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UNIT I FLUID PROPERTIES 10 hrs.

Fluid Properties: DensitySpecific WeightSpecific Gravityviscositysurfacetensioncapillaritycompressibility.Fluid Statics: Hydrostatic LawPressure Variationin static fluidHydrostatic force on a submerged plane surfacesLocation ofhydrostatic force. ManometersSimple U tube and differential manometersBuoyancyMeta-centric heightdetermination of stability of floating bodies andsubmerged bodies.

1. What is the difference between an ideal fluid and a real fluid? M09Ideal fluid is only imaginary which is incopresbible and has no viscosity.Real fluid posses viscosity and all fluids in practical are real.1. Define the following fluid properties-m13(a) Density (b) Specific gravity of a fluid: The mass per unit volume is defined as density. The unit used is kg/m3. . The symbolused is The ratio of the density of the fluid to the density of waterusually 1000 kg/m3 at a

standard conditionis defined as Specific Gravity or Relative Density of fluids. This isa ratio and hence no dimension or unit is involved.1. Define specific weight and specific gravity of a liquid.A13The force due to gravity on the mass in unit volume is defined as Weight Density orSpecific Weight. The unit used is N/m3. The symbol used is . At a location where g isthe local acceleration due to gravity,Specific weight, = g , Specific weight, = (g/go) (go = 1 kg m/N s2.) 1.Define the following propertiesviscosity and kinematic viscosity.Viscosity is that property of a real fluid by virtue of which it offers resistanceto shear force. The popular unit for viscosity is PoiseIt is defined as the ratio between dynamic viscosity and density of fluid ,Kinematic

viscosity,=/ , Popularly used unit is stoke (cm2/s) = 104 m2/s1. Define kinematics viscosity and give its significance.M12It is defined as the ratio between dynamic viscosity and density of fluid ,Kinematicviscosity, =/. It involves magnitudes of length & time only. It also increases withtemperature for gases and decreases for fluids.1. What is the difference between kinematic viscosity and dynamic viscosity? State theirunits of measurements. D09KV is obtained without cause of action whereas V is obtained with regard to the causeof motion.KV is concerned with length & time and V is not concerned.Unit of V is poise and KV unit is stoke

2.State Hydrostatic law.A11The law states that rate of pressure in a vertical direction is equal to weight density ofthe fluid at that point. p/z = x g = w: where p is pressure above atmosphere,z isheight

1.Define Newtonian and Non-Newtonian fluids.M12The Newtons Law of Viscosity states that shear stress ( ) on a fluid layer is directlyproportional to the rate of shear strain: = (du/dy) = (u/y)


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Fluids which obey the above are known as Newtonian fluids and fluids which do notobey the above relation known as Non-Newtonian fluids1. Define compressibility.It is the property by virtue of fluid undergoes a change in volume under the action ofexternal pressure.It is the reciprocal of bulk modulus and its unit is N/m2.

1. What is capillarity? A10It is a phenomenon of rise or fall of liquid surface relative to the adjacent general level ofliquid.It is due to combined effect of cohesion and adhesion of liquid particles.2. Explain about pressure head.A13Prssure Head(z) = p/ x g, is the ratio of pressure to weight density and is the height of

the point from free surfaces2. Define total pressure and centre of pressure. A10Total pressure is defined as the force exerted by a static fluid on a surface either planeor curved when the fluid comes in contact with the surfaces.It is always normal to thesurface.Centre of pressure is defined as the point of application of the total pressure on the

surface2. What is a manometer? How are they classified?m13Manometer is a device to measure pressure using a column of liquid to balance thepressure. It is used extensively in flow measurement.They are classified as I) Simple manometer.ii)Differential Manometer.. 2. What are types of manometers?a.Simple Manometer1.Piezometer,2.U-tube manometer,3.Single column manometer.b.Differential manometer1.U-tube diffl manometer,2.Inverted U-tube diffl Manometer1.Differentiate between Simple manometer and differential manometer.D12Simple Manometers are used to measure pressure at a point,while differentialmanometers are used for measuring the difference of pressure between two points in a

pipe or two different pipes.2. Define the terms buoyancy and centre of buoyancy. D09The upward force equal to weight of fluid displaced exerted on immerse body is knownas force of buoyancy or simply buoyancy.It is defined as the point,through which the force of buoyancy is supposed to act.2. What is center of buoyancy? M09It is defined as the point,through which the force of buoyancy is supposed to act.The force buoyancy is a vertical force equal to weight of fluid displaced by the immersedbody.COB will be centre of gravity of fluid displaced.2.Explain the terms Meta-centre and Meta-centric height.D12Meta centre is defined as the point about which a body starts oscillating when the body

is tilted by a small angle.The distance between the Meta Centre of a floating body and the centre of gravity of thebody is called Meta-Centric height.2.What is a manometer? How are they classified?M122. State the conditions for the stability of floating bodiesM12The meta centre point M shall be above G.The weight of floating body shall be equal tothe weight of the liquid displaced.

1. What is capillarity?


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1. Define viscosity. D112. State hydrostatic law.D11. 2.State Hydrostatic law.1.Define the following propertiesviscosity and kinematic viscosity.A11

1. Find the surface tension in a soap bubble of 40 mm diameter when the inside

pressure is 2.5 N/m2

above atmospheric pressure.2. Classify pressure measuring instruments.

Part-B

11. (a) What are the different types fluids? Explain each type. D11

1.Ideal fluid,2.Real fluid.3.Newtonian fluid,4.Non Newtonian fluid,5.Ideal plastic fluid.

Ideal Fluid- A fluid which is incompressible and is having no viscosity is known as idealfluid.It is an imaginary fluid as all the fluids which exist have some viscosity.

Real fluid- A fluid which poses viscosity is known as real fluid.All fluids that exists are

real fluid.

Newtonian fluid- Areal fluid in which shear stress is directly proportional to rate of shearstrain is known as Newtonian fluid.

Non Newtonian fluid- A real fluid in which shear stress is not proportional to the ratoshear strain is known as Non Newtonian fluid.

Ideal plastic fluidA fluid in which shear stress is more than the yield value and shearstress is proportional to the rate of shear strain is known as Ideal Plastic fluid

(b) Explain the stability of floating and submerged bodies with reference to its

metacentric height, with neat sketches.M11A sub-merged or floating body is said to be stable if it comes back to its original positionafter a slight disturbance.The relative position of centre of gravity(G) and centr ofBuoyancy(B) of a body determines the stability of sub-merged body.Meta centre is defined as the point about which a body starts oscillating when the bodyis tilted by a small angle.The distance between the Meta Centre of a floating body and the centre of gravity of thebody is called Meta-Centric height.Stability of Floating body.- The stability of a floating Body is determined from theposition of Meta centre(M).In case of floating body the weight of the body is equal to theweight of liquid displaced.


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When point M is above G the floating body will be stable,GM is the metacentric height.When angular displacement give to body COB shifts to B1,then FBthro B1 and W throG will consitut a couple acting in anticlockwise bringing the body to original position.

Stabilty of sub-merged bodyThe positon of G and B in this case is fixed,Consider aballon which is sub merged in air.Let lower portion of ballon contain heavier material sothat its G is lower than B. W be weight of ballon which acting thro G verticallydownwards and FB thro B acting upwards to maintain stability.For any angulardisplacement FB and W will produce a couple acting in anticlockwise to maintin thestability.11. A rectangular plate of size 25 cm x 50 cm and weighing 245.3 N slides down a 30inclined surface at a uniform velocity of 2m/s. If the uniform 2 mm gap between the plateand the inclined surface is filled with oil, determine the viscosity of the oil. A13

Hint ; Shear stress = : = F/A ; Shear stress = : = (du/dy) : F = weight X Sin Q(b) One litre of crude oil weighs 9.6 N. Calculate its Specific weight, density and specificvolume. D11Given data:Volume of oil= 1ltr =.001 cu.mWeight of oil = 9.6 NSolution:1.Speicific weight = Wt of Oil/ volume of oil =9.6/.001 = 9600 N/M32.Density =

= w/g = Specific wt of oil/acceleration dur to gravity =9600/9.81 =978.59 kg/ M

3


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3. specific volume = v = 1/ =1/978.59 =0.0010 M 3 /kg

11.(a) One litre of crude oil weighs 9.6 N. Calculate its specific weight, density andspecific gravity.M11

11. (a) Two large vertical plane parallel surfaces are 5 mm apart and the space betweenthem is filled with a fluid. A thin plate of 12.5cm square falls freely between the planes

along the central plane and reaches a steady velocity of 2 m/s. Determine the weight ofthe plate if the viscosity of the fluid filling the space is 0.02 Ns/m2. (5)M12Given Data:Distance between two plates =dy= 5mm = 5 x 10

-3m

Angle of inclination = 90Size of plate = 12.5cm = .125m

Area of plate = .125 x.125 =0.015625 sq.mFor both sides-area = 2 x 0.015625 = 0.03125 sq.mVelocity of plate = du = 2 m/sViscoscity of fluid = = 0,02 Ns/sq.mSolution:

Shear stress = : = (du/dy) = 0.02( 2/5 x 10

-3

) = 8 N/sq.mShear stress = : = F/AF= A x = 8 x 0.03125 =0.25 NF = weight x sin 90= weight x 1=0.25N

11. Calculate the dynamic viscosity of oil, which is used for lubrication between squareplate of size 0.8 m x 0.8 m and an inclined plane with an angle of inclination 30. Theweight of plate is 300 N and it slides down the inclined plane with uniform velocity of 0.3m/s. The thickness of oil film is 1.5 mmGiven Data:Distance between two plates =dy= 1.5mm = 1.5 x 10

-3m

Angle of inclination = 30Size of plate = 0.8 x 0.85cm = 0.008 x0.008mArea of plate = 0.008 x0.008 =0.000064 sq.mFor both sides-area = 2 x 0.000064 = 0.000128 sq.mVelocity of plate = du =0.3 m/sWeight of plate = = 300NSolution:Shear stress = : = F/A = 150/0.000128F= 300 x Sin 30 = 150: = (du/dy) ; = / (du/dy) =150/0.000128(0.3/1.5 x 10

-3)

11. Find the density of metallic body which floats at the inter face of mercury of specificgravity 13.6 and water such that 35 percent of its volume is submerged in mercury and65 percent in water. M09

Specific gravity = Speicific wt of given fluid/specific wt of standard fluid

Water be the standard fluid

Specific wt of mercury = 13.6 x 9.81 N/cubic m= 133.416


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Wt of floating body = wt of fluid displaced = 35% wt of mercury + 65% owt of water

Specific wt = w/v

Density = mass/volume =m/v = (w/g)/v = w/g kg/cu.m

11.An oil film of thickness 1.5mm is used for lubrications between a square plateof size 0.9m X 0.9m and an inclined plane having an angle of inclination 20. Theweight of the square is 392.4N and it slides down the plane with a uniformvelocity of 0.2m/s. find the dynamic viscosity of the oil.A11

Distance between two plates(oil flim thickness) =dy= 1.5mm = 1.5 x 10-3

mAngle of inclination =20Size of plate = 0.9 x 0.9m = .

Area of plate = .9 x.9 =0.81 sq.mVelocity of plate = du = 0.2 m/sWeight of plate = = 392.4N

Solution:Shear stress = : = (du/dy) = N/sq.mShear stress = : = F/A :F = 392.4 x sin20 , Area of plate = .9 x.9 =0.81 sq.mDynamic Viscoscity of fluid =(du/dy) / = Ns/sq.m11. The dynamic viscosity of an oil, used for lubrication between a shaft and sleeve is 6poise. The shaft is of diameter 0.4 m and rotates at 190 r.p.m. calculate the power lostin the bearing for a sleeve length of 90 mm. The thickness of the oil film is 1.5 mm.-m13

Shear stress on the shaft surface = = (du/dy) = (u/y)

u = DN/60 = 0.4 190/60 = 3.3493 m/s = 6 {3.3493/ 0.0015} = 13397.3 N/m2

Surface area of the bearings,A = 2 DLForce on shaft surface = A = 13397.3 (2 3.14 0.4 0.009) = 302.88 NTorque = tangential force D/2= 302.88 0.2 = 60.577 Nm

Power lost = 2= NT/60 = 2 3.14 190 60.577/60 = 1204.7 W.

11.A circular plate of 3 m diameter is under water with its plane making an angle of 30with the water surface. If the top edge of the plane is 1 m below the water surface, findthe force on one side of the plate and its location.D12

11. A rectangle plane surface is 2 m wide and 3 m deep. It lies in a vertical plane in

water. Determine the total pressure and position of centre of pressure on theplane surface when its upper edge is horizontal and (a) coincides with watersurface (b) 2.5 m below the free water surface. M12

11. Calculate the capillary effect in millimetres in a glass tube of 4 mm diameter, when

immersed in (a) water, and (b) Mercury. The temperature of the liquid is 20C and the

values of the surface tension of water and Mercury at 20C in contact with air are


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0.073575 N/m and 0.51 N/m respectively. The angle of contact for water is zero that

for mercury 1.30. Take density of water at 20C as equal to 998kg/m3.

11. (a) Determine the minimum size of glass tubing that can be used to measure water

level. If the capillary rise in the tube is not to exceed 2.5 mm. Assume surface tension of

water in contact with air as 0.0746 N/m.(8)

(b) What is the bulk modulus of elasticity of a liquid which is compressed in a cylinder

from a volume of 0.0125 m3at 80 N/cm2 pressure to a volume of 0.0124 m3 at pressure

150 N/cm2? D10

12. (a) State & Prove Pascals Law.D10 (4)

(b) A simple U tube manometer containing mercury is connected to a pipe in which an

oil of specific gravity 0.8 is flowing. The pressure in the pipe is vacuum. The other end of

the pipe is open to atmosphere. Find the vacuum pressure in the pipe, if the difference

of mercury level in the two limb from the centre of the pipe is 150mm below.

12. (a) Derive an expression for the centre of pressure of an inclined plane.M12

12. Write short notes onM09

(b) A rocket is accelerating horizontally to the right at 10 g. The pressure gauge isconnected by a 0.6 m length tube to the left end of the fuel tank. If the pressure in thetank is 35 bar, and if fuel specific gravity is 0.8, determine the pressure gauge reading.(7)M12

(a) Viscosity (b) Surface tension (c) Compressibility (d) Metacentric height.Surface tension is defined as the tensile force required to keep unit length of the surfaceflim in equilibrium. The surface tension is same everywhere on the surface irrespectiveof its curvature and acts in the plane of the surface.Surface tension depends directlyupon the intermolecular cohesion.it is also depends on i0nature of liquid,2)nature ofsurrounding liquid,3)kinectic energy of liquid.Its unit is N/m12.Derive a expression for the pressure at a height Z from sea-level for a static air whenthe compression of the air is assumed isothermal. The pressure and temperature at sealevels are p0 and T0 respectively.D12

12. A U tube differential manometer connects two pressure pipes A and B. pipe

A contains carbon tetrachloride having a specific gravity 1.594 under a pressure of11.772 N/cm2and pipe B contains oil of specific gravity 0.8 under a pressure of

11.772N/cm2. The pipe A lies 2.5m above pipe B. find the difference of

pressure measured by mercury as fluid Utube. A11

12. A differential manometer is connected at the points A and B of two pipes as shownin fig. the pipe A contain a liquid of specific gravity =1.5 while pipe B contains a liquid of


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specific gravity=0.9 . The pressure at A and B are 1 kgf/Cm2 and 1.80 kgf/Cm2respectively. Find the difference in mercury level in differential manometer. m1312. A Solid cylinder of diameter 4.0 m has a height of 3 metres. Find the meta centric

height of the cylinder when it is floating in water with its axis vertical. The sp. gravity of the

cylinder = 0.6.

12. Find the volume of water displaced and position of centre of buoyancy for a woodenblock of width 2.5 m and of depth 1.5 m when it floats horizontally in water. The densityof wooden block is 650 kg/m3 and its length is 6 m. A13

12.A block of wood of specific gravity 0.7 floats in water. Determine the meta-centricheight of the block if its size is 2 m x 1 m x 0.8 m. M12

(b) Determine the meta-centric height of the combined unit of a rectangular pontoon,9m long, 7m wide and 2 m deep weighing 500 kN carrying on its deck a boiler of 3 mdiameter weighing 300 kN. The centre of gravity of each unit may be takne to be at thegeometric centre and along the same line. Also calculate the restoring torque for a tilt of

4 from vertical. Assume the centre to be on the vertical line.M1212. A U-tube differential monometer is connecting two pressure pipes A and B. Pipe Acontains Carbon tetrachloride having a specific gravity 1.594 under a pressure of11.772 N/Cm and pipe B contains oil of specific gravity 0.8 under a pressure 11.72N/cm2 . The pipe A lies 2.5m above pipe B. Find the difference of pressure measuredby mercury as a fluid filling U-tube. D11

12. Calculate the capillary effect in mm in a glass tube of 4 mm diameter whenimmersed in (a) Water and (b) mercury. The temperature of the liquid is 20C and thevalues of surface tension of water and mercury at 20C in contact with air are 0.073575N/m and 0.51 N/m respectively. The angle of contact

for water is zero that for mercury 130. Take density of water as 998 kg/m3

12.(a) A uniform body 4m long, 2m wide, and 1 deep floats in water. What is the weightof the body if the depth of immersion is 0.6m. Determine the metacentric height.(b) A U-tube differential manometer connects pipes A and B. Pipe contains a liquid ofspecific gravity 1.6 under a pressure of 10.3 N/cm2and pipe B contains oil of specificgravity 0.8 under a pressure of 17.16 N/cm2. Pipe A lies m above pipe. B. Find thedifference of pressure measured by mercury as the fluid filling U tube if the mercurylevel in the left limb will remain 1.5 m below B.UNIT II EQUATIONS OF MOTION 10 hrs.

Basic equations of motion: Types of fluid flowContinuity, momentum and energy

equationsEulers and Bernoullis Equation and its applications.Flow Measurement:Orifice meter, Venturi meter, Piezometer, Pitot Tube.

3. Define continuity equation? m13

The continuity equation

for a fluidpassing through a tube in a steady flow, themass flowing through any section of the tube in a unit of time is constant.


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1A1V1 = 2A2V2 where = Air density (kg/m3)4. Define an orifice meter? m13

An orifice meter is a conduit and a restriction to create a pressure drop and it is an

instrument that measures fluid flow by recording differential pressure acrossa restriction.

3. Give continuity equation for a 3D flow in Cartesian coordinates. A13

4. Mention few practical applications of Bernoullis equation.A13

its application to the following measuring devices.

1) Venturimeter 2) Orifice meter 3) Pitot tube

Airflight,sailing and lifts

3. State any two merits of Venturimeter over orifice meter.D12

It is more accurate and requires lesser maintenance compare to orfice.

4. Define Stream function and Velocity potential function.D12

. The stream function can be defined for any two-dimensional flow, whether

the flow is irrotational or not, compressible or incompressible A stream function

is one which satisfies

is called the Velocity Potential function and velocity components are

related to through the following relations.

3. Define Bernoullis equation. M12

Bernoulli's Equation: .2

2

constgzVp

(the Bernoulli equation, which says that the total pressure is constant


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along a streamline:p1 + 1/2 V21= p2 + 1/2 V22

)

4. Define Notch and Weir. M12

A notchis an opening in the side of a measuring tank or reservoir extending above the free

surface. A weiris a notch on a large scale, used, for example, to measure the flow of a river,

3. State the assumptions for obtaining Bernoulli equation.M12

1- viscous effects are assumed negligible, 2- the flow is assumed to be steady,

3- the flow is assumed to be incompressible, 4- the equation is applicable along astreamline

4. Define Coefficient of velocity, Coefficient of contraction and Coefficient ofdischarge.M12

Coefficient of Contraction (Cc): It is defined as the ratio of the area of

cross section of the jet at Vena of cross section of the jet at Vena Contracta(ac) to the area of the orifice (a).Coefficient of Velocity (Cv): It is defined as the ratio of actual velocity (Vact)

to the theoretical velocity (Vth)Coefficient of discharge (Cd): It is defined as the ratio of actual discharge

(Qact) to the theoretical discharge (Qth)

3. What are the various types of fluid flow? D11Steady and Un-steady flows :2. Uniform and Non-uniform flows :3. Laminar and

Turbulent flows :4. Compressible and Incompressible flows :5. Rotational andIrrotational flows :6. One, Two and Three dimensional flows4. List the various flow measuring devices D11

orifices, venturi tubes, flow tubes, flow nozzles, pitot tubes,3. Define continuity equation.4. What are the types of notches?

Rectangular notch, Triangular notch, Trapezoidal notch, Stepped notch3. Distinguish between steady and unsteady flows.steady: A steady flow is one in which the conditions (velocity, pressure and cross-section) may differ from point to point but DO NOT change with time.unsteady: If at any point in the fluid, the conditions change with time, the flow is

described as unsteady

4. Name few applications of Bernoullis theorem.

3. Distinguish between steady and unsteady flows.

4. Name few applications of Bernoullis theorem.

3. What are the limitations of Bernoullis equation?


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Distinguish between laminar and turbulent flow

13. State Bernoullis equation for steady flow of an incompressible fluid. Drive anexpression for Bernoullis theorem from the first principle and state the assumption

made for the derivation.- m13

13. State and prove Bernoullis equation.

13. Derive the Eulers equation of motion and deduce the expressionto Bernoullisequation. A13

13.State and prove Bernoullis theorem from Eulers equation. Mention the assumptionsmade. How is it modified while applying in practice? List out its engineering application-

A07

13. State the Bernoullis theorem for steady flow of an incompressible fluid. Derive an

expression for Bernoullis equation. D11

13. State the assumption of Bernoullis equation. Derive Bernoullis equation from Eulers

equation of motion from Eulers equation of motion.D10

(b) State the derive Bernullis theorem, mentioning clearly the assumption underlying it.

A11

13. Explain in detail about the various classification of fluid flows. A-10

13. For the steady incompressible flow, are the following valves of u and v possible?

(a) u = 4xy+y2, v = 6xy+3x and

(b) u = 2x2+y2, v = -4xyD12

13. The velocity vector in a fluid flow is given V=4x3i10x2yj + 2tk. Find the velocityand acceleration of a fluid particle at (2,1,3) at time t=1. M12

13. An open tank of diameter D containing water to depth ho is emptied by a smoothorifice of diameter d at the bottom. Derive an expression for the time taken to reduce theheight to h. Also find the time tmax for emptying the tank. M12

13. Water flows through a pipe AB 1.2 m diameter at 3 m/s and then passes through a

pipe BC 1.5 m diameter, the pipe branches. Branch CD is 0.8 m in diameter and carriesone-third of flow in AB. The flow velocity in branch CE is 2.5 m/s. Find the volume rateof flow in AB, the velocity in BC, the velocity in CD and the diameter of CE.

13. The water is flowing through a pipe having diameters of 20 cm and 15 cm at sections 1 and

2 respectively. The rate of flow through the pipe is 40 liters/s. The section 1 is 6 m above the

datum line and section 2 is 3 m above the datum. If the pressure at section 1 is 29.43 N/cm2


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, Find the intensity of pressure atsection 2. D09

13. In a vertical pipe conveying oil of specific gravity 0.8, two pressure gauges has been

installed at A and B , where diameters are 16 cm and 8 cm respectively. A is 2m above

B. The pressure gauge readings have shown that pressure at B is greater than at A by

0.981 N/cm2

. Neglecting all losses calculate flow rate. D11

13. The water is flowing through a pipe having diameters of 20 cm and 15 cm at sections 1

and 2 respectively. The rate of flow through the pipe is 40 liters/s. The section 1 is 6 m

above the datum line and section 2 is 3 m above the datum. If the pressure at section 1

is 29.43 N/cm2, Find the intensity of pressure atsection 2.

13. (a) A horizontal venturimeter with an inlet diameter 30 cm and throat diameter15m is used to measure the flow of water. The reading in the differentialmanometer connected to the inlet and the throat is 10 cm of mercury. Determinethe discharge if the coefficient of venturimeter is 0.98.(b) State the derive Bernullis theorem, mentioning clearly the assumption

underlying it.13. (a) A horizontal venturimeter with an inlet diameter 30 cm and throat diameter 15m is used

to measure the flow of water. The reading in the differential manometer connected to the inlet

and the throat is 10 cm of mercury. Determine the discharge if the coefficient of venturimeter

is 0.98.

13. The velocity vector in a fluid flow is given V=4x3i10x

2yj + 2tk. Find the velocity and

acceleration of a fluid particle at (2,1,3) at time t=1. A12

14. Derive the expression for the rate of flow of fluid through venturimeter

14. The velocity components in a two dimensional flow field for an incompressible fluid are

expressed as u=y3/3 +2x-x2y; v=xy2-2y-x3/3

(a) Show that these functions represent a possible case of an irrotational flow.

(b) Obtain an expression for stream function .

(c) Obtain an expression for velocity potential . A11

14. A horizontal venturimeter with inlet and throat diameter 300 mm and 100 mm

respectively is used to measure the flow of water. The pressure intensity at inlet is 130 kN/m2

while the vacuum pressure head at throat is 350 mm of mercury. Assuming 3% head lost

between the inlet and the throat, find the value of co-efficient of discharge for the

venturimeter and also determine the rate of flow.

14. A horizontal Venturimeter with inlet diameter 200mm and throat diameter 100mm is

employed to measure the flow of the water. The reading of the differential manometer

connected to the inlet is 180 mm of mercury. If Cd = 0.98, determine the rate of

flow.D11


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14. The inlet and throat diameters of horizontal venturimeter are 300mm and 100mm

respectively. The liquid flowing through the meter is water. The pressure intensity at

inlet is 140 kPa while the vacuum pressure head at the throat is 370 mm of mercury.

Find the rate of flow. Assume that 4 percent of the differential head is lost between the

inlet and the throat. Find also the value of Cdfor the venturimeter.

14. A horizontal venturimeter with inlet and throat diameter 300 mm and 100 mm respectively

is used to measure the flow of water. The pressure intensity at inlet is 130 kN/m2 while the

vacuum pressure head at throat is 350 mm of mercury. Assuming 3% head lost between the

inlet and the throat, find the value of Co-efficient of discharge for the venturimeter and also

determine the rate of flow.

14. A 30cm x 15cm venturimeter is provided in a vertical pipeline carrying oil of specific gravity

0.9, the flow being upwards. The difference in elevations of the throat section and entrance

section of the venturimeter is 30cm. The differential U-tube mercury manometer shows a

gauge deflection of 25cm. Calculate (i) the discharge of the oil and (ii) the pressure difference

between the entrance and throat section. Take the discharge coefficient as 0.98 and the

specific gravity of mercury as 13.6.

14. An orifice meter with orifice diameter 10 cm is inserted in a pipe of 20 cm diameter.The pressure gauges fitted upstream and downstream of the orifice meter givesreadings of 19.62N/cm2 and 9.81N/cm2 respectively. Co-efficient of discharge for theorifice meter is given as 0.6. Find the discharge of water through the pipe. A13

(b) A venturimeter with throat diameter 0.065 m and coefficient of discharge 0.95 isused to calibrate a pitot static tube. Air flows through a 110 mm diameter horizontal pipein which the venturimeter is fitted. The difference in water level in the manometerattached to the venturimeter is 50mm. The pitot static tube is placed downstream of the

venturimeter and the water manometer attached to the pitot static tube shows a readingof 7 mm. Calculate the flow rate through the pipe and the coefficient of velocity of thepitot static tube. Assume the density of air as 1.13 kg/m3 and that of water as 1000kg/m3. (5)M1214. A liquid of specific gravity 0.85 is flowing through in an inclined venturimeter of

250m x 115mm size. The difference of pressures between the main and throat ismeasured by a liquid of specific gravity 0.65 contained in an inverted U tube which givesa reading of 275mm. If the loss of head between the main and throat is 0.3 times theKinetic head of the pipe. Determine the rate of flow of liquid. D11. 14. A pipe of 300 mm diameter conveying 0.30 m3 /sec. of water has a right anglebend in a horizontal plane. Find the resultant force exerted on the bend if the pressure

at inlet and outlet of the bend are 24.525 N/cm2 and 23.544 N/cm2,- m1314. The water is flowing through a pipe having diameters 20 cm and 10 cm at sections 1 and

2 respectively. The rate of flow through pipe is 35 liters/s. The section 1 is 6 m above

datum and section 2 is 4 m above datum. It the pressure at section 1 is 39.24 N/cm2,

find the intensity of pressure at section 2. A12

14. The water is flowing through a pipe having diameters 20 cm and 10 cm atsections 1 and 2 respectively. The rate of flow through pipe is 35 liters/s. The section 1


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is 6 m above datum and section 2 is 4 m above datum. It the pressure at section 1 is39.24 N/cm

2, find the intensity of pressure at section 2. M12

14. A pipe of 300 mm diameter conveying 0.30 m3/s of water has a right angled bendin a horizontal plane. Find the resultant force exerted on the bend if the pressure at inletand outlet of the bend are 24.525 N/cm2and 23.544 N/cm2.D12

14. (a) Water is discharged through a 15 cm diameter orifice in the vertical side of aopen tank at the rate of 190 litres per second. Water stands 15 m above the centerlineof the orifice. A point on the jet measured from the vena contracta has co-ordinates 5 mhorizontal and 0.5 m vertical. Find the hydraulic coefficients Cv, Cc and Cd of theorifice. (7)M1214. The velocity components in a two dimensional flow field for an incompressible

fluid are expressed as u=y3/3 +2x-x

2y; v=xy

2-2y-x

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(a) Show that these functions represent a possible case of an irrotational flow.

(b) Obtain an expression for stream function .

(c) Obtain an expression for velocity potential .

UNIT III FLOW THROUGH ORIFICES, LAMINAR AND TURBULENT FLOWS 10 hrs.

Flow through orifices: ClassificationHydraulic co-efficientFlow throughrectangular orifice, Notches and weirs.

Laminar and Turbulent flow: Reynolds experimentMajor and minor losses in pipesDarcy weisbachs equation,chezys formula pipes in series and pipes in paralleltotal energy linehydraulic gradient lineEquivalent pipe

5. Define the term= m13(a) Notch (b) Weir

A notchis an opening in the side of a measuring tank or reservoir extending above

the free surface. A weiris a notch on a large scale, used, for example, to measure the

flow of a river

6. What is different between orifice and mouthpiece? m13

An orifice is a small aperture through which the fluid passes. Thethickness of an orifice in the direction of flow is very small in comparison toits other dimensions.

The discharge through an orifice is increased by fitting a short length ofpipe to the outside known as external mouthpiece. The discharge rate isincreased due to a decrease in the pressure at vena contracta within themouthpiece.


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5. What is the physical significance of Reynolds number? A13

is used to help predict similar flow patterns in different fluid flowsituations and defined as theratioof inertial forces toviscousforcesand quantifies the relative importance of these two types of forces for

given flow conditions

6. Mention the minor losses in flow through pipes. A13

Minor losses are head losses that occur due to bends, elbows,

joints, valves, and other fittings in the systems.

5. Write the Chezys formula for loss of head due to friction in pipes.D12

V=C(RS)1/2where V=velocity,ft/s(m/s)

C=coefficient depending on surface roughness of conduitS=slope of energy grade line or head loss due to friction of

conduit R=hydraulic radius,ft(m)

Generally R=Area/wetted perimeter6. What do you understand by the terms Major energy loss and minor energy

losses in pipes?D12

the head loss due to viscous effects in the straight pipes, termed the major loss

The head loss, hL-major is given as ; h L major= f x l x V2/D x 2g

The head loss in various pipe components, termed the minor loss

Minor losses termed as ; ; h L minor = KLx V2/ 2g :KL is the loss coefficient.

5. Define Kinetic energy correction factor and momentum correction factor.M12

6. How will you determine the loss of head due to friction in pipes by using (a)Darcy formula and (b) Chezys formula?M12

5. What is hydraulic diameter and explain its significance.M12

The hydraulic diameter - dh- is used to calculate thedimensionlessReynolds Numberto determine if a flow is turbulent orlaminar.dh= 4 A / p where dh= hydraulic diameter (m, ft)

A = area section of the duct (m2, ft2)
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p = wetted perimeter of the duct (m, ft)

6. Define Reynolds number and give its significance in pipe flow.M12

the Reynolds numberRe is adimensionless numberthat gives a measureof the ratioofinertial forces( ) toviscous forces( /L )

5. List the various losses in pipes. D11

Major loss- friction in the straight portions of the pipes, partially closed valve

Minor loss-. Pipe entrance or exit. Sudden expansion or contraction, Bends, elbows,tees, and other fittings, Valves,open , Gradual expansions or contractions

6. What is a notch? D11

5. What are the minor losses in pipe?Minor loss-. Pipe entrance or exit. Sudden expansion or contraction, Bends, elbows,tees, and other fittings, Valves,open , Gradual expansions or contractions

6. What do you mean by vena contracta?

Vena contractais the point in a fluid stream where the diameter ofthe stream is the least, and fluid velocity is at its maximum,5. Define Hydraulic coefficient

The following four coefficients are known as hydraulic coefficientsor orificecoefficients.Coefficient of contraction:Coefficient of velocity:Coefficient ofdischarge:Coefficient of resistance.5. Define Hydraulic coefficient.

6. What is an equivalent pipe?

Two pipes or two systems of pipes in which the losses of head for equal rates of flow are thesame.

6. What is an equivalent pipe

Part-B15.Derive the Darcy-Weisbach equation for the pipe.

15. Derive the Darcy-Weisbach equation for the pipe.15. Derive an expression for the loss of head due to friction in pipes and also obtain the

relationship between co-efficient of friction and shear stress. A10

16. Derive an expression for total head loss for a flow through pipes in series. A13


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15. (a) Explain the terms (i) pipes in series and (ii) pipes in parallel. (5)M12

15. a. Classify the orifice. (4) A07

b. Derive the equation to find the discharge through fully sub-merged orifice. A07

15. State and derive Darcy-Weisbatch formula.D10

15.(a) Define the terms: Coefficient of Discharge and coefficient of velocity of an orifice.

(b) The head of water over an orifice of diameter 10 cm is 500 cm. Water coming out ofthe orifice is collected in a circular tank of diameter 2m. The rise of water in thecircular tank is 0.45 cm in 30 seconds. Also the coordinates of a certain point onthe jet measured from the vena contracta are 100 cm and 5.2 cm vertical. FindCv, Cd and Cc.

15. Prove that the velocity through the nozzle is given by

2

24

1

2

A

ax

D

fl

ghv

where a = Area of nozzle at outlet, A = Area of the pipe.D12

(b) A pipe line of total length 3000 m is made up of two diameters, 200 mm for the first

run and 150 mm for the second run, connects two reservoirs. The first run ends at alevel 1.5 m below the level of the higher reservoir and the total difference in levels is13.5m. The friction coefficient for both sections is 0.02m. Determine the maximumlength of the run so that the pressure at this point does not go more than 3 m belowatmosphere. Also calculate the flow rate. Neglect minor losses.M12

15. Determine the wall shearing stress in a pipe of diameter 100mm and which carries

water. The velocities at the pipe centre and 30 mm from the pipe centre are 2m/s and 1.5

m/s respectively. The flow in pipe is given as turbulent. A12

15. The head of water over an orifice diameter of 100 mm is 10 m. The water coming

out from the orifice is collected in a circular tank of diameter 1.5 m. The rise of waterlevel in this tank is 1m in 25 seconds. Also the co-ordinates of a point on the jet,measured from vena-contracta are 4.3 m horizontal and 0.5 m vertical. Find the co-efficient, Cd, Cv and Cc.- m1315. The rate of flow of water through a horizontal pipe is 0.25m3/s. The diameter of thepipe which is 200 mm is suddenly enlarged to 400 mm. The pressure intensity in thesmaller pipe is 11.22 N/cm2 . Determine the loss of head due to sudden enlargement.

A13


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15. Determine the wall shearing stress in a pipe of diameter 100mm and whichcarries water. The velocities at the pipe centre and 30 mm from the pipe centreare 2m/s and 1.5 m/s respectively. The flow in pipe is given as turbulent. M12

15.(a) Find the discharge through a rectangular orifice 3.0 m wide and 2 m deep fitted to a

water tank. The water level in the tank is 4 m above the top edge of the orifice, take co-efficient

of discharge Cd= 0.62

(b) A 25 mm diameter nozzle discharges 0.76 m3of water per minute when the head is 60 m.

The diameter of the jet is 22.5 mm. Determine the values of three hydraulic co-

efficients.

15. (a) Find the discharge through a rectangular orifice 3.0 m wide and 2 m deep fitted to a

water tank. The water level in the tank is 4 m above the top edge of the orifice, take co-efficient

of discharge Cd = 0.62 (b) A 25 mm diameter nozzle discharges 0.76 m3 of water per minute

when the head is 60 m. The diameter of the jet is 22.5 mm. Determine the values of threehydraulic co-efficients.

D09

15. A main pipe divides into two parallel pipes, which again forms one pipe. The lengthand diameter for the first parallel pipe are 2000m and 1m respectively, while the lengthand diameter of second parallel pipe are 2000 m and 0.8m respectively. Find the rate offlow in each parallel pipe, if total flow in the main is 3 m3/s. The coefficient of friction foreach parallel pipe is same and equal to 0.005. D11

15. Water discharge at the rate of 98.2 litres/s through a 120 mm diameter vertical

sharp- edge orifice placed under a constant head of 10 metres . A point, on the jet,

measured from the vena - contracta of the jet has co- ordinates 4.5 metres horizontal and

0.54 metres vertical. Find the coefficient Cv , Cc and Cd of the orifice. D11

16. Derive an expression for the velocity distribution for viscous flow through a circularpipe. D11

16. Derive Darcy-Weisback equation for determining the loss of head due to friction in pipes.

(12) A07

16. For turbulent flow in a pipe of diameter 300 mm, find the discharge when thecenterline velocity is 2 m/sec. and the velocity at a point 100 mm from the centre as

measured by Pitot tube is 1.6 m/sec.- m13

16. A pipe, 100 mm in diameter, has a nozzle attached to it at the discharge end, thediameter of the nozzle is 50 mm. The rate of discharge of water through thenozzle is 20 litres/s and the pressure at the base of the nozzle of 5.886 N/cm 2.Calculate the co-efficient of discharge. Assume that the base of the nozzle andoutlet of the nozzle are at the same elevation.D12


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16. A horizontal pipe of diameter 500 mm is suddenly contracted to a diameter of250 mm. The pressure intensities in the large and smaller pipe are given as 13.734N/cm

2and 11.772 N/cm

2 respectively. Find the loss of head due to contraction

if Cc=0.62. Also determine the rate of flow of water. M12

16. The difference in water surface levels in two tanks which are connected by three pipes

in series of lengths 300 m, 170 m and 210 m and diameters 300 mm, 200 mm and 400

mm respectively, is 12 m. Determine the rate of flow of water if co-efficient of friction

are 0.005, 0.0052 and 0.0048 respectively, considering: (a) minor losses also (b)

neglecting minor losses.

16. The difference in water surface levels in two tanks which are connected by three pipes in

series of lengths 300 m, 170 m and 210 m and diameters 300 mm, 200 mm and 400 mm

respectively, is 12 m. Determine the rate of flow of water if co-efficient of friction are 0.005,

0.0052 and 0.0048 respectively, considering: (a) minor losses also (b) neglecting minor

losses.D09

16. At a sudden enlargement of a water main from 240 mm to 480 mm diameter, the

hydraulic gradient rises by 10 mm. Estimate the rate of flow.

16. (a) A 30 cm pipe with friction factor f = 0.024 carries water to a turbine at the rate of0.25 m3/s over a distance of 160 m. The difference in levels between the water inlet and theturbine inletis 36 m. Determine the efficiency of transmission. The turbine outlet delivery issubmerged into the tailrace and the velocity at the exit is 0.4 times the velocity in thepipe.M12

(b) An oil of specific gravity 0.82 and kinematic viscosity 16 x 10-6 m2/s flows in asmooth pipe of 8 cm diameter at a rate of 2I/s. Determine whether the flow is laminar orturbulent. Also calculate the velocity at the centre line and the velocity at a radius of 2.5cm. What is head loss for a length of 10 m. What will be the entry length? Alsodetermine the wall shear. M12

16. A pipe 200mm in diameter and 1520m long discharges water from a nozzle. The total

head measured above the centre line of the nozzle is 275m. The velocity coefficient at

the nozzle is 0.96 and friction factor the pipe is 0.006. If the overall efficiency of power

transmission is 81%, find the power transmitted and the discharge.D10

16. At a sudden enlargement of a water main from 240 mm to 480 mm diameter, the

hydraulic gradient rises by 10 mm. Estimate the rate of flow. 15. Derive an expression for

the discharge over a rectangular notch in terms of head of water over the crest of notch.

16. A crude oil of viscosity 0.9 poise and relative density 0.9 is flowing through a horizontal

circular pipe of diameter 10mm and length 12m. Calculate the difference of pressure at the two

ends of the pipe, if 785 N of the oil is collected in a tank in 25 seconds.


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16.(a) Two pipes are connected by three pipes in series. The lengths of the pipes are300m, 170m and 210m, respectively and the corresponding diameters are 0.3m,0.2ma and 0.4m. Determine the rate of flow if the friction factors of the threepipes are 0.02, 0.0208 and 0.0192 respectively. Considering only loses due tofriction for solving this problem and the difference of water level is 12m.

(b) If three pipes of lengths 800m, 400m and 200m and diameters of 0.6m, 0.4m and0.2m respectively are connected in series. Three pipes are to be replaced by anequivalent pipe of length 1400m. Assuming friction factor of the compound pipe to thesame, determine the equivalent diameter of the equivalent pipe.

16. Water discharges at the rate of 98.2 litres per second through a 12cm diameter vertical

sharp edged orifice placed under a constant head of 10 metres. A point, on the jet, measured

from the vena-contracta has co-ordinates 4.5 metres horizontal and 0.54 metres vertical. Find

the hydraulic coefficients of the orifices.

16. (a) Two pipes are connected by three pipes in series. The lengths of the pipes are 300m,

170m and 210m, respectively and the corresponding diameters are 0.3m, 0.2ma and 0.4m.Determine the rate of flow if the friction factors of the three pipes are 0.02, 0.0208 and 0.0192

respectively. Considering only loses due to friction for solving this problem and the difference

of water level is 12m.

(b) If three pipes of lengths 800m, 400m and 200m and diameters of 0.6m, 0.4m and 0.2m

respectively are connected in series. Three pipes are to be replaced by an equivalent pipe of

length 1400m. Assuming friction factor of the compound pipe to the same, determine the

equivalent diameter of the equivalent pipe.A11

16. A horizontal pipe of diameter 500 mm is suddenly contracted to a diameter of 250 mm.

The pressure intensities in the large and smaller pipe are given as 13.734 N/cm2and 11.772N/cm

2 respectively. Find the loss of head due to contraction if Cc=0.62. Also determine the

rate of flow of water-A12

16. A 425 mm diameter pipe having 800 m length conveys water from high level tank

to a point 22 m below water level in the tank. Calculate the percentage error committed in

the calculation of discharge by neglecting the minor energy losses. Take

f = 0.03. D11

.16. (a) Two pipes are connected by three pipes in series. The lengths of the pipes are 300m,

170m and 210m, respectively and the corresponding diameters are 0.3m, 0.2ma and

0.4m. Determine the rate of flow if the friction factors of the three pipes are 0.02,0.0208 and 0.0192 respectively. Considering only loses due to friction for solving this

problem and the difference of water level is 12m.

(b) If three pipes of lengths 800m, 400m and 200m and diameters of 0.6m, 0.4m and 0.2m

respectively are connected in series. Three pipes are to be replaced by an equivalent pipe of

length 1400m. Assuming friction factor of the compound pipe to the same, determine the

equivalent diameter of the equivalent pipe


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UNIT IV PUMPS 10 hrs.

Centrifugal Pumps: DefinitionOperationsVelocity TrianglesPerformance curvesCavitationsMultistaging.Reciprocating Pumps: OperationSlipindicatorDiagramSeparationAir vessels.

7. Define a specific speed of a centrifugal pump? m13

Specific speed is defined as "the speed of an ideal pump

geometrically similar to the actual pump, which when running

at this speed will raise a unit of volume, in a unit of time

through a unit of head".

8. What is an air vessel? m13

It consists of a vessel containing air, which is placed between the deliveryvalveand themouth of the deliverypipe,helps to continue the flowing ofwaterafter the impellingforce

has ceased to act, as in the return stroke of aforcingpump7. Define the term slip in a reciprocating pump.8. What is a slip in reciprocating pump? D11

7. Define the term slip in a reciprocating pump.8. Explain the term slip. A13

Slip is defined as the difference between theoretical discharge and actual

discharge. If actual discharge is greater than theoretical discharge negative value

is found this negative value is called negative slip.

7.Differentiate between the volute casing and vortex casing for the centrifugalpump.D12

In volute pumps area of flow gradually increases from throat towards the

delivery pipe. The increase in area of flow decreases the exit velocity and

hence pressure increases in the casing.

Vortex casing is a casing in which circular chamber is provided between

the casing and the impeller. Vortex casing will increase pump efficiency by

reducing eddies formation to a considerable extent.

8.How will you classify the reciprocating pumps?D12

Reciprocating pumps are mainly classified according to use of piston sides and
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according to number of cylinders.piston sides -Single-acting reciprocating pump ,Double-acting reciprocating pump

number of cylinders -Single-cylinder pump,Double-cylinder pump,triple-cylinder pump

7.What do mean by the manometric efficiency and mechanical efficiency? M12

Manometric efficiency (): it is the ratio of the manometric head to the head actually

generated by the impeller .

Mechanical efficiency(mech): It is the ratio of the impeller power to the power of the

motor or the prime mover.

8.Find an expression for the head loss due to friction in suction and delivery pipes. M12

7. Define manometric head manometric efficiency of a centrifugal pump.M12

The manometric head is defined as the head against which a

centrifugal pump has to work. It is denoted by Hm.Manometric efficiency (): it is the ratio of the manometric head to the head actually

generated by the impeller

8. What are the advantages of installing air vessels in a reciprocating pump?M12

The advantages of installing air vessels are:

(i) The flow fluctuation is reduced and a uniform flow is obtained.

(ii) The friction work is reduced.

(iii) The acceleration head is reduced considerably.

(iv) Enables the use of higher speeds.7. What are the types of pumps available? D11

Pumps may bi placed in one of the two general categories.

(i) Dynamic pressure pumps: centrifugal pump,jet pump,

propeller, and turbine.


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(ii) Positive, displacement pump: Piston plunger, gear, lab,

vane, screw etc.

7. Define the specific speed of a pump.

Specific Speed is a dimensionless design index number used toclassify pumps by impeller type and proportion. It is defined as thespeed in revolutions per minute that a geometrically similar pumpwould operate to deliver one unit of flow at one unit of head.7. Define cavitation. A13

8. What is meant by cavitation?

8.. What is meant by cavitation?

8. What do you mean by cavitation in a pump?

the term cavitation implies a dynamic process of formation of bubbles inside theliquid, their growth and subsequent collapse as the liquid flows through the pump

17. With the help of a neat sketch explain the construction and working of acentrifugal pump.D12

17. Draw a neat sketch of Reciprocating pump and explain the working principle ofsingle acing and double acting Reciprocating pump. D11

17. Discuss the construction and working of a Reciprocating pump

18. a. What is air vessel in reciprocating pump? State its functions. (4) A07b. Explain with a neat sketch of double acting reciprocating pump with an air vesselfitted in the delivery side. (8)

18. (a) Explain the working principle of reciprocating pump with neat sketch.

(b) Why air vessels are used in reciprocating pumps?

(c) Why a reciprocating pump is called Positive displacement pump?

18. (a) Explain the working principle of reciprocating pump with neat sketch.A11

(b) Why air vessels are used in reciprocating pumps?(c) Why a reciprocating pump is calledPositive displacement pump?

18. (a) Write a short notes on types of casing in centrifugal pump.

(b) Define slip and negative slip in reciprocating pump.


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17. a. What is priming? Why is it necessary? (4) A07

b. Explain the following with formula i) Manometric efficiency ii) Mechanical efficiency iii)Overall efficiency of centrifugal pump. A07

17. What is priming? With a neat sketch give the working principle of a centrifugal

pump.D10

17. What is priming? With a neat sketch give the working principle of a centrifugal pump.

17. (a) Explain why priming is required to start a centrifugal pump. (3)mM12

(b) A centrifugal pump with an impeller diameter of 0.4 m runs at 1450 rpm. The angleat outlet of the backward curved vane is 25 with tangent. The flow velocity remainsconstant at 3 m/s. If the anometric efficiency is 84%, determine the fraction of the kineticenergy at outlet recovered as static head.M12

17. (a) Sketch the operating characteristic curves of a centrifugal pump. (4)

(b) A centrifugal pump impeller has an outer diameter of 30 cm and an inner diameter of 15

cm. the pump runs at 1200 r.p.m. The impeller vanes are set at a blade angle of 30 at the

outlet. If the velocity of flow constant at 2.0 m/s, calculate (i) the velocity and direction of

water at outlet,(ii) the head developed assuming a manometric efficiency of 0.85, and (iii) the

blade angle at the inlet. (8)

17. (a) Sketch the operating characteristic curves of a centrifugal pump.

(4)

(b) A centrifugal pump impeller has an outer diameter of 30 cm and an inner diameter

of 15 cm. the pump runs at 1200 r.p.m. The impeller vanes are set at a blade angle of

30at the outlet. If the velocity of flow constant at 2.0 m/s, calculate

(i) the velocity and direction of water at outlet,

(ii) the head developed assuming a manometric efficiency of 0.85, and

(iii) the blade angle at the inlet.

(b) A single acting reciprocating water pump of 180 mm bore and 240 mm stroke

operates at 40 rpm. Determine the discharge if the slip is 8%. Estimate the value ofcoefficient of discharge. If the suction and delivery heads are 6 m and 20 mrespectively, determine the theoretical power. If the overall efficiency was 80%, what isthe power required. (4)M12

17. The internal and external diameter of an impeller of a centrifugal pump which isrunning at 1000 r.p.m are 200 mm and 400 mm respectively. The discharge through


25/38

pump is 0.04 m3 /sec and velocity of flow is constant and equal to 2 m/sec. Thediameter of the suction and delivery pipes are 150 mm and 100 mm respectively andsuction and delivery heads are 6 m (abs) and 30 m (abs) of water respectively. If theoutlet vane angle is 45 and power required to drive the pump is 16.186 KW. Determine(a) Vane angle of the impeller at inlet.

(b) The overall efficiency of the pump.

(c) Manometric efficiency of the pump.- m13

17. A centrifugal pump having outer diameter equal to two times the inner diameter andrunning at 1000 rpm works against a total head of 40 m. The velocity of flow through theimpeller is constant and equal to 2.5 m/s. The vanes are set back at an angle of 40 atoutlet. If the outer diameter of the impeller is 500 mm and width at outlet is 50 mm,determine: (i) vane angle at inlet (ii)work done by impeller on water per second. A13

17. The internal and external diameters of the impeller of a centrifugal pump are 200

mm and 400 mm respectively. The pump is running at 1200 r.p.m. The vaneangles of the impeller at inlet and outlet are 200and 30

0respectively. The water

enters the impeller radially and velocity of flow is constant. Determine the workdone by the impeller per unit weight of water. M12

17. The outer diameter of a centrifugal pump is equal to two times the innerdiameter. The pump runs at 1200 rpm and works against the total head of 75m.The velocity of flow through the impeller is constant and equal to 3 m/s. Thevanes are curved back at an angle of 30 at the outlet. If the outer diameter of theimpeller is 60 cm and the width at the outlet is 5 cm, determine (a) Vane angle atthe inlet, (b) the minimum starting speed of the centrifugal pump.

17. A centrifugal pump running at 800 rpm is working against a total head of 20.2 m. Theexternal diameter of the impeller is 480 mm and the outlet width is 60 mm. If the vane

angle at outlet is 40 and manometer efficiency is 70%. Determine (a) flow Velocity at outlet.

(b) Absolute velocity of water leaving the vane. (c) Angle made by the absolute velocity

at outlet with the direction of motion. (d) Rate of flow through the pump.D11

17. The outer diameter of a centrifugal pump is equal to two times the inner diameter. The

pump runs at 1200 rpm and works against the total head of 75m. The velocity of flow

through the impeller is constant and equal to 3 m/s. The vanes are curved back at an

angle of 30 at the outlet. If the outer diameter of the impeller is 60 cm and the width at

the outlet is 5 cm, determine (a) Vane angle at the inlet, (b) the minimum starting speed

of the centrifugal pump.

17. A centrifugal pump is to discharge 0.11m3 /s at a speed of 1500 rpm against a head of 25m.

The impeller diameter is 250mm, its with outlet is 50mm and manometric efficiency is 75%.

Determine the vane angle at the outlet periphery of the impeller. A09

17. The outer diameter of a centrifugal pump is equal to two times the inner diameter. The

pump runs at 1200 rpm and works against the total head of 75m. The velocity of flow through


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the impeller is constant and equal to 3 m/s. The vanes are curved back at an angle of 30 at the

outlet. If the outer diameter of the impeller is 60 cm and the width at the outlet is 5 cm,

determine (a) Vane angle at the inlet, (b) the minimum starting speed of the centrifugal

pump.A11

17. The impeller of a Centrifugal pump has a diameter of 10 cm and breadth 3.5 cm at theinner periphery; the corresponding dimensions at the outer periphery are 20 cm and 1.7 cm

respectively. The pump runs at 1500 rpm, has 7 vanes with vane angle at entry and exit equal to

16and 30respectively. Calculate: (i) the theoretical discharge for shockless entrance, (ii) the

theoretical head developed, (iii) the actual head produced, the losses and power required to

drive the pump.Neglect the effect of vane thickness and presume that the hydraulic efficiency is

85% and the overall efficiency is 75%.

17. The impeller of a centrifugal pump is of 30 cm diameter and 5 cm width at the periphery

and has blades whose tip angles incline backwards 60 from the radius. The pump delivers 17

m3 /min and the impeller rotates at 1000 rpm. Assuming that the pump is designed to admit

radially, calculate (i) speed and direction of water as it leaves the impeller, (ii) torque exerted bythe impeller on water, (iii) shaft power required and (iv) lift of the pump. Take mechanical

efficiency as 95% and hydraulic efficiency as 75%. =A10

17. The internal and external diameters of the impeller of a centrifugal pump are 200 mm

and 400 mm respectively. The pump is running at 1200 r.p.m. The vane angles of the impeller at

inlet and outlet are 200and 30

0respectively. The water enters the impeller radially and velocity

of flow is constant. Determine the work done by the impeller per unit weight of water

18. (a) Explain the working principle of reciprocating pump with neat sketch.

(b) Why air vessels are used in reciprocating pumps?

(c) Why a reciprocating pump is called Positive displacement pump?

18.(a) Explain with neat sketch the working principle of Reciprocating pump-D10 (8)

(b) What is an air vessel? what are the uses of vessels in a reciprocating pump. D10 (4)

18. (a) Explain with neat sketch the working principle of Reciprocating pump

(8)

(b) What is an air vessel? what are the uses of vessels in a reciprocating pump

18. Explain with neat sketches the function of air vessels in a reciprocating pump. A09

dimensionless expression for R using Buckinghams theorem.A10

18. Derive an expression for work saved by a single acting reciprocating pump with airvessel. A13


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18. The cylinder bore diameter of a single acting reciprocating pump is 150 mm andits stroke is 300 mm. The pump runs at 50 r.p.m. and lifts water through a heightof 25 m. The delivery pipe is 22 m long and 100 mm in diameter. Find thetheoretical discharge and the theoretical power required to run the pump. If theactual discharge is 4.2 litres/sec, find the percentage slip. Also determine the

acceleration head at the beginning and middle of the delivery stroke.D12

18. The cylinder bore diameter of a single-acting reciprocating pump is 150mmand its stroke is 300 mm. The pump runs at 50r.p.m. and lifts water through aheight of 25 m. The delivery pipe is 22 m long and 100 mm in diameter. Findthe theoretical discharge and the theoretical power required to run the pump.If the actual discharge is 4.2 liters/s, find the percentage slip. Alsodetermine the acceleration head at the beginning and middle of the deliverystroke. M12

18. The cylinder bore diameter of a single acting reciprocating pump is 150 mm and itsstroke is 300 mm. The pump runs at 50 r.p.m and lifts water through a height of 25 m.

the delivery pipe is 22m long and 100 mm in diameter. Find the theoretical dischargeand theoretical power required to run the pump. If the discharge is 4.2 liters/sec, find thepercentage slip, Also determine the acceleration head at the beginning and middle ofthe delivery pipe.- m13

18. (a) A single acting reciprocating of pump handles water. The bore and stroke of theunit are 20 cm and 30 cm. The suction pipe diameter is 12 cm and length is 8 m. Thedelivery pipe diameter is 12 cm and length is 24 m. f = 0.02. The speed of operation is32 rpm. Determine the friction power with and

without air vessels.(8)M1218. A Centrifugal pump having outer diameter equal to 2 times the inner diameter andrunning at 1200 rpm works against a total head of 75m. The Velocity of flow through theimpeller is constant and equal to 3 m/s. The vanes are set back at an angle of 30 at outlet. If the outer diameter of impeller is 600mm and width at outlet is 50mm. determine(a) Vane angle at inlet

(b) Work done per second on impeller

(c) Manometric efficiency.D11

18. A centrifugal pump is to discharge 0.118 m3 at a speed of 1450 rpm against a headof 25 m. The diameter and width of the impeller at outlet are 250 mm and 50 mmrespectively. If the manometric efficiency is 75%, determine the vane angle at the outlet.

.18. The cylinder bore diameter of a single-acting reciprocating pump is 150mm and its

stroke is 300 mm. The pump runs at 50r.p.m. and lifts water through a height of

25 m. The delivery pipe is 22 m long and 100 mm in diameter. Find the

theoretical discharge and the theoretical power required to run the pump. If


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the actual discharge is 4.2 liters/s, find the percentage slip. Also determine

the acceleration head at the beginning and middle of the delivery stroke.

18. (a) Define indicator diagram. Prove that area of indicator diagram is proportional to the

work done by the reciprocating pump (b) A single acting reciprocating pump runs at 30 r.p.m.,

delivers

0.012 m3 /s of water. The diameter of the piston is 25 cm and stroke length 50 cm. Determine

(i) the theoretical discharge of the pump,

(ii) co-efficient of discharge, and

(iii) percentage slip of the pump.

18. A double acting reciprocating pump runs at 40 rpm. It has the cylinder of 200 mm

diameter and stroke of 400 mm. It delivers water to a height of 1m through a pipe of 150 mm

diameter and 40 m long. An air vessel is attached at 3m height from the centre of

cylinder. The coefficient of friction for the pipe is 0.01. Find the pressure head in the

cylinder at the beginning and at the end of delivery stroke. Assume motion of piston by SHM.

D11

18. (a) Define indicator diagram. Prove that area of indicator diagram is proportional to the

work done by the reciprocating pump

(b) A single acting reciprocating pump runs at 30 r.p.m., delivers 0.012 m3/s of water.

The diameter of the piston is 25 cm and stroke length 50 cm. Determine

(i) the theoretical discharge of the pump,

(ii) co-efficient of discharge, and

(iii) percentage slip of the pump.

18. A double acting single cylinder reciprocating pump of 20 cm bore and 40 cm stroke runs

at 35 rpm. The pump draws water from a sump 1 m below the pump through a suction pipe 10

cm in diameter and 2.5 m long. The water is delivered to a tank 30 m above the pump through

a delivery pipe 10 cm in diameter and 40 m long. The mechanism executes a simple harmonic

motion.Determine the net force due to fluid pressure on the piston when it has moved througha distance of 10 cm from the inner dead centre. Neglect size of piston rod and take friction

factor f= 0.0075 for both the suction and delivery pipes.

.18. A centrifugal pump is to discharge 0.118 m3at a speed of 1450 rpm against a head of 25

m. The diameter and width of the impeller at outlet are 250 mm and 50 mm respectively. If the

manometric efficiency is 75%, determine the vane angle at the outlet.


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(or)

UNIT V TURBINES AND DIMENSIONAL ANALYSIS 10 hrs.

Hydraulic Turbines: Classification of hydraulic turbinesWorking principle of Peltonwheel, Francis and Kaplan turbinesvelocity trianglesdraft tubehydraulic turbinecharacteristics.

Dimensional Analysis: Buckinghams Theorem, Non-Dimension Numbers, Similaritiesof Flow. Model studies

9. Difference between the turbines and pumps? m13

A pump absorbs useful energy and converts it to kinetic energy and givesit to a fluid stream. The turbine does the exact opposite as it absorbs energy from a fluidstream and converts it to work. A pump increases the energy of the fluid stream whereas a turbinedecreases the energy.

9. What is hydraulic turbine? State its types.

The hydraulic machines which convert hydraulic energy into mechanical energy are

known as Turbines.

The hydraulic turbines can be classified based on type of energy at the inlet, direction offlow through the vanes, head available at the inlet, discharge through the vanes andspecific speed.Pelton Wheel,Francis Turbine,Kaplan Turbine

9. List any three hydraulic turbines. D11

Pelton Wheel,Francis Turbine,Kaplan Turbine

9. Differentiate between impulse and reaction turbines.M12

1. In impulse turbine, there are nozzle and moving blades are in serieswhile there are fixed blades and moving blades are present inReaction turbine (No nozzle is present in reaction turbine).

2. The number of stages is required less in impulse turbine whilerequired more in reaction turbine

3. Efficiency of impulse turbine is lower than reaction turbine4. Impulse turbine requires less space than reaction turbine.


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5. Blade manufacturing of impulse turbine is not difficult as in reactionturbine it is difficult10. What is meant by draft tube? D11

Draft tube is a divergent tube one end of which is connected to the outlet

of the turbine and other end is immersed well below the tailrace (Water

level).

The water after working on the turbine, imparts its energy to the vanes

and runner, thereby reducing its pressure less than that of atmospheric

pressure (Vacuum). As the water flows from higher pressure to lower

pressure, it cannot come out of the turbine and hence a Draft tube (divergent tube) is

connected to the end of the turbine.

9. What is the function of draft tube? A13

The major function of the draft tube is to increase the pressure from the inlet to outlet ofthe draft tube as it flows through it and hence increase it more than atmosphericpressure. The other function is to safely discharge the water that has worked on theturbine to tailrace.

10. Why draft tube in mandatory in reaction turbines

In absence of draft tubes,the water would get discharged to the tail

race(Analogous to exhaust of engines)and that would need discharge ofmore water from the dam and optimizing the required amount of pressureneeded to keep the turbine rotating at desired speed.It would result in lossof head,which in return affects the performance ability of turbines

10. Explain the term dimensionally homogeneous equations? m13

An equation is dimensionally homogenous if all the terms have the samedimensions. An equation is true if both sides of it are numerically anddimensionally identical.

9. Define speed ratio and flow ratio. M12

Speed ratio: It represents ratio of peripheral velocity (linear) of buckets at their mean

diameter to theoretical or sprouting velocity of jet.

Flow Ratio: It is the ratio of flow velocity (Vf1) at the inlet of the name to the

spouting velocity (2gH))

10. What is meant by cavitations? Define Thomas cavitations number.M12


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The Thomas cavitations numberisratio of the difference between totalhead and the vapour pressure (upstream of the impeller ofrotating machinery) to the total head produced or absorbed by

the machine.

10. Draw inlet and outlet velocity triangles for a Pelton turbine.D12

10. State Buckinghams -theorem. A13

Buckingham theoremstates that an equation involving nnumber of physical variables

which are expressible in terms of kindependent fundamental physical quantities can beexpressed in terms ofp = n - kdimensionless parameters.

9. State Buckinghams -theorem.D12

A relationship betweenmvariables (physical properties such as velocity, density etc.)

can be expressed as a relationship between m-n non-dimensionalgroups of variables

(called groups), where nis the number of fundamental dimensions (such as mass,

length and time) required to express the variables.

State Buckinghams Pi theorem of dimensional analysis.

The theorem may be interpreted to state that one can form (n-3) independent

Dimensionless groups of q1,q2qn variables so that h(1,2n-3)=0,where s are

the dimensionless groups, and M (mass), L (length) and T (time) are the primary
http://en.wikipedia.org/wiki/Buckingham_%CF%80_theoremhttp://en.wikipedia.org/wiki/Buckingham_%CF%80_theoremhttp://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem


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dimensions used to describe the system

10. What are the types of similitude?

a. Geometric similitude- model is of exact scale of the prototype

including object dimensions and surface roughness.

b. Kinematic similitude- the velocity at a particular point in the model is

proportional to the corresponding velocity in the prototype. It includes

magnitudes and directions.

c. Dynamic similitude- This is achieved when all forces in the model are

proportional to all forces in the prototype. Kinematic similitude is necessary

but not sufficient for dynamic similitude.

? 10. Define the following Reynolds number and Machs number. M12

In fluid mechanics, the Reynolds number (Re) is a dimensionlessnumber that gives a measure of the ratio of inertial forces to viscousforces and consequently quantifies the relative importance of thesetwo types of forces for given flow conditions.

Reynolds number inertial, viscous force ratio

Mach number Local velocity, local velocity of sound ratio

19. A Pelton wheel is to be designed for a head of 60 m when running at 200 r.p.m. ThePelton wheel develops 95.6475 kW shaft power. The velocity of the buckets = 0.45times of the velocity of the jet, overall efficiency = 0.85 and co- efficiency of the velocity

is equal to 0.98.- m13

(or)

20. The pressure difference p in a pipe ofdiameter D and length l due to turbulent flowdepends on the velocity V, viscosity , density and roughness k. Using Buckinghams theorem, obtain an expression for p.- m13


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19. A Pelton wheel is to be designed for the following specifications: Shaft power =11,772 kW, H = 380 m, speed = 750 rpm, overall efficiency = 86%. Jet diameter is not toexceed one sixth of the wheel diameter. Determine: (i) wheel diameter (ii) Number of

jets required (iii) Diameter of jet. Take Cv =0.985, speed ratio = 0.45. A13

(or)

20. Using Buckingham theorem show that the discharge Q consumed by an oil ring isgiven by

Q = Nd3. A13

19. A Kaplan turbine runner is to be designed to develop 7357.5 kW S.P. The netavailable head is 10 m. Assume that the speed ratio is 1.8 and flow ratio 0.6. Ifthe overall efficiency is 70% and diameter of the boss is 0.4 times the diameter ofthe runner, find the diameter of the runner, its speed and specific speed.-D12

(or)

20. Explain briefly about Dimensionless number and Model laws.D12

19. The following data is related to a pelton wheel:

Head at the base of the nozzle = 80 mDiameter of the jet = 100 mmDischarge of the nozzle = 0.30 m3/sPower at the shaft = 206 kWPower absorbed in mechanical resistance = 4.5 kW

Determine (i) power lost in nozzle and (ii) power lost due to hydraulic resistance

in the runner. M12

(or)

20. A spillway model is to be built to a geometrically similar scale of 1/50 across aflume of 600 mm width. The prototype is 15 m high and maximum head on it isexpected to be 1.5 m.

(a) What height of model and what head on the model should be used?

(b) If the flow over the model at a particular head is 12 liters per second, whatflow per meter length of the prototype is expected? (c) If the negative pressure in

the model is 200 mm, what is the negative pressure in prototype? Is itpracticable? M12

19. (a) State the conditions required to obtain a similarity between the models and theprototype. (3)

(b) The following details are available about a Francis turbine. Diameters are 2.25 mand 1.5 m. Widths are 0.25 m and 0.375 m. The guide blade outlet angle is 18 and therunner blade angle is


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85, both angles with the blade velocity direction. Frictional loss is 15% of the pressurehead 60 m available between the inlet and outlet of the runner. Calculate, the speedand output of the

turbine. Also find the blade outlet angle. Mechanical efficiency is 92%. Blade thicknessblocks the flow area by 8%. (9)M12

(or)

20. (a) Explain the principle of dimensional homogeneity. (3)M12

(b) Players use spin in ball plays like tennis, golf etc. As the ball moves the spin rate willdecrease. If the aerodynamic torque on the ball in flight depends on the forward s peedu, density and viscosity of air, the ball diameter D, angular velocity of spin, and theroughness height on the ball surface, determine the dimensionless parameters tocorrelate the situation. (9)M12

19. A pelton turbine is required to develop 9000 KW when working under a head of

300mm the impeller may rotate at 500 rpm. Assuming a jet ratio of 10 And an overallefficiency of 85% calculate

(a) Quantity of water require

(b) Diameter of the wheel

(c) Number of jets

(d) Number and size of the bucket vanes on the runner. D11

(or)

20. Explain Francis turbine with neat sketchD11

19. A pelton wheel is to be designed for the following specifications: Shaft power=11772kW; Head = 380 m; Speed =750 rpm; overall efficiency = 86%; Jet diameter is not toexceed one-sixth of thewheel diameter. Determine: The wheel diameter (b) The number of jets required and (b)Diameter of jet. Take Kvl = 0.985 and Kul = 0.45 where, Kvl = Coefficient of velocity andKul=speed ratio.(or)20. The pressure difference p in a pipe of diameter D and length 1 due to viscous flowdepends on the velocity V, viscosity , density , obtain an expression for , using

Buckinghams theorem.

19. Design a Francis turbine runner with the following data: Net head = 68 m, speedN=750 rpm, output power P = 330kW, Hydraulic efficiency = 94%, Overallefficiency=85%, flow ratio = 0.15, breadth ratio = 0.1, inner diameter of the runner= 0.5 (outer diameter). Also assume 6% of circumferential area of the runner tobe occupied by the thickness of the vanes. Velocity of the flow remains constantthroughout and the flow is radial at the exit.


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(or)

20. (a) What are the types of similarity to be maintained in Model testing?A07

(b) Define the following dimensionless numbers: Reynolds number and FroudeNumber.

19. a. Distinguish between Impulse and Reaction turbines. (4)

b. Explain the working principle of Pelton wheel turbine with a neat sketch by indicating all

parts. (8)

(or)

20. A kalpan turbine working under a head of 20m develops 11772 kW shaft power. The outer

diameter of the runner is 3.5m and hub diameter 1.75m. The guide blade angle at the extreme

edge of the runner is 35. The hydraulic and overall efficiencies of the turbines are 88% and 84%respectively. If

the velocity of whirl is zero at outlet, determine:

i. Runner vane angles at inlet and outlet of the extreme edge

of the runner, and

ii. Speed of the turbine

19. A Kaplan turbine develops 22000kW at an average head of 35m.

Assuming a speed ratio of 2, flow ratio of 0.6, diameter of the boss

equal to 0.35 times the diameter of the runner and an overall

efficiency of 90 percent, calculate the diameter, speed and specific

speed of the runner. A09

(or)

20. Write short notes on: (a) Geometric similarity (b) Kinematic similarity

(c) Dynamic similarity

19. The following data relate to a Pelton wheel turbine is given below. Head at the base of the

nozzle = 82m, diameter of the jet = 100 mm, discharge of the nozzle = 0.3m3/s, shaft power =

206kW. Determine the power lost in nozzle and power lost due to hydraulic resistance in water.

A10 (or)


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20. The resistance R experienced by a partially submerged body depends upon the velocity V,

length of the body 1, viscosity of the fluid , density of the fluid and gravitational acceleration

g. Obtain a

19. Design a Francis turbine runner with the following data: Net head = 68 m, speed N=750

rpm, output power P = 330kW, Hydraulic efficiency = 94%, Overall efficiency=85%, flow ratio =

0.15, breadth ratio = 0.1, inner diameter of the runner = 0.5 (outer diameter). Also assume 6%of circumferential area of the runner to be occupied by the thickness of the vanes. Velocity of

the flow remains constant throughout and the flow is radial at the exit.A11

(or)

20. (a) What are the types of similarity to be maintained in Model testing?A11

(b) Define the following dimensionless numbers: Reynolds number and Froude Number

19. The following data is related to a pelton wheel:

Head at the base of the nozzle = 80 mDiameter of the jet = 100 mmDischarge of the nozzle = 0.30 m

3/s

Power at the shaft = 206 kW

Power absorbed in mechanical resistance = 4.5 kW

Determine (i) power lost in nozzle and (ii) power lost due to hydraulic resistance in the

runner. A12

(or)

20. A spillway model is to be built to a geometrically similar scale of 1/50 across a flume of

600 mm width. The prototype is 15 m high and maximum head on it is expected to be

1.5 m.

(a) What height of model and what head on the model should be used?

(b) If the flow over the model at a particular head is 12 liters per second, what flow per

meter length of the prototype is expected? (c) If the negative pressure in the model is

200 mm, what is the negative pressure in prototype? Is it practicable? A12

19. The pressure difference p in pipe of diameter D and length L due to viscous flow depends

on the velocity V, viscosity and density . Using Buckinghams - theorem, obtain an

expression for p. D09

(or)

20. (a) What are unit quantities? Define the unit quantities of a turbine. (4) D09

(b) A Kaplan turbine develops 15000 kW power at a head of 30m. the diameter of the boss is

0.35 times the diameter of the runner. Assuming a speed ratio of 2.0, a flow ratio of 0.65 and

an overall


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efficiency of 90% calculate (i) diameter of the runner, (ii) rotational speed and (iii) specific

speed

19. A Pelton wheel has a mean bucket speed of 10m/s with a jet of water flowing at the rate

of 0.7 ,3/s under a head of 30 m. The buckets deflects the jet through an angle of 160

degree. Calculate the power given by water to the runner and the hydraulic efficient byof the turbine. Assume coefficient of velocity as 0.98.D10

(or)

20. A Kaplan turbine works under a head of 60m at a speed of 145 rpm utilizing 175 m3/s of

water. The diameter of the runner and hub are respectively 5.60m and 3.20m

respectively. The turbine develops 82500kW. Find the flow ratio, the speed ratio, overall

efficiency and the specific speed.D10

19. A Pelton wheel is to develop 13,250 kw under a net head of 800 m while running at a

speed of 600 rpm. If the coefficient of jet = 0.97, speed ratio = 0.46 and the ratio of the

jet diameter is 1/15 of wheel diameter. Calculate (a) number of jets. (b)

Diameter of jets. (c) Diameter of pitch circle. (d) Quantity of water supplied

to wheel. Assume overall efficiency as 85%. D11(or)

20. It is desired to obtain the dynamic similarity between a 30 cm diameter pipe

carrying linseed oil at 0.5 m3

/s and a 5 m diameter pipe carrying water. What should be the

rate of flow of water in lps?. If the pressure loss in the model is 196 N/m2

, What

is the pressure loss in the prototype pipe?. Kinematic viscosities of linseed oil and water

are 0.457 and 0.0113 stokes respectively. Specific gravity of linseed oil = 0.82.D11

20. Explain briefly about Dimensionless number and Model laws

19. The pressure difference p in pipe of diameter D and length L due to viscous flow

depends on the velocity V, viscosity and density . Using Buckinghams - theorem,

obtain an expression for p.(or)

20. (a) What are unit quantities? Define the unit quantities of a turbine. (4)

(b) A Kaplan turbine develops 15000 kW power at a head of 30m. the diameter of the

boss is 0.35 times the diameter of the runner.

Assuming a speed ratio of 2.0, a flow ratio of 0.65 and an overall efficiency of 90%

calculate (i) diameter of the runner, (ii) rotational speed and (iii) specific speed

19. (a)How does a single jet Pelton wheel differ from a multi jet wheel?(2)

(b) A Pelton wheel is required to develop 6 MW when working under a head of 300m. It

rotates with a speed of 550 rpm. Assuming jet ratio as 10 and overall efficiency as 85%

calculate: (i) diameter of wheel (ii) quantity of water required and number of jets.

Assume suitable values for the velocity coefficient and the speed ratio. (10)

(or)


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20. The runner of an inward flow reaction turbine is of 45 cm diameter and 5 cm width at

the outer periphery; the corresponding dimensions at the inner periphery are 30 cm and

7.5 cm respectively, and vanes occupy 8% of the periphery. The guide vane angle is 25

to the tangent to the runner and the moving vanes have an inlet angle of 95 (vanes

inclined forward to the direction of motion) and an exit angle of 30, Hydraulic and

mechanical friction losses respectively amount to 10% and 5% of the supply head, andthe pressure in the outer casing is 55 m more than that at discharge from the runner.

Calculate speed of the runner for no shocks at entry and the power available at the

turbine shaft.

19. A pelton wheel is to be designed for the following specifications:

Shaft power=11772

fm consolidated

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