MAHALAKSHMImahalakshmiengineeringcollege.com/pdf/mec/IIIsem/CE6351/CE6351... · Prepared by A.Bovas Herbert Bejaxhin Asst. Prof / MECHANICAL, MEC 1

Prepared by A.Bovas Herbert Bejaxhin Asst. Prof / MECHANICAL, MEC

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MAHALAKSHMI ENGINEERING COLLEGE

TIRUCHIRAPALLI – 621213

QUESTION BANK

DEPARTMENT : MECHANICAL SEMESTER : III

SUBJECT: FLUID MECHANICS & MACHINERY SUBJECT CODE: ME2204

UNIT I- INTRODUCTION

PART – A (2 Marks)

01. Why are some fluids classified as Newtonian fluid? Give examples to Newtonian fluids.

(NOV’2)

Newtonian fluids are the simplest mathematical models of fluids that account for viscosity. While

no real fluid fits the definition perfectly, many common liquids and gases, such as water and air,

can be assumed to be Newtonian for practical calculations under ordinary conditions.

02. What is specific gravity? How is it related to density? (Apr’08)

The ratio of the density of a substance to the density of a standard, usually water for a liquid or

solid, and air for a gas

03. Define the term pressure .What are its units? (Dec’05)

The continuous physical force exerted on or against an object by something in contact with it.

04. State Pascal’s law? (Dec’05 & Dec’08)

Pascal's law or the principle of transmission of fluid-pressure is a principle in fluid mechanics

that states that pressure exerted anywhere in a confined incompressible fluid is transmitted

equally in all directions throughout the fluid such that the pressure ratio (initial difference)

remains the same


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05. What is meant by stagnation pressure? (Dec’08)

In fluid dynamics, stagnation pressure (or pitot pressure) is the static pressure at a

stagnation point in a fluid flow. At a stagnation point the fluid velocity is zero and all

kinetic energy has been converted into pressure energy (isentropically). Stagnation

pressure is equal to the sum of the free-stream dynamic pressure and free-stream static

pressure. Stagnation pressure is sometimes referred to as pitot

pressure because it is measured using a pitot tube.

06. What is the difference between gauge pressure and absolute pressure? (Dec’07)

Gauge pressure is zero-referenced against ambient air pressure, so it is equal to

absolute pressure minus atmospheric pressure. Negative signs are usually omitted. To

distinguish a negative pressure, the value may be appended with the word "vacuum" or

the gauge may be labeled a "vacuum gauge."

Absolute pressure is zero-referenced against a perfect vacuum, so it is equal to gauge

pressure plus atmospheric pressure

07. Define compressibility and viscosity of a fluid? (Apr’05)

Compressibility is a measure of the relative volume change of a fluid or solid as a

response to a pressure (or mean stress) change.

The viscosity of a fluid is a measure of its resistance to gradual deformation by shear

stress or tensile stress. For liquids, it corresponds to the informal notion of "thickness".

For example, honey has a higher viscosity than water.

08. State the Newton’s law of viscosity? (Apr’04)

Newton's law of viscosity defines the action of some fluids under a restricted range of conditions

and such fluids are referred to as Newton's fluids. The law states that when a shear stress is

applied to a fluid, the velocity gradient that it yields in the direction perpendicular to the stress is

proportional to the applied shear stress. The resultant velocity decreases with distance from a

plane over which the shear stress is applied to.


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09. What is the effect of temperature on viscosity of water and that of air? (Nov’04)

where is a constant for the gas.

Let μ = dynamic viscosity in (Pa·s) at input temperature T,

μ0 = reference viscosity in (Pa·s) at reference temperature T0,

T = input temperature in kelvins,

T0 = reference temperature in Kelvin,

C = Sutherland's constant for the gaseous material in question.

10. Define capillarity? (Dec’05)

Capillary action (sometimes capillarity, capillary motion, or wicking) is the ability of a liquid to

flow in narrow spaces without the assistance of, and in opposition to, external forces like gravity.

The effect can be seen in the drawing up of liquids between the hairs of a paint-brush, in a thin

tube, in porous materials such as paper, in some non-porous materials such as liquefied carbon

fiber, or in a cell. It occurs because of intermolecular forces between the liquid and solid

surrounding surfaces. If the diameter of the tube is sufficiently small, then the combination of

surface tension (which is caused by cohesion within the liquid) and adhesive forces between the

liquid and container act to lift the liquid

11. Explain the effect of property of capillarity (Nov’04)

The liquid rise is known as capillary rise. And the liquid drop is nothing but capillary depression.

12. What are the three major assumptions made in the derivation of the Bernoulli’s equation?

(Apr’03)

The fluid is incompressible and non viscous.

There is no energy loss due to friction between the fluid and the wall of the pipe.

There is no heat energy transferred across the boundaries of the pipe to the fluid as

either a heat gain or loss.

There are no pumps in the section of pipe under consideration.

The fluid flow is laminar and steady state.


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13. Mention any three applications of bernouills equation? (Apr’05)

1. pitot tube

2. Pitot static tube

3. Venture meter

4. Orifice meter

5. Notches and weirs

PART-B ( 16 Marks )

01. Calculate the specific weight, density, and specific gravity of 1 litre of a liquid which weighs

7N. (APR-03)


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02. State and prove Pascal’s law.


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03. Calculate the capillary rise in glass tube of 2.5mm dia when immersed in mercury take the

surface tension and angle of contact of mercury as 0.52N/m and 130⁰ respectively .Also

determine the minimum size of the glass tube, if it is immersed in water, given that the

surface tension of water is 0.0725N/m and the capillary rise in the tube is not to exceed

0.5mm. (NOV-03)


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04. Derive from the first principles, the Euler’s equation of motion for a steady flow along a

stream line. Hence derive Bernoulli’s equation. State the various assumptions involved in

the above derivation.


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05. A 15 cm vertical cylinder rotates concentrically inside another cylinder of diameter 15.10cm.

Both cylinders are 25 mm high. The space between the cylinders is filled with a liquid

whose viscosity is unknown. If a torque of 12 Nm is required to rotate the inner cylinder at

100 r.pm, determine the viscosity of the fluid (DEC-08)


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06. An oil film of thickness 10mm is used for lubrication between the two square parallel plates

of size 0.9m×0.9m each, in which the upper plate moves at 2m/s required a force of 100N

to maintain this speed. Determine,

1. Dynamic viscosity of oil 2. Kinematic viscosity of oil If the specific gravity of the oil is

0.95 (NOV-03)

Given:

A = 0.9 x 0.9 m = 0.81 m2 dy = 10 mm u= 2 m/s

F = 100 N S = 0.95

Solution:

(i) Dynamic viscosity of oil :-

Shear stress = = F/A = µ du/dy

Force / area = 100/0.81 = 123.456

123.456 = µ (2/0.01)

µ = 0.61728 Ns/m2

(ii) Kinematic viscosity of oil If the specific gravity of the oil is 0.95: -

K = µ/ρ

The value of µ is 0.61728 Ns/m2

K = 0.61728 / ρ

Value of ρ is determining from S = ρ of oil / ρ of water

0.95 = ρ of oil / 1000

ρ oil = 950 kg/m3

Therefore, K = 0.61728/950 = 6.5 x 10-5


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07. The space between two square parallel plates is filled with oil. Each side of the plate is

75cm. The thickness of the oil film is 10mm. The upper plate which moves at 3M/s requires

a force of 100N to maintain the speed. Determine

1. Dynamic viscosity of oil, 2. Kinematic viscosity of oil. If the specific gravity of oil is

0.9 (NOV-04)

Given:

A = 75 x 75 cm = 5625 cm2

= 0.5625 m2 dy = 10 mm u= 3 m/s

F = 100 N S = 0.9

Solution:

(i) Dynamic viscosity of oil :-

Shear stress = = F/A = µ du/dy

Force / area = 100/0.5625 = 177.78

177.78 = µ (3/0.01)

µ = 0.5926 Ns/m2

(ii) Kinematic viscosity of oil If the specific gravity of the oil is 0.9: -

K = µ/ρ

The value of µ is 0.5926 Ns/m2

K = 0.5926 / ρ

Value of ρ is determining from S = ρ of oil / ρ of water

0.9 = ρ of oil / 1000

ρ oil = 950 kg/m3

Therefore, K = 0.61728/950 = 6.5 x 10-5


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08. If the velocity distribution of over a plate is given by u = (2/3)Y – Y2 in which ‘U’ is the

velocity in meter per second at a distance ‘Y’ meter above the plate , determine the shear

stress at Y=0 and Y=0.15m the dynamic viscosity of fluid is 8.63 poises. (DEC-03)

09. The velocity distribution over a plate is given by U = (3/4) Y – Y2 where U is the velocity in

M/S and at the depth Y in m above the plate. Determine the shear stress at a distance of

0.15m from the top of plate. Assume dynamic viscosity of the fluid is taken as 0.85Ns/m^2.

(APR-05)


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10. Derive the momentum equation for steady flow.

11. Derive an expression for capillarity rise


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12. An orifice meter with orifice dia 15cm is inserted in a pipe of 30cm dia the pressure on the

upstream and downstream of orifice meter is respectively. Find discharge (Take cd= 0.6)


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13. The water is flowing through a taper pipe of length 100m having diameters 600 mm at the

upper end and 300 mm at the lower end at the rate of 50litres/s. The pipe has a slope of

1 in 30. Find the pressure at the lower end if the pressure at the higher level is 19.62

N/cm2.


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14. Find the displacement thickness momentum thickness and energy thickness for the velocity

distribution in the boundary layer given by u/U = y/δ where u is the velocity at a distance y

from the plate and u =U and y=δ where δ is the boundary layer thickness. Also calculate

the value of δ*/θ.


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15. In a 45 degree bend a rectangular air duct of 1 m2 cross sectional area is gradually reduced

to 0.5 m2 area. Find the magnitude and direction of the force required to hold the duct in

position if the velocity of flow at the 1 m2 section is 10 m/s and pressure is 2.943 N/m2 .

Take density of air 1.16 kg/m3 .


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16. Find the quantity of water flowing through a Venturimeter size 30cm x 15cm when the

differential manometer connected between the inlet and throat of Venturimeter gives 20cm

mercury reading. Co-efficient of discharge is 0.98.


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17. A Venturimeter with 20Cm inlet dia and 10cm throat is laid with axis horizontal and is used

for measuring the flow of oil of specific gravity 0.8 The discharge of oil through

Venturimeter is 60LPS, Find the reading of the oil mercury differential manometer.


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18. A 30cm x 15cm Venturimeter is provided in a provided in a vertical pipe line carrying oil of

specific gravity 0.9, the flow being upward. The difference in elevation of the throat section

and entrance section of Venturimeter is 30cm. The pressure difference in manometer is

25cm of Hg. Take Cd= 0.98. Calculate discharge of oil and pressure difference between

entrance and throat.


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UNIT II- FLOW THROUGH CIRCULAR CONDUITS


01. Write down the Hagen- Poiseuille Equation for laminar flow? (APR-05)

or

Where, is the pressure loss

is the length of pipe

is the dynamic viscosity

is the volumetric flow rate

is the radius

is the diameter

is the mathematical constant Pi

02. What is boundary layer? Give a sketch of boundary- layer region over a flat plate.

(APR-03)

In fluid mechanics, a boundary layer is the layer of fluid in the immediate vicinity of a bounding

surface where the effects of viscosity are significant. In the Earth's atmosphere, the planetary

boundary layer is the air layer near the ground affected by diurnal heat, moisture or momentum

transfer to or from the surface. On an aircraft wing the boundary layer is the part of the flow

close to the wing, where viscous forces distort the surrounding non-viscous flow.

03. Define displacement thickness? (NOV-04)

The displacement thickness, δ* or δ1 is the distance by which a surface would have to

be moved in the direction perpendicular to its normal vector away from the reference

plane in an in viscid fluid stream of velocity u_0 to give the same flow rate as occurs

between the surface and the reference plane in a real fluid. In practical aerodynamics,

the displacement thickness essentially modifies the shape of a body immersed in a fluid

to allow an in viscid solution. It is commonly used in aerodynamics to overcome the

difficulty inherent in the fact that the fluid velocity in the boundary layer approaches

asymptotically to the free stream value as distance from the wall increases at any given

location.

http://en.wikipedia.org/wiki/Dynamic_viscosity

http://en.wikipedia.org/wiki/Volumetric_flow_rate

http://en.wikipedia.org/wiki/Radius

http://en.wikipedia.org/wiki/Diameter

http://en.wikipedia.org/wiki/Pi


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04. Define the terms : Drag and lift (DEC-07)

In aerodynamics, the lift-to-drag ratio, or L/D ratio, is the amount of lift generated by a wing or

vehicle, divided by the drag it creates by moving through the air. A higher or more favorable L/D

ratio is typically one of the major goals in aircraft design; since a particular aircraft's required lift

is set by its weight, delivering that lift with lower drag leads directly to better fuel economy, climb

performance, and glide ratio.

05. What are energy lines and hydraulic gradient lines? (APR-03)

1. Hydraulic Gradient Line: It is defined as the line which gives the sum of pressure head (p/w)

and datum head (z) of a flowing fluid in a pipe with respect to some reference line or it is the line

which is obtained by joining the top of all vertical ordinates, showing the pressure head (p/w) of

a flowing fluid in a pipe from the centre of the pipe. It is briefly written as H.G.L (Hydraulic

Gradient Line).

2. Total Energy Line: It is defined as the line which gives the sum of pressure head, datum

head and kinetic head of a flowing fluid in a pipe with respect to some reference line. It is also

defined as the line which is obtained by joining the tops of all vertical ordinates showing the sum

of pressure head and kinetic head from the centre of the pipe. It is briefly written as T.E.L

(Total Energy Line).

06. Write down four examples of laminar flow? (DEC-06)

Fluid flow in which the fluid travels smoothly or in regular paths. The velocity, pressure, and

other flow properties at each point in the fluid remain constant. Laminar flow over a horizontal

surface may be thought of as consisting of thin layers, all parallel to each other, that slide over

each other. It is common only where the flow channel is relatively small, the fluid is moving

slowly, and its viscosity is relatively high. Examples include the flow of oil through a thin tube

and blood flow through capillarity.

07. What is the physical significance of Reynolds number? (DEC-07)

In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions


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08. Diff between laminar and turbulent flow. (DEC-05)

Laminar

Laminar flow (or streamline flow) occurs when a fluid flows in parallel layers, with no disruption between the layers.[1] At low velocities the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross currents perpendicular to the direction of flow, nor eddies or swirls of fluids.[2] In laminar flow the motion of the particles of fluid is very orderly with all particles moving in straight lines parallel to the pipe walls.[3] In fluid dynamics, laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection Turbulent

Turbulence or turbulent flow is a flow regime characterized by chaotic and suspectedly stochastic[citation needed] property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time.

09. What are the losses experienced by a fluid while passing through a pipe? (APR-05)

Head loss is a loss in pressure head due to the viscosity of a fluid and obstructions to a fluid such as pipe elbows, valves, etc. By knowing the head loss, you can successfully modify Bernoulli's energy equation accordingly; refer to equation 1. Bernoull's energy equation is Bernoulli's equation divided by the fluid's specific weight.

10. What is equivalent pipe? (DEC-06)

Equivalent pipe is a method of reducing a combination of pipes into a simple pipe system for easier analysis of a pipe network, such as a water distribution system. An equivalent pipe is an imaginary pipe in which the head loss and discharge are equivalent to the head loss and discharge for the real pipe system. There are three main properties of a pipe: diameter, length, and roughness. 11. What do you mean by a flow through parallel pipes? (NOV-04)

When two or more pipes are connected, as shown in Fig. 36.3, so that the flow divides and subsequently comes together again, the pipes are said to be in parallel. In this case equation

of continuity gives where; Q is the total flow rate and are the flow rates through pipes A and B respectively.

12. What do you mean by Net Positive Suction Head?

NPSH is particularly relevant inside centrifugal pumps and turbines, which are parts of a hydraulic system that are most vulnerable to cavitation. If cavitation occurs, the drag coefficient of the impeller vanes will increase drastically - possibly stopping flow altogether - and prolonged exposure will damage the impeller.

http://en.wikipedia.org/wiki/Centrifugal_pump

http://en.wikipedia.org/wiki/Turbine

http://en.wikipedia.org/wiki/Drag_coefficient

http://en.wikipedia.org/wiki/Impeller


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PART-B (16 Marks)

01. The diameter of water pipe is suddenly enlarged from 200mm to 400mm. The rate of flow

through it is 0.25m^3/s. Calculate the loss of head in enlargement. (NOV’02)


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02. The rate of flow of water through a horizontal pipe is 0.25m3/s. The dia of the pipe is

suddenly enlarged from 200Mm to 400Mm. The pressure intensity in the smaller pipe is

11.772N/Cm2. Determine the i) loss of head due to sudden enlargement ii) Pressure

intensity in the large pipe iii) Power lost due to enlargement.

(NOV’03)


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03. A pipe line carrying oil of specific gravity 0.87 changes in dia from 200mm at position 1 to

500mm dia to a piston 2 which is at 4m at a higher level If the pressure at position 1 and 2

are taken as 9.81N/cm^2 and 5.886N/cm^2 respectively and the discharge through the pipe

is 0.2 m^3/s. Determine the loss of head and determine the flow. (NOV’03)


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04. Derive an expression for head loss due to friction. Obtain an expression for Darcy-

weishbach friction factor for flow in a pipe.


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05. The water is flowing through a pipe having diameters 20cm and 10cm at sections 1 and 2

respectively. The rate of flow through pipe is 35 lit/sec. the section 1 is 6m above datum and

section 2 is 4 m above the datum. If the pressure at section 1 is 39.24 n/cm2 (MAY’04)


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06. Water is flowing through a tapering pipe of length 100m having dia 500m at the upper end

and 300mm at the lower end the pipe has a slope of 1 in 30. The rate of flow through the

pipe is 50lit/s. The pressure at the higher level 19.62 n/cm2. Find the pressure at the lower

end. (NOV’04)


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07. Two sharp ended pipes of diameters 50 mm and 100 mm respectively each of length 100 m

are connected in parallel between two reservoirs which have a difference of level of 10 m

if the coefficient of friction for each pipe is 4f 0.32, calculate the rate of flow for each pipe

and also the diameter of the single pipe 100 m length which would give the same discharge.

If it were submitted the same discharge. (DEC’07)


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08. A pipe of dia 20 cm, and length 2000 m connects two reservoirs having difference of water

levels as 20 m determein the discharge through the pipe. If an additional pipe of diameter

20 cm length 1200m is attached to the last 1200 m length of the existing pipe. Fine the

increase n discharge. Take f = 0.015. and neglect minor losses. (DEC’06)


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09. A flat plate 1.5m x 1.5m moves at 50Km/h in a stationary air of density 1.15Kg/m^3. If the

co-efficient of drag and lift are 0.15 and 0.75. Determine 1) The lift force 2) The drag force 3)

the resultant force 4) The power required (DEC 07)


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10. A pipe in 100 mm diameter has a nozzle attached to it at the discharge end, the diameter of

the nozzle is 50 mm. the rate of discharge of water flowing through the nozzle is 20 LPS and

the pressure at the base of the nozzle is 5.886 N/cm2. Calculate the coefficient of discharge.

Assume that the base of the nozzle and outlet of the nozzle are at the same elevation.

(DEC 07)


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11. When a sudden contraction is introduced in a horizontal pipeline from 15cm to 20cm, the

pressure changes from 10500kg/m2 to 6900kg/m2 calculate the rate of flow. Assume

coefficient of friction 0.65. following this if there is a sudden enlargement from 25cm to 50cm

and if the pressure at the 25cm section is 6900kg/m2 (MAY’05)


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UNIT III- DIMENSIONAL ANALYSIS


01. What is a dimensionally homogenous equation? Give example (NOV-04)

Dimensional analysis is the practice of checking relations among physical quantities by identifying their dimensions. The dimension of any physical quantity is the combination of the basic physical dimensions that compose it. Some fundamental physical dimensions are length, mass, time, and electric charge. All other physical quantities can be expressed in terms of these fundamental physical dimensions.

02. Give the dimensions for physical quantities: Pressure, Surface tension, Dynamic

viscosity, Kinematic viscosity? (APR-03)

Pressure - N/m2 Surface tension – N/m Dynamic viscosity – Ns/m2 Kinematic viscosity – Ns/m2

03. State the Buckingham’s π theorem. (APR-04)

If there are n variables (independent and dependent variables) in a physical phenomenon and if these variables contain m fundamental dimensions (M, L, T), then the variables are arranged into (n-m) dimensionless numbers. Each term is called π term. f1 (π1, π 2, π 3,……… π n-m)=0

π1= Φ [π 2, π 3,……… π n-m ] π2= Φ[π 1, π 3,……… π n-m ]

04. What are the similarities between models and prototype? (NOV-04)

Similitude is defined as the similarity between the model and its prototype in every respect, which means that the model and prototype are completely similar. Three types of similarities must exit between the model and prototype. They are 1. Geometric Similarity 2. Kinematic Similarity 3. Dynamic Similarity

05. Submarine is tested in the air tunnel .Identify the model law applicable? (NOV-03)

Dynamic similarity means the similarity of forces between the model and prototype. Thus dynamic similarity is said to exist between the model and prototype if the ratios of the corresponding forces acting at the corresponding points are equal. Also the directions of the corresponding forces at the corresponding points should be same. (Fi)p= Inertia force at a point in prototype, (Fv)p= Viscous force at the point in prototype, (Fg)p= Gravity force at the point in prototype,

06. What is meant by dimensionless number?

Dimensionless quantities are often defined as products or ratios of quantities that are not

dimensionless, but whose dimensions cancel out when their powers are multiplied. This

is the case, for instance, with the engineering strain, a measure of deformation. It is

http://en.wikipedia.org/wiki/Product_%28mathematics%29

http://en.wikipedia.org/wiki/Ratio

http://en.wikipedia.org/wiki/Quantity

http://en.wikipedia.org/wiki/Exponentiation

http://en.wikipedia.org/wiki/Engineering_strain


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defined as change in length, divided by initial length, but since these quantities both

have dimensions L (length), the result is a dimensionless quantity.

07. Define Reynolds number.

In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that is used to help predict similar flow patterns in different fluid flow situations. The Reynolds number is defined as the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions.[5] Reynolds numbers frequently arise when performing scaling of fluid dynamics problems, and as such can be used to determine dynamic similitude between two different cases of fluid flow.

They are also used to characterize different flow regimes within a similar fluid, such as

laminar or turbulent flow: laminar flow occurs at low Reynolds numbers, where viscous

forces are dominant, and is characterized by smooth, constant fluid motion; turbulent

flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to

produce chaotic eddies, vortices and other flow instabilities

08. Define Mach number

In fluid mechanics, Mach number (M or Ma) is a dimensionless quantity representing the

ratio of speed of an object moving through a fluid and the local speed of sound

Mach number varies by the composition of the surrounding medium and also by local

conditions, especially temperature and pressure. The Mach number can be used to

determine if a flow can be treated as an incompressible flow. If M < 0.2–0.3 and the flow

is (quasi) steady and isothermal, compressibility effects will be small and a simplified

incompressible flow model can be used.

http://en.wikipedia.org/wiki/Fluid_mechanics

http://en.wikipedia.org/wiki/Dimensionless_quantity

http://en.wikipedia.org/wiki/Ratio

http://en.wikipedia.org/wiki/Viscous

http://en.wikipedia.org/wiki/Reynolds_number#cite_note-Falkovich-5

http://en.wikipedia.org/wiki/Dynamic_similitude

http://en.wikipedia.org/wiki/Laminar_flow

http://en.wikipedia.org/wiki/Turbulence

http://en.wikipedia.org/wiki/Eddy_%28fluid_dynamics%29

http://en.wikipedia.org/wiki/Vortex

http://en.wikipedia.org/wiki/Fluid_mechanics

http://en.wikipedia.org/wiki/Dimensionless_quantity

http://en.wikipedia.org/wiki/Fluid

http://en.wikipedia.org/wiki/Speed_of_sound

http://en.wikipedia.org/wiki/Incompressible_flow

http://en.wikipedia.org/wiki/Steady_flow

http://en.wikipedia.org/wiki/Isothermal_flow


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PART-B (16 Marks)

01. The frictional torque T of disc diameter D rotating at a speed N in fluid of viscosity μ and

density ρ in a turbulent flow is given by T= D5 N2 ρ φ [ μ / D2 N P ] . Prove it by

Buckingham’s π theorem. (NOV-03)


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02.

(APR -10) Solution:


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03. The losses per unit length of pipe h/E in turbulent flow through a smooth pipe depend

upon velocity V, diameter D, gravity g, dynamic viscosity p, and density p. With

dimensional analysis, determine the general form of the equation. (NOV-04)


44

04. State Buckingham’s π theorem and describe how the steps involved in Buckingham’s

method differ from Raleigh’s method. (APR-08)


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05. The pressure diff Δp in a pipe of dia D and length L due to viscous flow depends on the

velocity V viscosity μ and density ρ using Buckingham’s π theorem. Obtain an

expression for Δp (APR-04)


46

06. State the similarity laws used in model analysis. (APR-10)


47


48

07. Derive on the basis of dimensional analysis suitable parameters to present the thrust developed by the propeller. Assume that the thrust P depends upon the angular velocity ώ, speed of advance V, diameter D, Dynamic viscosity µ, mass density ρ, elasticity of the fluid medium which can be denoted by the speed of sound in the medium C.

(MAY-13)


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08. The pressure diff Δp in a pipe of dia D and length L due to turbulent flow depends on the

velocity V viscosity μ and density ρ and roughness k using Buckingham’s π theorem.

Obtain an expression for Δp (Nov-06)


50

09. The thrust due to any one of a family of geometrically similar airplane propellers is to be

determined experimentally from a wind-tunnel test on a model. By means of dimensional

analysis find suitable parameters for plotting test results. The thrust F T depends upon

speed of rotation ώ, speed of advance VO, diameter D, air viscosity p, density p, and

speed of sound c. The function

Solution:


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10. Derive an expression showing the relationship between the torque and the variables

diameter, rotational speed, viscosity and density by Buckingham’s π theorem. (Nov-04)


52

11. A fluid-flow situation depends upon the velocity V, the density p, several linear

dimensions l1 ,l2, l3 pressure drop p, gravity g, viscosity p, surface tension σ, and bulk

modulus of elasticity K. ' Apply dimensional analysis to these variables to' find a set of

П-parameters. (NOV-04)


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UNIT IV- ROTODYNAMIC MACHINES


01. Define hydraulic machines

Hydraulic Machines are defined as those machines which convert either hydraulic energy (energy possessed by water) into mechanical energy (which is further converted into electrical energy) or mechanical energy into hydraulic energy. The hydraulic machines, which convert the hydraulic energy into mechanical energy, are called turbines

02. Give example for a low head, medium head and high head turbine.

Low head – Screw type, water wheels, hydrokinetic wheels

Medium head – propeller type, Francis turbine.

High head – Pelton, turbo, cross flow turbines

03. What is impulse turbine? Give example.

The basic idea of an impulse turbine is that a jet of steam from a fixed nozzle pushes against the rotor blades and impels them forward. The velocity of the steam is about twice as fast as the velocity of the blades. Only turbines utilizing fixed nozzles are classified as impulse turbines.

04. What is reaction turbine? Give example

Axial flow turbines are those turbines in which the water flows in the radial direction. The water may radially from outwards to inwards (i.e., towards the axis of rotation) or from inwards to outwards. If the water flows from outwards to inwards through the runner, the turbine is known as inward radial flow turbine. And if the water flows from inwards to outwards through the runner, the turbine is known as outward radial flow turbine

05. What is axial flow turbine?

If the water flows parallel to the axis of the rotation of the shaft, the turbine is known as axial flow turbine. And if the head at the inlet of the turbine is the sum of pressure energy and kinetic energy and during the flow of water through runner a part of pressure energy is converted into kinetic energy, the turbine is known as reaction turbine.

06. Define mechanical efficiency?

Mechanical efficiency measures the effectiveness of a machine in transforming the energy and power that is input to the device into an output force and movement. Efficiency is measured as a ratio of the measured performance to the performance of an

ideal machine


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07. Define volumetric efficiency?

Volumetric efficiency is a technical term used for comparing performance or some other measurable parameter per unit of physical volume. This figure of merit concept appears in several otherwise unrelated contexts, including design of internal combustion engines, hydraulic pumps, and miniaturized components used in electronic circuits.

08. Define unit discharge?

In fluid mechanics, discharge is the volume rate of water flow, including any suspended solids (e.g. sediment), dissolved chemicals (e.g. CaCO3(aq)), and/or biologic material (e.g. diatoms), which is transported through a given cross-sectional area.[1] Frequently, other terms synonymous with discharge are used to describe the volumetric flow rate of water and are typically discipline dependent. For example, a fluvial hydrologist studying natural river systems may define discharge as streamflow, whereas an engineer operating a reservoir system might define discharge as outflow, which is contrasted with inflow

09. Define unit power?

Unit Power is defined as the amount of energy consumed per unit time. In the MKS system, the unit of power is the joule per second (J/s), known as the watt (in honor of James Watt, the eighteenth-century developer of the steam engine). For example, the rate at which a light bulb converts electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit time

10. What is draft turbine?

The turbine does not need to be at the lowest point of water flow as long as the draft tube remains full of water. In Reaction turbine as Francis turbine and Kaplan turbine a diffuser tube is installed at the exit of the runner known as Draft Tube.

11. What is the function of nozzle?

A nozzle is a device designed to control the direction or characteristics of a fluid flow (especially to increase velocity) as it exits (or enters) an enclosed chamber or pipe. A nozzle is often a pipe or tube of varying cross sectional area, and it can be used to direct or modify the flow of a fluid (liquid or gas). Nozzles are frequently used to control the rate of flow, speed, direction, mass, shape, and/or the pressure of the stream that emerges from the

12. Define hydraulic efficiency?

gH

uVuVefficiencyHydraulic ww 2211

2

cos1hfficiencyHydraulice


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13. Define overall efficiency?

14. Define unit speed of turbine?

Where,

is specific speed (unitless)

is pump rotational speed (radians per second)

is flowrate (m³/s) at the point of best efficiency

is total head (m) per stage at the point of best efficiency

is acceleration due to gravity (m/s²)

15. Write the function of draft tube in turbine outlet?

In Reaction turbine as Francis turbine and Kaplan turbine a diffuser tube is installed at the

exit of the runner known as Draft Tube. In Impulse turbine the available head is

considerably high and there is no significant effect on the efficiency if the turbine is placed

a couple of meters above the Tail Race


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PART-B (16 Marks)

01.


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02. A pelton wheel is having a mean bucket dia of 1m and is running at 1000 rpm .The net

head on the pelt on wheel is 700m if the size clearance angle is 15° and discharge

through the nozzle is 0.1m^3/s. Find i) power available at nozzle ii) Hydraulic efficiency

of the turbine. (Take CV=1)

03. A pelton wheel is working under a head of 400 m. the water is supplied through penstock of diameter 1 m and length 4km from reservoir to the pelton wheel. The coefficient of friction for the penstock is given as 0.008. the jet of water of diameter 150 mm strikes the buckets of the wheel and gets deflected through an angle of 1650 . the relative velocity of water at outlet is reduced by 15% due to friction between inside surface of the bucket and water. If the velocity of the buckets is 0.45 times the let velocity at inlet and mechanical efficiency as 85% determine. (i) Power given to the runner. (ii) Shaft power (iii) Hydraulic efficiency and overall efficiency.


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04. A 137 mm diameter jet of water issuing from a nozzle impinges on the buckets of a

pelton wheel and the jet is deflected through an angle of 1650 by the buckets. The head

available at the nozzle is 400 m. assuming coefficient of velocity as 0.97. speed ratio as

0.46 and reduction in relative velocity while passing through buckets as 15% find:

(i) The force exerted by the jet on buckets in tangential direction.

(ii) The power developed


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05.


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06.


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07. As inward flow reaction turbine has external and internal diameters are 1 m and 0.6m respectively. The hydraulioc efficiency of the turbine is 90% when the head on the turbine is 36m. The velocity of flow at outlet is 2.5 m/s and discharge at the outlet is radial. If the vane angle at outlet is 150 and width of the wheel is 100 mm at inlet and outlet. Determine (i) Guide blade angle (ii) Speed of the turbine (iii) Vane angle of the runner at inlet (iv) Volume flow rate of turbine (v) Power developed


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08.


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09. An outward flow reaction turbine has internal and external diameters of the runner s 0.6m and 1.2m respectively. The guide blade angle is 150 and velocity of flow through the runner is constant and is equal to 4 m/s. if the speed of the turbine is 200rpm. Head on the turbine is 10m and discharge at outlet is radial. Determine (i) The runner vane angles at inlet and outlet (ii) Work done by the water on the runner per second per unit weight of water (iii) Hydraulic efficiency (iv) Degree of reaction.


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10.


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11. The following data is given for a francis turbine. Net head 60 m speed 700 rpm. Shaft

power 294.3 kW. Overall efficicency 84 % hydraulic efficiency 93% flow ratio 0.20.

breadth ratio 0.1 outer diameter of the runner 2 x inner diameter of the runner. The

thickness of vanes occupy 5% of circumferential area of the runner. Velocity of flow is

constant at inlet and outlet and discharge is radial ar ooutlet. Determine

(i) Guide blade angle (ii) runner vane angles at inlet and outlet

(ii) Diameters at inlet and outlet of the runner (iv) width of the wheel at inlet


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71

12.


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13.


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14.


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14. Kaplan turbine runner is to be designed to develop 9100 kW. The net available head is

5.6m. if the speed ratio 2.09. Flow ratio 0.68, overall efficiency 86% and the diameter of

the boss is 1/3rd the diameter od the runner. Find the diameter of the runner, its speed

and specific speed of the turbine.


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15. Characteristics curves of Hydraulic Turbines.


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16. Explain the working of pelton turbine.

Hydraulic Turbine is a machine which converts the energy of an elevated water supply (hydraulic energy) into mechanical energy. This mechanical energy is used in running an electric generator which is directly coupled to the shaft of the turbine. Thus the mechanical energy is converted to electrical energy. The electric power which is obtained from the hydraulic energy is known as Hydro-electric power.

None of the Hydraulic Turbines are purely axial flow or purely radial flow. There is always a component of radial flow in axial flow turbines and of axial flow in radial flow turbines.

1. Impulse Turbine: The pressure of liquid does not change while flowing through the rotor of the machine. In Impulse Turbines pressure change occur only in the nozzles of the machine. One such example of impulse turbine is Pelton Wheel.

2. Reaction Turbine: The pressure of liquid changes while it flows through the rotor of the machine. The change in fluid velocity and reduction in its pressure causes a reaction on the turbine blades; this is where from the name Reaction Turbine may have been derived. Francis and Kaplan Turbines fall in the category of Reaction Turbines.

Pelton turbine

The Pelton wheel is an impulse turbine which is among the most efficient types of water turbines.

It was invented by Lester Allan Pelton in the 1870s.

Pelton wheel is a high head turbine. It is used with heads of more than 500 m.

A head is the distance by which the water falls before it strikes the turbine blades

The flow of water is tangential to the runner. So it is a tangential flow impulse turbine.

A Pelton’s runner consists of a single wheel mounted on a horizontal shaft.

Waterfalls towards the turbine through a pipe called penstock and flows through a nozzle.

http://en.wikipedia.org/wiki/Water_turbines



http://en.wikipedia.org/wiki/Lester_Allan_Pelton


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The high speed jet of water coming out from the nozzle hits the buckets (vanes) on the wheel and causes the wheel to rotate producing torque and power.

The Pelton wheel extracts energy from the impulse (momentum) of moving water as opposed to its weight like traditional overshot water wheel.

DESIGN OF PELTON WHEEL

The Pelton Turbine has a circular disk mounted on the rotating shaft or rotor. This circular disk has cup shaped blades, called as buckets, placed at equal spacing around its circumference. Nozzles are arranged around the wheel such that the water jet emerging from a nozzle is tangential to the circumference of the wheel of Pelton Turbine. Water flows along the tangent to the path of the runner. According to the available water head (pressure of water) and the operating requirements, the shape and number of nozzles placed around the Pelton Wheel can vary.

PELTON TURBINE HYDRO-ELECTRIC SET UP

A typical setup of a system generating electricity by using Pelton Turbine will have a water reservoir situated at a height from the Pelton Wheel. The water from the reservoir flows through a pressure channel to the penstock head and then through the penstock or the supply pipeline to the nozzles, from where the water comes out as high speed jets striking the blades of the Pelton Turbine. The penstock head is fitted with a surge tank which absorbs and dissipates sudden fluctuations in pressure.For a constant water flow rate from the nozzles the speed of turbine changes with changing loads on it. For quality hydroelectricity generation the turbine should rotate at a constant speed. To keep the speed constant despite the changing loads on the turbine water flow rate through the nozzles is changed. To control the gradual changes in load servo controlled spear valves are used in the jets to change the flow rate. And for sudden reduction in load the jets are deflected using deflector plates so that some of the water from the jets do not strike the blades. This prevents over speeding of the turbine.

http://en.wikipedia.org/wiki/Momentum

http://en.wikipedia.org/wiki/Water_wheel

http://www.brighthub.com/guides/generating-electricity.aspx


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Working Principle of Pelton Turbine

High speed water jets emerging from the nozzles (obtained by expanding high pressure water to the atmospheric pressure in the nozzle) strike a series of spoon-shaped buckets mounted around the edge of the pelton wheel. High pressure water can be obtained from any water body situated at some height or streams of water flowing down the hills. As water flows into the bucket, the direction of the water velocity changes to follow the contour of the bucket. These jets flow along the inner curve of the bucket and leave it in the direction opposite to that of incoming jet. When the water-jet contacts the bucket, the water exerts pressure on the bucket and the water is decelerated as it does a "u-turn" and flows out the other side of the bucket at low velocity. The change in momentum (direction as well as speed) of water jet produces an impulse on the blades of the wheel of Pelton Turbine. This "impulse" does work on the turbine and generates the torque and rotation in the shaft of Pelton Turbine. To obtain the optimum output from the Pelton Turbine the impulse received by the blades should be maximum. For that, change in momentum of the water jet should be maximum possible. This is obtained when the water jet is deflected in the direction opposite to which it strikes the buckets and with the same speed relative to the buckets. For maximum power and efficiency, the turbine system is designed such that the water-jet velocity is twice the velocity of the bucket. A very small percentage of the water's original kinetic energy will still remain in the water. However, this allows the bucket to be emptied at the same rate at which it is filled, thus allowing the water flow to continue uninterrupted. Often two buckets are mounted side-by-side, thus splitting the water jet in half (see photo). The high speed water jets emerging from the nozzles strike the buckets at splitters, placed at the middle of the buckets, from where jets are divided into two equal streams. This balances the side-load forces on the wheel, and helps to ensure smooth, efficient momentum transfer of the fluid jet to the turbine wheel. Because water and most liquids are nearly incompressible, almost all of the available energy is extracted in the first stage of the hydraulic turbine. Therefore, Pelton wheels have only one turbine stage, unlike gas turbines that operate with compressible fluid.

Applications of Pelton Wheel

Pelton wheels are the preferred turbine for hydro-power, when the available water source has relatively high hydraulic head at low flow rates. Pelton wheels are made in all sizes. There exist multi-ton Pelton wheels mounted on vertical oil pad bearings in hydroelectric plants. The largest units can be up to 200 megawatts. The smallest Pelton wheels are only a few inches across, and can be used to tap power from mountain streams having flows of a few gallons per minute. Some of these systems utilize household plumbing fixtures for water delivery. These small units are recommended for use with thirty meters or more of head, in order to generate significant power levels. Depending on water flow and design, Pelton wheels operate best with heads from 15 meters to 1,800 meters, although there is no theoretical limit.Thus, more power can be extracted from a water source with high-pressure and low-flow than from a source with low-pressure and high-flow, even though the two flows theoretically contain the same power.


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Also a comparable amount of pipe material is required for each of the two sources, one requiring a long thin pipe, and the other a short wide pipe.

17. Explain the working of Francis turbine.

Spiral Casing: The spiral casing around the runner of the turbine is known as volute casing . All

throughout its length, it has numerous openings at regular intervals to allow the working fluid to impound

on the blades of the runner. these openings convert the pressure energy of the fluid into momentum

energy just before the fluid impound on the blades. to maintain a constant flow rate despite the fact that

numerous openings have been provided for the fluid to gain entry to the blades,the cross-sectional area

of this casing decreases uniformly along the circumference.

Guide or Stay Vanes: The primary function of the guide or stay vanes is to convert the pressure energy

of the fluid into the momentum energy. it also serves to direct the flow at design angles to the runner

blades.

Runner Blades: Runner blades are the heart of any turbine as these are the centers where the fluid

strikes and the tangential force of the impact causes the shaft of the turbine to rotate and hence electricity

is produced. In this part one has to be very careful about the blade angles at inlet and outlet as these are

the major parameters affecting the power production.

Draft tube: The draft tube is a conduit which connects the runner exit to the tail race where the water is

being finally discharged from the turbine. The primary function of the draft tube is to reduce the velocity of

the discharged water to minimize the loss of kinetic energy at the outlet. This permits the turbine to be set

above the tail water without any appreciable drop of available head. The purpose of providing a draft tube

will be better understood if we carefully study the net available head across a reaction turbine.

Working: Francis turbine has a purely radiate flow runner. Water under pressure, enters the runner from

the guide vanes towards the center in radial direction and discharges out of the runner axially. Francis

turbine operates under medium heads. Water is brought down to the turbine through a penstock and

directed to a number of stationary orifices fixed all around the circumference of the runner. These

stationary orifices are called as guide vanes.The head acting on the turbine is transformed into kinetic

http://en.wikipedia.org/wiki/Draft_tube


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energy and pressure head. Due to the difference of pressure between guide vanes and the runner (called

reaction pressure), the motion of runner occurs. That is why a Francis turbine is also known as reaction

turbine.

18. Explain the working of Kaplan turbine.

Kaplan Turbine is designed for low water head applications. Kaplan Turbine has propeller like

blades but works just reverse. Instead of displacing the water axially using shaft power and creating axial

thrust, the axial force of water acts on the blades of Kaplan Turbine and generating shaft power.

Most of the turbines developed earlier were suitable for large heads of water. With increasing demand of power need was felt to harness power from sources of low head water, such as, rivers flowing at low heights. For such low head applications Viktor Kaplan designed a turbine similar to the propellers of ships. Its working is just reverse to that of propellers. The Kaplan Turbine is also called as Propeller Turbine

Design of Kaplan Turbine

To generate substantial amount of power from small heads of water using Kaplan Turbine it is

necessary to have large flow rates through the turbine. Kaplan Turbine is designed to accommodate the

required large flow rates. Except the alignment of the blades the construction of the Kaplan Turbine is

very much similar to that of the Francis Turbine. The overall path of flow of water through the Kaplan

Turbine is from radial at the entrance to axial at the exit. Similar to the Francis Turbine, Kaplan Turbine

also has a ring of fixed guide vanes at the inlet to the turbine

Unlike the Francis Turbine which has guide vanes at the periphery of the turbine rotor (called as runner in the case of Francis Turbine), there is a passage between the guide vanes and the rotor of the Kaplan Turbine. The shape of the passage is such that the flow which enters the passage in the radial direction is forced to flow in axial direction. The rotor of the Kaplan Turbine is similar to the propeller of a ship. The rotor blades are attached to the central shaft of the turbine. The blades are connected to the shaft with moveable joints such that the blades can be swiveled according to the flow rate and water head available.

Working of the Kaplan Turbine

The working head of water is low so large flow rates are allowed in the Kaplan Turbine. The water

enters the turbine through the guide vanes which are aligned such as to give the flow a suitable degree of

swirl determined according to the rotor of the turbine. The flow from guide vanes pass through the curved

passage which forces the radial flow to axial direction with the initial swirl imparted by the inlet guide

vanes which is now in the form of free vortex.


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The axial flow of water with a component of swirl applies force on the blades of the rotor and loses its

momentum, both linear and angular, producing torque and rotation (their product is power) in the shaft.

The scheme for production of hydroelectricity by Kaplan Turbine is same as that for Francis Turbine.

19. Explain the working and construction of Centrifugal pump.


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85

20.


86

21.


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UNIT V- POSITIVE DISPLACEMENT MACHINES


01. Mention the main components of reciprocating pump? (NOV-02)

Main ports of a reciprocating pump: 1. A cylinder with a piston, piston rod, connecting rod and a crank, 2. Suction pipe 3. Delivery pipe, 4. Suction valve and 5.Delivery valve.

02. Define Slip of reciprocating pump. When the negative slip does occur? (DEC-08)

Slip of a reciprocating pump is defined as the difference between the theoretical discharge and the actual discharge of the pump

actth QQSlip 100th

actth

Q

QQslippercentage

03. When will you select a reciprocating pump? (DEC-05)

Pumps are used throughout society for a variety of purposes. An early application includes the use of the windmill or watermill to pump water. Today, the pump is used for irrigation, water supply, gasoline supply, air conditioning systems, refrigeration (usually called a compressor), chemical movement, sewage movement, flood control, marine services, etc.

04. What are rotary pumps? Give examples (Apr-03)

A rotary vane pump is a positive-displacement pump that consists of vanes mounted to a rotor that rotates inside of a cavity. In some cases these vanes can be variable length and/or tensioned to maintain contact with the walls as the pump rotates.

05. Write short notes on types of rotary pumps? (NOV-02)

The simplest vane pump is a circular rotor rotating inside of a larger circular cavity. The centers of these two circles are offset, causing eccentricity. Vanes are allowed to slide into and out of the rotor and seal on all edges, creating vane chambers that do the pumping work. On the intake side of the pump, the vane chambers are increasing in volume. These increasing volume vane chambers are filled with fluid forced in by the inlet pressure. Inlet pressure is actually the pressure from the system being pumped, often just the atmosphere. On the discharge side of the pump, the vane chambers are decreasing in volume, forcing fluid out of the pump. The action of the vane drives out the same volume of fluid with each rotation. Multistage rotary vane vacuum pumps can attain pressures as low as 10−3 mbar (0.1 Pa).


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PART-B (16 Marks)

01.

(APR-08)


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02. Explain the working principles of reciprocating pump (NOV-07)


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03. The length and the dia of suction pipe of a single acting reciprocating pumps are 5m and 10cm the pumps has a plunger of dia 15cm and of stroke length of 35cm. the centre of the pump is 3 m above the water surface in the pump. The atmospheric pressure head is 10.3m of water and the pump is running at 35rpm Determine

i) Pressure head due to the acceleration at the beginning of the suction stroke ii) Maximum pressure head due to acceleration iii) Pressure head in the cylinder at the cylinder at the beginning and the end of the

stroke. (NOV-04)


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04. How the work will be saved by using air vessels in reciprocating pumps? (NOV-03)


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05. Explain the working of gear pump with neat sketch. (APR-10)


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06. (NOV-06)


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07. A single acting reciprocating pump running at 50rpm delivers 0.01m3/s of water. The

diameter of the piston is 200mm and stroke length 400mm determine the pump co-

efficient of discharge and pump , co-efficient of discharge and slip and % of slip.

(APR-06)

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MAHALAKSHMImahalakshmiengineeringcollege.com/pdf/mec/IIIsem/CE6351/CE6351... · Prepared by A.Bovas Herbert Bejaxhin Asst. Prof / MECHANICAL, MEC 1