COLLEGE OF ENGINEERING PATHANAPURAM (UNDER CAPE, GOVT. OF KERALA) AFFLIATED TO CUSAT

DEPARTMENT OF ELECTRICAL & ELECTRONICS (2013-2017)

B.TECH DEGREE 3 SEMESTER EE1303 FLUID MECHANICS AND HEAT ENGINES (2012 SCHEME)

PREVIOUS YEAR SOLVED QUESTIONS

Q)State Bernoulli’s theorem? Point out its limitation? It states that in a steady ideal flow of an incompressible fluid, the total energy at any point of the fluid is constant. The total energy consist of pressure energy kinetic energy and potential energy or datum energy . these energies per unit weight of the fluids are Pressure energy = p/ g Kinetic energy= Datum energy=

/2g z

Thus mathematically Bernoulli’s theorem is written as p/ g +

/2g + z =0

Limitations 1. It can applicable to only steady flow 2. It can applicable to only incompressible flow 3. It can applicable to only ideal flow

Q) Define net positive suction head and explain how this quantity is used to ensure that cavitation does not occur in a pump? The net positive suction head is defined as the absolute pressure head at the inlet to the pump, minus the vapour pressure head corresponding to the temperature of the liquid pumped, plus the velocity head at this point. Thus NPSH=Pa/w + Ps/w –Pv/w+Vs2/2g

Introducing the value of (Ps/w) from eqn in the above expression it becomes NPSH=Pa/w – Pv/w – hs – hfs The right hand side of eqn also represents the total suction head Hsv,

i.e,

Hsv= Pa/w – Pv/w – hs – hfs

and hence NPSH = Hsv

For determining the required NPSH, the pump is operated at the designed speed with different suction lifts and for each setting of the pump, the head v/s discharge and efficiency v/s discharge characteristics are obtained. At a certain value of discharge there is an abrupt reduction in the head developed by the pump. Further corresponding to this discharge an abrupt reduction in the efficiency of the pump also occurs. The abrupt reduction in the head as well as the efficiency of the pump indicates the inception of the cavitation. As such the value of the discharge at which there is an abrupt reduction in the head as well as the efficiency of the pump is the maximum discharge which the pump is able to provide without cavitation.

Q) List any four minor losses in pipes. Write the equations. The loss of head due to friction is known as major loss while the loss of energy due to change in velocity of fluid in magnitude and direction is called minor loss of energy. The minor loss of energy (head) includes (a)

Loss of head due to sudden enlargement

Consider a liquid flowing through a pipe which has sudden enlargement as shown in figure. Consider two sections 1-1 and 2-2 before and after the enlargement.

(b)

Loss of head due to sudden contraction

Consider a liquid flowing in a pipe which has a sudden contraction in area as shown in figure. Consider two sections 1-1 and 2-2 before and after contraction. As the liquid flows from large pipe o smaller pipe, the area of flow goes on decreasing and becomes minimum at section C-C. This section is called Venacontracta. The loss of head due to sudden contraction is actually due to sudden enlargement from vena-contracta to smaller pipe. (c)

(d)

Loss of head due to obstruction in pipe Whenever there is an obstruction in a pipe , the loss of energy takes place due to reduction of the area of the cross section of pipe at the place where obstruction is present. There is a sudden enlargement of the area of flow beyond the obstruction due to which loss of head takes place. Loss of head due to bend in pipe When there is a bend in pipe , the velocity of flow changes, due to which the separation of flow from the boundary and also formation of eddies takes place. Thus the energy lost.

Q). Define any two dimensionless numbers in model analysis.

Dimensionless numbers are those which have no dimension since they are obtained by dividing the inertia force by viscous force or gravity force or pressure force etc. As this is a ratio of one force to another. They are also called non dimensional parameters. Eg; Reynold’s number : It is defined as the ratio of inertia force of a fluid to the viscous force of the fluid. The expression for Reynold”s number is obtained as Inertia force

= Mass Acceleration of flowing fluid

Viscous force = Shear stress

Froude’s number : It is defined as the square root of the ratio of inertia force of a fluid to the gravity force.

Q) How turbines are classified? Give examples. The hydraulic turbines are classified according to the type of energy available at the inlet of the turbine, direction of flow through the vanes, head at the inlet of the turbine and specific speed of the turbines. Thus the following are the important classification of the turbines ; I.

According to the type of energy at inlet (a) Impulse turbine eg : Pelton wheel turbine (b) Reaction turbine

II.

According to the direction of flow through the runner (a) Tangential flow turbine (b) Radial flow turbine (c) Axial flow turbine (d) Mixed flow turbine

III.

IV. (a) (b) (c)

According to the head at the inlet of turbine (a) High head turbine (b) Medium head turbine (c) Low head turbine According to the specific speed of the turbine Low specific speed turbine Medium specific speed turbine High specific speed turbine

Q) What is the purpose of fitting draft tube? The draft tube is a pipe of gradually increasing area which connects the outlet of the runner to the tail race. It is used for discharging water from the exit of the turbine to the tail race. This pipe of gradually increasing area is called a draft-tube. One end of the draft-tube is connected to the outlet of the runner while the other end is submerged below the level of water in the tail race. The draft-tube, in addition to serve a passage for water discharge, has the the following purposes  It permits a negative head to be established at the outlet of the runner and thereby increase the net head on the turbine. The turbine may be placed above the tail race without any loss of net head and hence turbine may be inspected properly.

 It converts a large proportion of the kinetic energy rejected at the outlet of the turbine into useful pressure energy. Without the draft-tube the kinetic energy rejected at the outlet of the turbine will go waste to the tail race.

Q) What is cavitation ? How can it be avoided ? Cavitation is defined as the phenomenon of formation vapour bubbles of a flowing fluid in a region where the pressure of the liquid falls below its vapour pressure and the sudden collapsing of these vapour bubbles in a region of higher pressure. When the vapour bubbles collapse, a very high pressure is created. The metallic surfaces, above which these vapour bubbles collapse, is subjected to these high pressure, which cause pitting action on the surface. Thus cavities are formed on the metallic surface and also considerable noise and vibrations are produced. Precautions against cavitation ; (a)

(b)

The pressure of the flowing liquid in any part of the hydraulic system should not be allowed to fall below its vapour pressure. If the flowing liquid is water , then the absolute pressure head shouldn’t be below 2.5 m of water. The special materials or coatings such as aluminium-bronze and stainless steel, which are cavitation resistant materials, should be used.

Q)What is meant by specific speed of turbine? Derive a relation for specific speed of turbine ? It is defined as the speed of a turbine which is identical in shape, geometrical dimensions, blade angles. gate opening etc. with the actual turbine but of such a size that it will develop unit power when working under unit head It is denoted by the symbol N The specific speed is used in comparing the different types of turbines as every type of turbine has different specific speed. In M.KS. units, unit power is taken as one horse power and unit head as one metre. But in S. units, unit power is taken as one kilowatt and unit head as one meter. DERIVATION OF THE SPECIFIC SPEED: The overall efficiency (η0) of any turbine is given by:

Q. Draw the inlet and outlet velocity triangle of pelton wheel and explain the terms.?(cusat 2008)

The figure shows the shape of the vanes or buckets of the Pelton wheel. The jet of water from the nozzle strikes the bucket at the splitter, which split up the jet into two parts. These parts of the jet glids over the inner surfaces and come out at the outer edge. V1 = velocity of jet at inlet U1 = velocity of vane at inlet Vr1 = relative velocity of jet and vane at inlet Vw1 and Vf1 = the components of velocity of the jet V1 in the direction of motion and perpendicular to the direction of motion of the vane respectively Vw1 = velocity of whirl at inlet Vf1 = velocity of flow at inlet V2, U2, Vr2, Vw2, Vf2 are the corresponding values at outlet. Β = angle made by velocity of jet at outlet with direction of motion of the vane at outlet Φ = angle between relative velocity with direction of motion of vane at outlet

Q) Explain similitude . What is its importance in model studies ? Similitude is defined as the similarity between the model and its prototype in every respect ,which means that the model and prototype have similar properties or model and prototype are completely similar. Three types of similarities are 1. Geometric similarities The geometric similarity is said to be exists between the model and the prototype . The ratio of all corresponding linear dimension in the model and prototype are equal . L m = length of model bm = breadth of the model Dm = diameter of the model Am = area of model Vm = volume of model Lp, bP , Dp,Ap,Vp = corresponding values of prototype For geometric similarity between model and prototype , we must have the relation , LP/Lm = bp/bm = Dp/Dm = Lr Where Lr is called the scale ratio.

KINAMATIC SIMILARITY : Kinamatic similarity means the similarity of motion between model and prototype. Thus Kinamatic similarity is said to exist between the model and the prototype if the ratios of the velocity and acceleration at the corresponding points in the model and at the corresponding points in the prototype are the same. Since velocity and acceleration are vector quantities. Hence not only the ratio of magnitude of velocity and acceleration at the corresponding points in model and prototype should be same ; but the direction

of velocity and accelerations at the corresponding points in the model and prototype also should be parallel. Let Vp1 = velocity of fluid at point 1 in prototype. Vp2 = velocity of fluid at point 2 in prototype. ap1 = Acceleration of fluid at point 1 in prototype. ap2 = acceleration of fluid at point 2 in prototype And Vp1,Vm2,am2,am2 are the corresponding values at the corresponding points of fluid velocity and acceleration in the model. For kinematic similarity, we must have (Vp1/Vm1)=(Vp2/Vm2)= Vr Where Vr is the velocity ratio. For acceleration , we must have (ap1/am2)=(ap2/am2)=ar Where ar is the acceleration ratio. Also the directions of the velocities in the model and prototype should be same.

DYNAMIC SIMILARITY : Dynamic similarit means the similarity of forces between the model and prototype. Thus dynamic similarity is said to exist between the model and the prototype if the ratios of the corresponding forces at the corresponding points should be same. Let. (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.

And (Fim,(Fv)m,(Fg)m is the corresponding values of forces at the corresponding point in model. Then for dynamic similarity ,we have [(Fi)p/(Fi)m]=[(Fv)p/(Fv)m]=[(Fp)m/(Fg)m].....= Fr where Fr is the force ratio. Also the directions of the corresponding forces at the corresponding points in the model and prototype should be same.

Q. Calculate the gauge pressure and absolute pressure at a point 3m below the free surface of a having a sp.gravity of 1.53. The atmospheric pressure is equivalent to 750mm of mercury, the sp.gravity of mercury is 13.6 and density of water be 1000kg/m³? [ cusat 2008] Given, Depth of liquid, Z1 = 3m Sp.gravity, Sᶠ =1.53 Atmosperic pressure head, Zₒ = 750mm of Hg=750/1000 of Hg =.75 m of Hg Atmosperic pressure, pᵃᵗᵐ = ρₒ x g x Zₒ ρₒ= density of Hg= Sp.gra of Hg x density of water = 13.6 x 1000 kg/m³ Zₒ = pressure head in terms of Hg pᵃᵗᵐ = 13.6 x 1000 x 9.81 x 0.75 N/m² = 100062 N/m² Pressure at a point 3m below the free surface of the liquid,

p = ρ₁ x g x h Gauge press

p

Absolute pressure

= 1.53 x 1000 x 9.81 x 3 = 45028 N/m² = p + pᵃᵗᵐ = 45028 + 100062 = 145090 N/m²

Q. What is pilot tube? With the help f a neat sketch explain how a pilot tube can be used to determine the velocity at any point in a pipe [cusat 2008] It is a device used for measuring the velocity of flow at any point in a pipe or a channel. it is based on the principle that if the velocity of flow at a point becomes zero, the pressure there is increased due to the conversion of kinetic energy to pressure energy . In its simplest form, the pilot tube consists of a glass tube bent at right angles. The lower end which is bent through 90ᵒ is directed in the upstream direction. The liquid rises up in the tube due to the conversion of kinetic energy to pressure energy. The velocity is determined by measuring the rise of liquid in the tube. Consider two points [1] and [2] at the same level in such a way that point [2] is just as the inlet of the pilot tube and point [1]is far away from the tube p₁ = intensity of pressure at point [1]; v₁ = velocity of flow at [1] p₂ = intensity of pressure at point [1]; v₂ = velocity of flow at [1] H = depth of tube in liquid; h= rise of liquid in the tube above free surface Applying Bernoulli’s equation at [1] and [2] [p₁/ρg]+ [v₁²/2g] + z₁ = [p₂/ρg]+[ v₂²/2g]+z₂ But z₁= z₂; v₂=0;

[p₁/ρg] = pressure head at [1] =H;

[p₂/ρg] = pressure head at [2] =h + H So

H + [v₁²/2g] = h +H or h = [v₁²/2g] or

v = [2gh]½

This is theoretical velocity, but actual velocity is given by vᵃ = Cᵛ [2gh]½ Cᵛ<1

Q. What do you understand by the terms major energy loss and minor energy loss in pipes? Give reasons for loss of head due to sudden enlargement in pipes. [cusat 2008] The loss of head or energy due to friction in a pipe is known as major loss. These losses are large. It is mainly obtained from two formulae [i] Darcy- Weisbach formula hᶠ = 4.f.L.V²/ d x 2g [ii] Chezy’s Formula hᶠ = [f´/ρg][P/A].L.V² V = C[mi]½

: m is chezy’s formula

The loss of head or energy due to change in velocity of the following fluid in magnitude or direction is called minor loss of energy. It includes the following cases: 1. 2. 3. 4. 5. 6. 7.

loss of head due to sudden enlargement loss of head due to sudden contraction loss of head at the entrance of a pipe loss of head at exit of a pipe loss of head due to an obstruction in pipe loss of head due to bent in the pipe loss of head due to various pipe fittings

Loss of head due to sudden enlargement

Due to sudden enlargement that is change in diameter of the pipe , the liquid flowing from the smaller pipe is not able to follow the abrupt change of the boundary. Thus the flow separates from the boundary and turbulent eddies are formed hᵉ = [V₁ – V₂]²/2g

Q. Define an indicator. Draw a theoretical indicator diagram for a reciprocating pump. [Cusat 2008] The indicator for a reciprocating pump is defined as the graph between the pressure head in the cylinder and the distance travelled by piston from inner dead centre for one complete revolution of crank. As the maximum distance travelled by the piston is equal to the stoke length and hence the indicator diagram is a graph between pressure head and stroke length of the piston for one revolution. The pressure head is taken as ordinate stroke length as abscissa. Ideal indicator diagram: The graph between pressure head in the cylinder and stroke length of the piston for one complete revolution of the crank under ideal conditions is known as ideal indicator or theoretical indicator diagram. In the diagram the EF represents the atmospheric pressure head equal to 10.3m of water. Hᵃᵗᵐ = Atmosperic pressure head = 10.3m of water L = length of the stroke h = suction head

and h = delivery head

FIG. 1003

Q. Derive an expression for work done, when a jet of water strikes a flat vertical plate moving with a uniform velocity away from jet? [cusat 2008 ]

V = velocity of the jet a = area of cross section of the jet u = velocity of the flat plate here the jet will not strike with velocity V, but with a relative velocity (V - u) mass of water striking the plat per sec = ρ x area of jet x velocity with which jet strikes the plate = ρ x a (v – u) Force exerted by the jet on moving plat in the direction of the jet, Fˣ =mass of water striking per sec x [final velocity of striking – initial velocity] = ρ x a (v – u)[(v – u) – 0] = ρ x a (v – u) ² The work done by the jet on the plate, as plate is moving. For the stationary plates, the work done is zero. Work done per second by the jet on plat = force x distance in the direction of force/ time = Fx x u = ρ x a (v – u) ² x u

The unit here is watt (W).

Q) Distinguish between a) Absolute pressure and guage pressure? b) Simple manometer & differential manometer? Ans) The pressure on a fluid is measured in two different system. In one system, It is measured above the absolute zero or complete vaccum and it is called the absolute pressure and in other system, pressure is measured above the atmospheric pressure and it is called guage pressure. Thus:

1) Absolute Pressure: It is defined as the pressure which is measured with reference to absolute vaccum pressure. 2) Guage Pressure: It is defined as the pressure which is measured with the help of a pressure measuring instrument, in which the atmospheric pressure is taken as datum. The atmospheric pressure on the scale is marked as zero.

b) A 'manometer' is an instrument that uses a column of liquid to measure pressure, although the term is often used nowadays to mean any pressure measuring instrument. They are classified as 1. SIMPLE MANOMETER 2. DIFFERENTIAL MANOMETER Simple Manometer: A simple nanometer consist of a glass tube having one of uts end connected to a point where pressure is to be measured and the other end remains open to the atmosphere. Common types of simple manometer are a) Piezometer, b) U-tube manometer c) Single column manometer. A simple piezometer tube manometer: This method can only be used for liquids (i.e. not for gases) and only when the liquid height is convenient to measure. It must not be too small or too large and pressure changes must be detectable. The "U"-Tube Manometer : Using a "U"-Tube enables the pressure of both liquids and gases to be measured with the same instrument. The "U" is connected as in the figure below and filled with a fluid called the manometric fluid. The fluid whose pressure is being measured should have a mass density less than that of the manometric fluid and the two fluids should not be able to mix readily - that is, they must be immiscible.

Single column manometer: Single column manometer is used to measure small pressure intensities.

A single column manometer consists of a shallow reservoir having large cross sectional area when compared to cross sectional area of U – tube connected to it. For any change in pressure, change in the level of manometeric liquid in the reservoir is small and change in level of manometric liquid in the U- tube is large. b) Differential Manometer: An instrument in which the difference in pressure between two sources is determined from the vertical distance between the surfaces of a liquid in two legs of an erect or inverted U-shaped tube when each of the legs is connected to one of the sources. Most commonly types of differential manometers are a) U-tube differential manometer, b) Inverted U-tube differential manometer. Pressure measuring devices using liquid columns in vertical or inclined tubes are called manometers. One of the most common is the water filled u-tube manometer used to measure pressure difference in pitot or orifices located in the airflow in air handling or ventilation system. Vertical U-Tube Manometer

The pressure difference in a vertical U-Tube manometer can be expressed as pd = γ h =ρgh

(1)

where pd = pressure γ = specific weight of the fluid in the tube (kN/m3, lb/ft3 ) ρ = density (kg/m3, lb/ft3) g = acceleration of gravity (9.81 m/s2, 32.174 ft/s2) h = liquid height (m, ft)

The specific weight of water, which is the most commonly used fluid in u-tube manometers, is 9.81 kN/m3 or 62.4 lb/ft3. Example - Differential Pressure Measurement in an Orifice A water manometer connects the upstream and downstream of an orifice located in an air flow. The difference height of the water column is 10 mm. The pressure difference head can then be expressed as: pd = (9.8 kN/m3) (103 N/kN) (10 mm) (10-3 m/mm) = 98 N/m2 (Pa) where 9.8 (kN/m3) is the specific weight of water in SI-units. Inclined U-Tube Manometer

Common problems when measuring pressure differences in low velocity systems as air ventilation system are the low column heights and satisfying accurately. inclined tube manometer The pressure difference in a inclined u-tube can be expressed as pd = γ h sin(θ)

(2)

where h = length, difference in position of the liquid column along the tube (mm, ft) θ = angle of column relative the horizontal plane Inclining the tube manometer will increase the accuracy of the measurement. Example - Differential Pressure Measurement with an Inclined U-Tube manometer

We use the same data as in the example above, except that the U-Tube is inclined to 45o. The pressure difference head can then be expressed as: pd = (9.8 kN/m3) (103 N/kN) (10 mm) (10-3 m/mm) sin(45) = 69.3 N/m2 (Pa)

Q) Write short note on clasification of pump If the mechanical energy is converted in to hydraulic energy by means of centrifugal force acting on the liquid the pump is known as centrifugal pupm but if the machanical energy is converted to hydraulic energy(pressure energy) by sucking the liquid into the cylinder in which a piston is resiprocicating (moving backword and forward) which exert the trust on the liquid and increases its hydraulic energy(pressure energy) CETRIFUGAL PUMP: The discharge is 1)continuous and smooth 2)It handles large contity of 3)It can be used for lifting higly viscos liquid 4)It can be used for largedischarge tubes to smaller heads 5)Cost of centrifugal pump is less as compaired to recipocicating pum 6)Centrifugal pumps runs at high speed .They can be coupled to electric motors 7)The opration of centrifugal pump is smooth and without much noise .the maitanence cost is low 8)Centrifugal pumps needs smaller floor area and instalation cost is low 9)Efficency is high

Q)Explain Newton’s law of viscosity ? It states that the shear stress on a fluid element layer is directly proportional to the rate of shear strain . The constant of proportionality is called the coefficient of viscosity . Mathematically Ʈ ₌ µ du/dy

Fluids which obey the above relation are known as Newtonian fluids and the fluids which do not obey the relation are called Non Newtonian fluids.

Q)Explain the significance of stream function and velocity potential function ? Velocity potential function It is defined as a scalar function of space and time such that its negative derivative with respect to any direction gives the fluid velocity in that direction . It is defined by (ɸ) mathematically velocity potential is defined as ɸ ₌ (x,y,z) for steady flow such that u ₌ ∂ɸ/∂x v₌ - ∂ɸ/∂y w =-∂ɸ/∂z If velocity potential exists, the flow should be irrotational . If ɸ satisfies the Laplace equation, it represents the possible steady incompressible irrotational flow Stream function It is defined as the scalar function of space and time , such that its partial derivative with respect to any direction .It is denoted by (ᵠ). ∂ᵠ/∂x =v

∂ᵠ/∂y =-u If stream function exists , it is a possible case of fluid flow which may be rotational or irrotational . If ᵠ satisfies the Laplace equation , it is a possible case of an irrotational flow

Q.Differentiate the following: (1) steady and unsteady flow. (2) uniform and non uniform flow. Ans: (1) Steady and unsteady flow. Steady flow is defined as that type of flow in which the fluid characteristics like velocity,pressure,density etc.,at a point do not change with time.Thus for steady flow,mathematically, we have

Where(x0,y0,z01)is a fixed point in fluid field. Unsteady flow is that type of flow,in which the velocity,pressure or density at a point changes with respect to time.Thus, mathematically , for unsteady flow

(2) Uniform and Non uniform flows.

Uniform flow is defined as that type of flow in which the velocity at any given time does not changes with respect to space(i.e,length of direction of the flow).mathematically, for uniform flow

Where V = change of velocity. ɗS = length of flow in the direction S. Non uniform flow is that type of flow in which the velocity at any given time changes with respect to space. Thus mathematically, for non uniform flow

Q2.Explain the multistage centrifugal pumps with the help of a diagram? Ans: If a centrifugal pump consists of two or more impellers ,the pump is called a multistage centrifugal pump. The impellers may be mounted on the same shaft or on different shafts. A multistage pump is having the following two important functions: 1To produce a high head ,and 2To discharge a large quantity of liquid. If a high head is to developed, the impellers are connected in series(or on the same shaft ) while for discharge large quantity of liquid,the impellers (or pumps) are connected in parallel. *MULTISTAGE CENTRIFUGAL PUMPS FOR HIGH HEADS. For developing a high head,a number of impellers are mounted in series or on the same shaft as shown in fig.

The water from suction pipe enters the 1st impeller at inlet and is discharged at outlet with increased pressure. The water with increased pressure from the outlet of the 1st impeller is taken to the inlet of the 2nd impeller with the help of a connecting pipe as shown in fig. At the outlet of the 2nd impeller, the pressure of water will be more than the pressure of water at the outlet of the 1st impeller. Thus if more impellers are mounted on the same shaft ,the pressure at the outlet will be increased further.

Let, n= Number of identical impellers mounted on the same shaft, Hm= Head developed by each impeller. Then total head developed = n* Hm The discharge passing through ea h impeller is same. *MULTISTAGE CENTRIFUGAL PUMPS FOR HIGH DISCHARGE: For obtaining high discharge,the pumps should be connected in parallel as shown in fig. Each of the pumps lifts the water from a common pump and discharges

water to a common pipe to which the delivery pipes of each pump is connected. Each of the pump is working against the same head.

Let, n = Number of identical pumps arranged in parallel. Q = Discharge from one pump. .'. Total discharge = n * Q.

Q. Differentiate between impulse turbine and reaction turbine? Ans: 1. In impulse turbine,there are nozzle and moving blades are in series while there are fixed blades and moving blades are present in reaction turbine.(no nozzle is present in reaction turbine). 2. In impulse turbine pressure falls in nozzle while in reaction turbine in fixed blade boiler pressure falls.

3. In impulse turbine velocity of stream increases in nozzle while this work is to be done by fixed blades in the reaction turbine. 4. Compounding is to be done for impulse turbines to increase their efficiency while no compounding is necessary in reaction turbine. 5. In impulse turbine pressure drop per stage is more than reaction turbine. 6. The number of stages is required less in impulse turbine while required more in reaction turbine. 7. Not much power can be developed in impulse turbine than reaction turbine. 8. Efficiency of impulse turbine requires less space than reaction turbine. 10. Blade manufacturing of impulse turbine is not difficult as in reaction turbine it is difficult.

Q4. Write a note on kinematics similarity and dynamic similarity? Ans: KINAMATIC SIMILARITY : Kinamatic similarity means the similarity of motion between model and prototype. Thus Kinamatic similarity is said to exist between the model and the prototype if the ratios of the velocity and acceleration at the corresponding points in the model and at the corresponding points in the prototype are the same. Since velocity and acceleration are vector quantities. Hence not only the ratio of magnitude of velocity and acceleration at the corresponding points in model and prototype should be same ; but the direction of velocity and accelerations at the corresponding points in the model and prototype also should be parallel. Let Vp1 = velocity of fluid at point 1 in prototype. Vp2 = velocity of fluid at point 2 in prototype. ap1 = Acceleration of fluid at point 1 in prototype.

ap2 = acceleration of fluid at point 2 in prototype And Vp1,Vm2,am2,am2 are the corresponding values at the corresponding points of fluid velocity and acceleration in the model. For kinematic similarity, we must have (Vp1/Vm1)=(Vp2/Vm2)= Vr Where Vr is the velocity ratio. For acceleration , we must have (ap1/am2)=(ap2/am2)=ar Where ar is the acceleration ratio. Also the directions of the velocities in the model and prototype should be same.

DYNAMIC SIMILARITY : Dynamic similarit means the similarity of forces between the model and prototype. Thus dynamic similarity is said to exist between the model and the prototype if the ratios of the corresponding forces at the corresponding points should be same. Let. (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. And (Fim,(Fv)m,(Fg)m is the corresponding values of forces at the corresponding point in model. Then for dynamic similarity ,we have [(Fi)p/(Fi)m]=[(Fv)p/(Fv)m]=[(Fp)m/(Fg)m].....= Fr where Fr is the force ratio. Also the directions of the corresponding forces at the corresponding points in the model and prototype should be same.

Q5. Explain how fluids are classified. Using stress strain diagram explain the behavior of fluids? Ans: The fluids may be classified into the following five types: * Ideal fluid. * Real fluid. * Newtonian fluid. * Non Newtonian fluid. * Ideal plastic fluid.

* Ideal fluid: Fluid, which is incompressible and is having no viscosity,is known as an ideal fluid. Ideal fluid is only an imaginary fluid as all the fluids, which exist , have some viscosity. * Real fluid: A fluid, which possesses viscosity, is known as real fluid. All the fluids, in actual practice, are real fluids. * Newtonian fluid: A real fluid, in which the shear stress is directly proportional to the rate of shear strain is known as a Newtonian fluid.

* Non Newtonian fluid: A real fluid, in which the shear stress is not proportional to the rate of shear strain is known as a Newtonian fluid. * Ideal plastic fluid: A fluid , in which shear is proportional to the rate of shear strain is known as ideal plastic fluid.

Q.Describe differential manometer? Ans: Differential manometers are the devices used for measuring the difference of pressures between two points in a pipe or in two different pipes. A differential manometer consists of a U-tube, contain measured. Most commonly types of differential manometers are: 1. U-tube differential manometer. 2. Inverter U-tube differential manometer. *"U- TUBE DIFFERENTIAL MANOMETER" Fig shows the differential manometers of U- tube type.

In fig(a), the points A and B are at different level and also contains liquids of different sp.gr. These points are connected to the differential manometer. Let the pressure at A and B are Pa and Pb. Let. H= difference of mercury level in the U-tube. y= Distance of the centre of B, from the mercury level in the right limb. x= Distance of the centre of A, from the mercury level in the right limb. ρ1= Density of liquid at A. ρ2= Density of liquid at B. ρg= Density of heavy liquid or mercury.

*"INVERTED U-TUBE DIFFERENTIAL MANOMETER: It consists of an inverted U-tube,containing a light liquid. The two ends of the tube are connected to the points whose difference of inverted U-tube differential manometer connected to the points A and B. Let the pressure at A is more than the pressure at B.

Q7. What is priming? Why is it necessary? Ans: Priming of a centrifugal pump is defined as the operation in which the suction pipe, casing of the pump and a portion of the delivery pipe upto the delivery valve is completely filled up from outside source with the liquid yo be raised by the pump before starting the pump. Thus the air from these parts of the pump is removed and these parts are filled with the liquid to be pumped. The work done by the impeller per unit weight of liquid per sec is known as the head generated by the pump. Equation gives the head generated by the pump as = (1/g)Vw2*u2 metre. This equation is independent of the density of the liquid. This means that when pump is running in air, the head generated is in terms of metre of air. If the pump is primed with water, the head generated is same metre of water head is negligible and hence the water may not be sucked from the pump. To avoid this difficulty, priming is necessary.

Q. Derive Dancy-Weisbach equation for the loss of head due to friction in a pipe? Ans: The loss of head in pipe due to friction is calculated from Dancy Weisbach equation Let P1 = pressure intensity at section 1-1 V1 = velocity of flow at section 1-1 L =length of the pipe between section 1-1 and 2-2 d = diameter of pipe f’ =frictional resistance per unit wetted area per unit velocity hf = loss of head due to friction and P2 , V2 = are values of pressure intensity and velocity at section 2-2

Q9.Define equivalent length for minor losses in pipe flow. Derive an expression for determining the size of an equivalent pipe? Ans:Often a compound pipe consisting of several pipes of varying diameters and lengths is to be replaced by a pipe of uniform diameter,which is known as equivalent pipe. The uniform diameter of the equivalent pipe is known as the

equivalent diameter of the compound pipe. The size of the equivalent pipe may be determined as follows. If L1,L2,L3 etc., are the lengths and D1,D2,D3 etc.,are the diameters respectively of the different pipes of a compound pipeline, then the total head loss in the compound pipe ,nefleting the minor losses is

If D is the diameter and L is the length of the equivalent pipe then it would carry the same discharge Q if the head loss due to friction in the equivalent pipe is same as that in the compound pipe. The loss of head due to friction in the equivalent pipe is

Above equation is known as Dupuit's equation. Which may be used to determine the size of the equivalent pipe. Thus if the length of the equivalent pipe is equal to the total length of the compound pipe i.e, L=(L1+L2+L3+.......),then the diameter D of the equivalent pipe may be determined by using the given equation. Sometimes a pipe of given diameter D which is available may be required to be

used as equivalent pipe to replace a compound pipe, in which case the length of the equivalent pipe may be required to be determined and the same may also be determined by the equation.

Q) Define circulation and vorticity.

The flow along a closed curve is called circulation. The mathematical concept of circulation is the line integral, taken completely around a closed curve, of the tangential component of the velocity vector. Consider a closed curve C as shown in figure, and let at any point on the curve, the velocity of flow of fluid be V. If α is the angle between a small element dsalong the curve in the tangential direction and the velocity V, then the component of the velocity in the direction tangential to the curve is Vcosα. By the definition г around a closed curve C is Г=∫C V cosα ds

The vorticity at any point is defined as the ratio of the circulation around an infinitesimal closed curve at that point to the area of the curve, ie, it is defined as circulation per unit area. Thus the vorticity ζ may be expressed as ζ=Circulation/Area =

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Q)Explain the principle of differential manometer The differential manometer work on the principle of “PASCAL’S LAW. It states that the pressure or intensity of pressure at a point in a static fluid is equal in all directions. This is proved as: The fluid element is of very small dimensions ie,dx,dy and dz. Differential manometer are the devices used for measuring the difference of pressure between two points in a pipe or in two different pipes .A differential manometer consist of a u-tube , containing a heavy liquid,whose two ends are connected to the points ,whose difference of pressure is to be measured.Most commonly type of differential manometer are: 1.U-tube differential manometer 2.Inverted U-tube manometer .

Q)Explain the significances of Reynold’s number in classifying fluid flow. Laminar flow is defined as that type of flow in which the fluid move along well defined path or stream line and all the stream lines are straight and parallel .Thus the particle move in laminas or layers gliding smoothly over the adjacent later.This type of flow is also called stream line flow or viscous flow. Turbulent flow is that type of flow in which the fluid particle move in a zig-zag way .Due to the movement of fluid particle in a zig-zag way,the eddies formation takes place which are responsible for high energy loss .For a pipe flow ,the type is determined by a non dimensional number VD/v ,called the Reynold’s number . Where D = diameter of pipe

V =mean velocity of flow in pipe V =kinematic viscosity of fluid . If the Reynold’s number is less then 2000,the flow is called laminar .If the Reynold’s number is more than 4000,it is called turbulent flow.If the Reynold’s number is between 2000 and 4000,the flow may be laminar or turbulent

Q)Derive the expression for the force exerted by a jet impinging centrally on a stationary curved plate Let a jet of water strikes a fixed curved plate at the centre .The jet after strikes the plate,comes the same velocity if the plate is smooth and there is no loss of energy due to impact of jet,in the tangential direction of the curved plate .The velocity at outlet of the plate can be resolved into two component,one in the direction of jet and other perpendicular to the direction of the jet. Component of velocity in the direction of jet= -VcosƟ

(-ve sign is take as the velocity at outlet is in the opposite direction of the jetof water component from nozzle). Component of velocity perpendicular to the jet =VsinƟ Force exerted by the jet in the direction of jet, Fx=Mass per sec*[V1x-V2x] Where

V1x = initial velocity in the direction of jet =V

V2x = final velocity in the direction of jet = -VcosƟ Fx =ρaV[V-(-VcosƟ)] =ρaV[V+VcosƟ] Fx=mass per sec *[V1y-V2y] Where V1y = initial velocity in the direction of y =0 V2y =final velocity in the direction of y =VsinƟ Fy = ρaV[0-VsinƟ] =-ρaVsinƟ -ve sin means that force is acting in the downward direction .In this case the angle of deflection of jet=(1800-Ɵ)