

07

(b) Experiments on a flat plate of 1 m length and 0.5 m width were

conducted in a wind tunnel in which wind was blowing horizontally at a

speed of 60 Km/hour. The plate was kept at such an angle that the

coefficients of drag and lift were 0.2 and 0.88 respectively. Calculate,

(i) drag and lift forces, (ii) resultant force and its direction and, (iii)

power exerted by the air stream on the plate. Take specific weight of air

equal to 11.28 KN/m3.

07

Q.5 (a) Derive equation for sonic velocity of sound wave in a compressible fluid

in terms of the bulk modulus of elasticity of the fluid medium.

07

(b) An aeroplane is flying at 950 Km/hour through still air having an

absolute pressure of 80 KN/m2 and temperature -7

o C. Calculate

stagnation pressure, stagnation temperature and stagnation density, on

the stagnation point on the nose of the plane. Take R = 287 J/ Kg K and

γ = 1.4 for air.

07

OR

Q.5 (a) Derive continuity equation for three dimensional incompressible flow. 07

(b) (i). An inverted differential manometer, having an oil of specific

gravity 0.8 as manometric liquid, is connected two pipes A and B

which are at same level and both carrying water. Level of the oil

in left limb is 0.2 m above centre of pipe A and, level of the oil in

right limb is 0.45 m above centre of pipe B. Calculate difference

in pressure between the two pipes.

(ii). A solid cylinder having 1.5 m diameter and 2 m height is floating

in water with its axis vertical. If the specific gravity of material of

cylinder is 0.85, calculate metacentric height and state whether

the equilibrium is stable or unstable.

04

03

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III (OLD) - EXAMINATION – SUMMER 2017

Subject Code: 130602 Date: 02/06/2017 Subject Name: Fluid Mechanics Time: 10:30 AM to 01:00 PM Total Marks: 70 Instructions:

1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks.

Q.1 (a) Define fluid. Enlist its properties and explain any two properties in detail. 07

(b) Explain the relationship between absolute pressure, atmospheric pressure and

gauge pressure with neat sketch.

07

Q.2 (a) Explain stability of submerged and floating body with neat sketch. 07

(b) State Bernoulli’s theorem and obtain the equation from Euler’s equation. 07

OR

(b) Derive Darcy- Weisbach equation for friction loss in pipes. 07

Q.3 (a) State and prove Pascal’s law. 07

(b) Calculate dynamic viscosity of an oil, which is used for lubrication between

rectangular plate 1m x 0.3m and an inclined plane with angle of inclination 300.

The weight of plate is 500 N and slides down the inclined plane with uniform

velocity 0.4 m/s. Thickness of oil film is 1.5 mm.

07

OR

Q.3 (a) Write the statement of continuity equation and derive the expression. 07

(b) The pipe A carrying water at pressure 150 KN/m2 is connected by differential

manometer to another pipe B. The distance between axis of two pipes A& B is

1.0m. The vertical height of water column in pipe A is 1.5 m. If difference in

height of mercury in two limbs of manometer is equal to 60 mm. What is

pressure in pipe B.

07

Q.4 (a) Explain flow net in detail. Also discuss its characteristics and limitations. 07

(b) A circular plate 3.5 m in diameter is immersed vertically in water in such a

way that it’s greatest and least depth below the free surface are 4 m and 1 m

respectively. Find the total pressure on one face of plate and position of center

of pressure.

07

OR

Q.4 (a) What is hydraulic coefficient? Give name and derive equation Cc= Cd/Cv. 07

(b) A stream function is given by ψ = 5x-10y. Determine the velocity component

and also magnitude and direction of the resultant velocity at any point.

07

Q.5 (a) What are the major losses and minor losses in pipe flow? Discuss in detail. 07

(b) A horizontal venture meter with inlet diameter 150 mm and throat diameter 70

mm is employed to measure the discharge of water. The differential manometer

connected to the inlet gives reading of 150 mm of mercury. Determine the rate

of flow if the co-efficient of discharge is 0.98

07

OR

Q.5 (a) What do you understand by stagnation pressure? Obtain an expression for

stagnation pressure of compressible fluid in terms of Mach number.

07

(b) Differentiate between ( 1) Orifice and Mouthpieces

(2)Weir and Notches. Also enlist its types.

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III(OLD) • EXAMINATION – WINTER 2016



Time: 10:30 AM to 01:00 PM Total Marks: 70 Instructions:




Q.1 (a) Explain term dynamic viscosity and kinematic viscosity. Discuss effect of

temperature on viscosity.

07

(b) State and prove Pascal’s law. 07

Q.2 (a) Derive an expression for total pressure and position of pressure when vertical

surface immersed inside the liquid.

07

(b) A single U-tube manometer is used to measure water pressure in pipe line. The

left limb of manometer is connected to the pipe and the right lime is open to

atmosphere. The mercury level in the left limb is 80 mm below the center of the

pipe and the right limb is 220mm above the center of the pipe. Calculate the

pressure of water in meter and also in KN/m2.

07

OR

(b) A body with a gravity force of 500 N with a flat surface area 0.2 m2 slides down

a lubricated inclined plane making a 300 angle with the horizontal. For viscosity

of 0.981 N-S/m2 and body speed of 1 m/sec. Determine the lubricant film

thickness.

07

Q.3 (a) Write Euler’s equation of motion. Derive expression for Bernoulli’s equation. 07

(b) A circular lamina 125 cm in diameter is immersed in water so that the distance of

its edge measured vertically below the free surface varies 60 cm to 150 cm

respectively. Find the total pressure force due to water on one side of the lamina

and vertical distance of the center of pressure below the water surface.

07

OR

Q.3 (a) What is meta center? Explain how metacentric height is determine analytically? 07

(b) A uniform rectangular body 2 m long, 1 m wide and 0.8 m deep floats in water,

the depth of immersion being 0.6 m. What is the weight of the body? Find also

the position of metacenter. Is the equilibrium is stable?

07

Q.4 (a) What is flownet? Write uses of flownet. Explain various methods to obtain

flownet.

07

(b) A horizontal pipe, 12 cm in diameter is joined by sudden enlargement to a 15

cm diameter pipe. Water is flowing through it at rate of 2 m3/min. Find the loss

of head due to sudden expansion and the pressure difference in the two pipes.

If the change of section is gradual without any loss, what would be the change

in pressure?

07

OR

Q.4 (a) Define Hydraulic co-efficient. Derive equation Cc = Cd / Cv 07

(b) Water flows over a rectangular weir 1 m wide at a depth of 150 mm and

afterwards passes through a triangular right angled weir. Taking Cd for

rectangular and triangular weir as 0.62 and 0.59 respectively. Find the depth

over triangular weir.

07

2

Q.5 (a) Write brief note on:

(1) Types of notches

(2) Ogee wier

07

(b) Given the velocity field V = y2i – 6xj, obtain the equation of the streamline

passing through (1, 1).

07

OR

Q.5 (a) Define stagnation pressure. Obtain an expression for stagnation pressure of

compressible fluid in terms of mach number and pressure.

07

(b) Write the statement of continuity equation and derive the expression. 07

*************

1



BE - SEMESTER–III EXAMINATION – SUMMER 2016



Time:10:30 AM to 01:00 PM Total Marks: 70

Instructions: 1. Attempt all questions.



Q.1 (a) Define the following terms:

Specific weight, Relative density, Cohesion, Pressure, Capillarity, Steady flow,

Streamline.

07

(b) State and explain: Newton’s law of viscosity.

A rectangular plate, 0.7m X 0.4m, weighing 750N slides down a 30˚ inclined

surface at a uniform speed of 1.1m/s. If the 2mm gap between the plate and the

inclined surface is filled with castor oil, determine the viscosity of the oil.

07

Q.2 (a) Enlist different types of manometer. Explain, with suitable sketch, working of a

differential U-tube manometer.

07

(b) State and explain ‘Bernoulli’s theorem’. What are the assumptions in Bernoulli’s

theorem? Write Bernoulli’s equations for real fluid and ideal fluid. 07

OR

(b) Differentiate between the following:

(i) Absolute pressure and Gauge pressure

(ii) Rotational flow and Irrotational flow

(iii) Source and Sink

07

Q.3 (a) State and explain: Hydrostatic law of pressure variation.

Compute the pressure at the bottom of the tank, 2m diameter, filled with water

to a depth of 3m. Also, work out the absolute pressure at the bottom, if the local

atmospheric pressure head is 75cm of mercury.

07

(b) Explain the terms: Metacenter, Center of buoyancy.

What are the different stability conditions for the floating body? Discuss each of

them in detail.

07

OR

Q.3 (a) Derive an equation for the discharge passing over a rectangular notch and show

that percentage error in estimation of discharge is 1.5 times the percentage error

in head measurement.

07

(b) Explain: Center of pressure

Determine the pressure force and the position of centre of pressure on a circular

plate 1m diameter which is placed vertically in water in such a way that the

centre of plate is 2m below the free surface

07

Q.4 (a) An oil of specific gravity 0.9 flows through a Venturimeter (VM) with inlet

diameter of 15cm and throat diameter 7.5cm. The mercury manometer

connected between the inlet and throat of VM shows a deflection of 15cm.

Calculate the discharge of the oil, coefficient of discharge of VM Cd = 0.95.

07

(b) Show that the equipotential lines and streamlines are orthogonal to each other.

What are the uses of flownet?

07

OR

2

Q.4 (a) Differentiate between ‘Major’ and ‘Minor’ energy losses, for the flow through

pipes. Explain, Total Energy Line (TEL) and Hydraulic Grade Line (HGL).

Also sketch TEL and HGL for the flow through a Venturimeter.

07

(b) What are different devices used for the measurement of flow through pipes?

Enlist the components of a Venturimeter and explain the functions of one of

them.

07

Q.5 (a) Define: Mach number. Classify the compressible flow based on Mach number.

If an aircraft moves with a speed of 250kmph through an atmosphere where

velocity of sound is 330m/s, find the Mach number. What type of flow it

represents?

07

(b) State: Momentum principle. Starting from Newton’s second law of motion,

obtain an equation for momentum principle. Discuss different applications of

momentum principle.

07

OR

Q.5 (a) How does an orifice differ from a mouthpiece? State different hydraulic

coefficient of an orifice and obtain the relation between them.

07

(b) Discuss, with the help of a representative sketch, propagation of sound for the

flow having Mach number less than one.

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III EXAMINATION – WINTER 2015



Time: 2:30pm to 5:00pm Total Marks: 70 Instructions:




Q.1 (a) Explain the following terms:

(i) Dynamic viscosity (ii) Ideal fluid (iii) Non-newtonion fluid (iv) Newtonion

fluid (v) Weight density (vi) Specific gravity (vii) Specific volume

07

(b) A circular plate of diameter 1 m is immerged in a liquid of specific gravity 0.9

with its plane making an angle of 300 with horizontal. The center of the plate is

at a depth of 2 m below the free surface. Calculate (1) total pressure force on

one side of the plate (2) location of the center of pressure.

07

Q.2 (a) Define atmospheric pressure. Enlist different types of pressure and explain

difference between U-tube differential manometer and inverted U-tube

manometer.

07

(b) A U-tube manometer contains the mercury as menometric liquid. One end of

manometer is connected to a pipe in which a fluid of specific gravity 0.8. The

level of mercury in right limb is 8 cm above the center of pipe. Calculate

pressure of fluid in a pipe when the difference of mercury level in two limb is

18 cm.

07

OR

(b) Differentiate between notch and weir. Classify the weirs on basis of shapes of

crest and describe all in brief.

07

Q.3 (a) A solid wooden cylinder of 3 m diameter and 2 m height floating in water with

its axis is vertical. Find metacentric height of cylinder. Specific gravity of

wood=0.6

07

(b) What is flownet? Write uses of flownet and explain various methods in brief to

Obtain flownet.

07

OR

Q.3 (a) State the Bernoulli’s equation and write the assumption made in it.

07

(b) A rectangular notch of crest width 0.5 m is used to measure the flow of water in

a rectangular channel. 0.6 m wide and 0.45 m deep. If the water level in the

channel is 0.25 m above the weir crest, find the discharge in the channel. Take

Cd=0.63 and take velocity of approach in to account.

07

Q.4 (a) Derive an expression for the total pressure and position of centre of pressure on

a plane surface immersed vertically in a liquid.

07

2

(b) What is flownet? Write uses of flownet and explain various methods in brief to

Obtain flownet.

07

OR

Q.4 (a) Stream function is represented by Ψ=x2+y2. Find the velocity and direction at

point P (1, 3). Also sketch the stream lines.

07

(b) Explain (1) coefficient of velocity (2) coefficient of contraction (3) coefficient

of discharge

07

Q.5 (a) What is metacentre? Explain how metacentric height is determined analytically.

07

(b) A venturimeter having inlet and throat diameter of 200 mm and 100 mm

respectively is fitted in a pipe conveying water. The pressure intensity at inlet is

130 KN/m2 and vacuum pressure head of 35 cm of mercury at throat. Assuming

4 percent of the differential head is lost between inlet and throat section, find

the rate of flow

07

OR

Q.5 (a) An airplane travel in air at 100 C at a speed of 1600 km/hour. Find the mach

number and mach angle. Take K=1.4 and R= 287 J/kg0k

07

(b) What do you mean by venturihead? Derive expression for rate of flow through

venturimeter

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER– III EXAMINATION – SUMMER 2015

Subject Code: 130602 Date:29/05/2015

Subject Name: FLUID MECHANICS

Time: 02.30pm-05.00pm Total Marks: 70 Instructions:




Q.1 (a) What do you understand by fluid? What are the types of fluid? Enlist the

properties fluid and define any two of them.

07

(b) State and prove Pascal’s law with reference to pressure intensity in a static fluid. 07

Q.2 (a) Explain with sketch the relationship between the absolute pressure, atmospheric

pressure and gauge pressure.

07

(b) A 1m wide and 1.5m deep rectangular plane surface lies in water in such a way

that its plane makes an angle of 30˚ with the free water surface. Determine the

total pressure and position of centre of pressure when the upper edge is 0.75m

below the free water surface.

07

OR

(b) A rectangular plain surface is 2 m wide and 4 m deep. It lies in vertical plane in

water. Determine the total pressure force and position of centre of pressure on

the plane surface when its upper edge is horizontal and (i) coincides with water

surface and (ii) 2.5 m below the free surface.

07

Q.3 (a) What is meta centric height? Explain analytical Method to determine Meta

centric height of a floating body.

07

(b) Weight of a stone in air is 530N and reduces to 200 N while submerging it into

water. Find the specific gravity of the stone.

07

OR

Q.3 (a) Derive continuity equation in three dimensions. 07

(b) What is flow net? State properties, applications and limitations of flow net. 07

Q.4 (a) Derive expression for discharge through Venturimeter. 07

(b) Derive Darcy-Weisbach equation for head loss due to friction in pipe. 07

OR

Q.4 (a) Classify orifice and mouth piece on various basis. 07

(b) Find the discharge over a rectangular notch of 1.5m length when the constant

head over the notch is 250 mm. Take Cd = 0.60. Neglect end contraction.

07

Q.5 (a) Derive an expression for discharge over a rectangular notch. 07

(b) Derive Bernoulli’s equation for the flow of an incompressible friction less fluid

from consideration of momentum.

07

OR

Q.5 (a) Explain stream function and velocity potential function. 07

(b) A stream function in a two dimensional flow is xy2 . Calculate the velocity

at the point (3, 2).

07

*************

1/2


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III • EXAMINATION – WINTER 2013







Q.1 (a) Define the following terms:

Weight density, Specific gravity, Capillarity, Surface tension, Stream function,

Velocity potential function

06

(b) 1) Differentiate between the following in brief:

(i). Laminar flow and Turbulent flow

(ii). Steady flow and Unsteady flow

(iii). Rotational flow and Irrotational flow

(iv). Free vortex flow and forced vortex flow

2) Left limb of a simple U-tube mercury (specific gravity = 13.6) manometer is

attached to a pipe carrying flow of water and the right limb is open to atmosphere.

If levels of mercury in the left and right limbs are 20 and 30 cm below centre of the

pipe respectively, calculate absolute pressure in the pipe.

04

04

Q.2 (a) Derive equation for static thrust and centre of pressure for an inclined plane surface

immersed in static liquid.

07

(b) A cylindrical gate, having diameter 3 m and length 5 m, is placed on a 5 m wide

horizontal canal bed with its axis parallel to the floor. The gate retains 1.5 m depth of

water on only one side, calculate magnitude, direction and coordinates of point of

application of the total force exerted by water on the gate.

07

OR

(b) A tank having 2 m x 2 m dimension in plan is filled with water up to depth of 3 m. A

circular opening having diameter 0.2 m is provided at a depth of 1.5 m from the free

surface, which is closed with a circular plate. Calculate static thrust and depth of centre

of pressure on: (i) one of the sides of the tank, (ii) bottom of the tank and, (iii) the

circular plate.

07

Q.3 (a) Derive Bernoulli’s equation for steady-incompressible fluid flow. State assumptions

made in the derivation.

07

(b) (i). The velocity potential function for a two-dimensional flow is given by Ф = 2xy –

3x. Calculate the velocity and value of the stream function at a point (2, 3) in the

flow field.

(ii). For a two-dimensional flow, the velocity components are represented by u =

x/(x2 + y

2) and u = y/(x

2 + y

2). Determine whether the flow is irrotational.

04

03

OR

Q.3 (a) Define hydraulic coefficients for flow through an orifice and derive relationship

between these coefficients.

07

(b) A venturimeter having inlet and throat diameters 0.3 and 0.15 m respectively is fitted

in a vertical pipe which carries water in upward direction. The differential mercury

manometer shows a deflection reading of 0.35 m. The difference in elevation of the

07

2/2

throat and inlet sections is 0.25 m. calculate, (i) rate of flow of water and, (ii)

differential pressure between the inlet and throat sections. Take coefficient of

discharge = 0.98.

Q.4 (a) Enlist major and minor energy losses for flow through pipes. Derive the Darcy-

Weisbach equation for frictional head loss for the flow.

07

(b) A horizontal pipe of diameter 25 cm and length 500 m connects two tanks. The rate of

flow through the pipe is 200 liters/sec. Determine difference of elevations between the

water surfaces in the two tanks. Also sketch total energy line and hydraulic gradient

line. Take value of the coefficient of friction as 0.004

07

OR

Q.4 (a) Give classification of notches and weirs. Derive equation for the flow over a triangular

notch.

07

(b) Discuss conditions of stability for a floating body and describe method of experimental

determination of the metacentric height.

07

Q.5 (a) (i). Define subsonic, sonic and supersonic flows.

(ii). Write Bernoulli’s equations for isothermal and adiabatic processes.

03

04

(b) Prove that velocity of sound wave in a compressible fluid is given by C = (k/ρ)1/2

,

where k and ρ are bulk modulus and density of fluid respectively.

07

OR

Q.5 (a) Enlist various types of manometers and explain inverted differential manometer in

details.

07

(b) Derive equation for time required for emptying a tank through an orifice provided at

base of the tank.

07

***********

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III • EXAMINATION – SUMMER 2013







Q.1 (a) Define and explain following fluid properties.

(1) Surface tension

(2) Dynamic viscosity

(3) Capillarity

07

(b) What is the use of manometer? Prove that intensity of pressure at any point in a

fluid at rest has same magnitude in all directions.

07

Q.2 (a) State Bernoulli’s equation for compressible flow. Derive Bernoulli’s equation

for adiabatic process.

07

(b) A circular plate 3.5 m diameter is immersed in water in such a way that its

greatest and least depth below free surface is 4 m and 1.5 m respectively.

Determine the total pressure on one face of the plate and position of the center

of pressure.

07

OR

(b) Define force of buoyancy and meta-centre. Discuss the conditions of equilibrium

for floating and sub-merged bodies with neat sketches.

07

Q.3 (a) (i) A stream function in a two dimensional flow is ѱ = 4xy. Calculate the

velocity at the point (4, 3). Find the corresponding velocity potential ɸ.

04

(ii) State Bernoulli’s equation for steady incompressible fluid flow. What

assumptions are made in its derivation?

03

(b) What is venturimeter? Derive an expression for discharge through a

venturimeter.

07

OR

Q.3 (a) (i) Define the terms : Stream line , Equipotential line , Flownet

03

(ii) What is pitot tube? How velocity at any point is determined by pitot tube?

04

(b) A horizontal venturimeter with inlet diameter 30 cm and throat diameter 10 cm

is used to measure the flow of oil of specific gravity 0.8. The discharge of oil

through venturimeter is 50 liters/s. Find the reading of the oil-mercury

differential manometer. Take Cd = 0.98.

07

Q.4 (a) What are major and minor energy losses in pipes? Derive an expression for loss

of head due to sudden enlargement and sudden contraction of pipe.

07

(b) (i) Explain hydraulic gradient line and total energy line

03

(ii) Classify orifices and mouthpieces based on their shape, size and sharpness. 04

2

OR

Q.4 (a) A horizontal pipe of diameter 450 mm is suddenly contracted to a diameter of

250 mm. The pressure intensities in larger and smaller pipe are given as 14.5

N/cm2

and 12.5 N/cm2 respectively. If Cc = 0.62. Find loss of head due to

contraction and discharge of water.

07

(b) (i) What do you understand by pipes in series and pipes in parallel?

04

(ii) Define: Co-efficient of velocity, Co-efficient of discharge, Vena-contracta. 03

Q.5 (a) Derive an expression for discharge through fully submerged and partially

submerged orifice.

07

(b) Water is flowing in a rectangular channel of 1.5 m wide and 0.75 m deep. Find

discharge over a rectangular weir of crest length 65 cm, if head of water over

the crest of weir is 25 cm and water flow over the weir. Take Cd = 0.62. Take

approach velocity into consideration.

07

OR

Q.5 (a) (i) What is orifice and mouthpiece? What is its use?

02

(ii) A circular tank of diameter 3 m contains water up to height of 4 m. The tank

is provided with an orifice of diameter 0.4 m at the bottom. Find time taken by

water to fall from 4.0 m to 1.0 m and for completely emptying the tank.

Take Cd = 0.98.

05

(b) Prove that the discharge through a triangular notch or weir is

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III • EXAMINATION – WINTER 2013







4. Draw neat sketch where ever necessary.

Q.1 (a) Enlist the properties of fluid and explain any three of them in detail. 07

(b) Determine the dynamic viscosity of an oil used for lubrication between a plate

1.0m X 0.4m and an inclined plane inclined at 30°. The weight of plate is 600 N

and it slide down the inclined plane with a uniform velocity of 0.35 m/sec.

Thickness of oil film is 2 mm.

07

Q.2 (a) Define atmospheric pressure. Enlist different types of pressure and explain how

atmospheric pressure is measured by various devices.

07

(b) The pressure intensity at a point in a fluid is given 5 N/cm2 . Find the

corresponding height of fluid when fluid is (i) water (ii) oil of sp. Gravity=0.80

and (iii) kerosene of sp. Gravity = 0.74

07

OR

(b) A trapezoidal channel 2m wide at the bottom is a 1.5m deep has slide slopes 1:1.

Determine total pressure and centre of pressure on a vertical gate of channel when

it is full of water.

07

Q.3 (a) What is metacentre ? Explain how metacentric height is determined analytically. 07

(b) State the Archimedes principle and determine the density of a metallic body

which floats at the interface of mercury and water. The sp. Gravity of mercury is

13.6 gm/cm3. The body floats at the interface such that 40% of its volume is

submersed in mercury and 60% in water.

07

OR

Q.3 (a) A rectangular open tank 3m x 2m x 1.5m deep is filled with oil of sp. Weight of

85 kN/m3 up to a depth of 1.0m. Find the force acting on side of tank when

(i) Tank moves upward with acceleration = g/2

(ii) Tank moves downward with acceleration = g/4

(iii) Tank moves downward with acceleration = g

07

(b) Explain with sketch stable , unstable and neutral equilibrium of floating body. 07

Q.4 (a) Derive the continuity equation

∂u/∂x + ∂v/∂y + ∂w/∂z = 0 in three dimension.

07

(b) Write characteristics of flow net, uses of flow net and limitations of flow net. 07 OR

Q.4 (a) State the Bernoulli’s equation and write the assumption made in it. 07

(b) The top and bottom dimensions of 3m long vertical pipe are 10cm and 5cm

respectively. Water flows down the pipe at 40 lit/sec. Calculate the pressure

difference between two ends of pipe.

07

Q.5 (a) A pipe 25cm in diameter and 60m long conveys water at a velocity of 3 m/sec.

Calculate the head loss in friction using (i) Darcy – wesbach formula and (ii)

Chezy’s formula. Take f = 0.006 and C = 55.

07

2

(b) Explain with sketch the Hydraulic grade line, Total energy line and Equivalent

pipe.

07

OR

Q.5 (a) Classify different types of orifices according to its size, shape, discharge

condition and shape of edge. Explain each in brief.

07

(b) Define Notch and Weir and find the Constant of notch for a right angled

triangular notch with 60 lit/min discharge. The head of sill measured was 60mm

07

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GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III • EXAMINATION – SUMMER 2013







Q:1 (a) Define ‘Fluid’ and State its properties. [14]

(b) An open tank contains 1m of water, above which there is an oil of specific gravity 0.8 to a depth

of 0.4 m. Find the pressure at (i) the interface (ii) at the bottom of the tank.

(c) Velocity distribution in a viscous flow over a plate is given by u=4y-y2 for y ≤ 2m. Where u is

velocity in m/sec. at distance y from the plate. If coefficient of viscosity is 1.5 Pa. s. determine the

shear stress at y=0 and y=2m.

(d) An open cylindrical tank 1 m diameter and 2m high contains water up to a depth of 1.5 m. If the

cylinder rotates about its vertical axis, what maximum angular velocity can be attained without water in

the tank to spil ?

Q: 2 (a) An inclined rectangular sluice gate AB 1.20 m and 5 m wide at 45 degree to water surface with

end B5 m below water surface is installed to control the flow of water. Upper end A of gate is hinged.

Find the force F applied normal to the gate at B to open the gate. [6]

(b) (i) Sketch the stability of a floating body. [3]

(ii) A uniform rectangular body 2 m long 1 m wide and 0.8 m deep floats in water, the depth of

immersion being 0.6 m. Find (i) the weigth of the body and (ii) check the stability [5]

OR

(b) (i) Describe the terms atmospheric, absolute, gauge and vacuum pressure with a sketch. [3]

(ii) Differentiate between Liquid and gases [5]

Q: 3 (a) Derive continuity equation for 2-D incompressible flow in Cartesian form stating the assumption

made and principle involved. [5]

(b) In a 3-D incompressible flow the velocity component in x and y directions are u = x2 + 2z

2 +8

and v = 2y2 + z

2 -6 . Find the velocity component w in z- direction. [5]

(c) Show that 2-D flow described by u = 6xy , v = 3x2 – 3y

2 is continuous and irrotational. [4]

OR

Q : 3 (a) Distinguish between : [5]

(i) Local acceleration and convective acceleration

(ii) Steady, unsteady, uniform and non uniform flow

(iii) Rotational and irrotational flow

(iv) Metacentre and metacentric height

(v) Stream line and stream tube

(b) A 2-D flow is described by u = 5x3 and v = -15 x

2 y. Evaluate the stream function and sketch the

stream line ψ = 1. [5]

(c) Show that ψ- line and Φ – line intersect orthogonally. [4]

Q : 4 (a) classify different types of orifices and write down the equations for hydrantic coefficients used

in it. [4]

(b) A tank has two identical orifices in one of its vertical sides. The upper orifice is 1m below the

water surface and lower one is 2 m below the water surface. Find the point at which the two jets will

intersect if co efficient of velocity is 0.9. The flow being as constant head. [7]

(c) Write down the devices used to measure (i) pressure (ii) velocity and (iii) discharge in a pipe

carrying flow of water. [3]

OR

Q :4 (a) State and Prove Euler’s equation of motion of a fluid element along a stream line stating the

principle used. [5]

(b) A 400 m long pipe tapers uniformly from 1.2 m diameter at high end to 0.6 m diameter at the

lower end, the slope of the pipe being 1 in 100 falling. The pipe conveys a discharge of 1.25 cu. m/sec if

the pressure at the high end is 75 K pa. find the pressure at the lower end. Ignore losses. [5]

(c) The velocity components in a 2-D flow of an incompressible flow are given by u = 5x3 and v =

-15x3y , find the acceleration at (1,2) at t = 1. [4]

Q : 5 (a) An oil of specific gravity 0.8 is flowing through a venturimeter having inlet diameter of 150

mm and throat diameter of 75 mm. The oil mercury manometer shows a reading of 20 cm. Compute the

discharge of oil. Take Cd = 0.8 Draw the hydraulic gradient lint for the venturimeter. [5]

(b) Classify briefly different types of notches and weirs. [4]

(c) Water flows over a rectangular weir 1 m wide at a depth of 150 mm and afterwards passes

through a triangular right angled weir. Taking Cd for rectangular and triangular weir as 0.62 and 0.59

respectively. Find the depth over the triangular weir. [5]

OR

Q : 5 (a) Derive Darcey weisbatch equation for loss of head due to friction in a pipe line. [4]

(b) Explain (i) Total Pressure and resultant pressure (ii) Specific mass and specific weight [5]

(c) (i) Distinguish between: (A) compressible and incompressible flow

(B) isothermal process and adiabatic process [2]

(ii) For a perfect gas, equation of state is PV = RT with the usual terms. Get the differential

equation. [3]

*******

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GUJARAT TECHNOLOGICAL UNIVERSITY - …mytoolbag.in/media/GTUPAPERS/1/2/CIVIL/S3/FM.pdfTotal pressure and center of pressure, pressure diagram, ... Analyze forces on floating and immersed