FLUID POWER ENGINEERING
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ASSINGNMENT – 1
FLOW THROUGH THE PIPE
Derive the Borda Carnot Equation for loss of head in pipe.
Derive the equation of Darcy Weisbach formula and Chezy’s formula.
Define and explain the term (i) H.G.L. and (ii) T. E. L.
What is compound pipe?
Derive the equation for the loss of head when pipes are connected in series and parallel.
Prove that head loss due to friction is equal to one- third of total head at inlet of maximum power
transmission through pipe. And find maximum efficiency.
7) Show that the diameter of the nozzle for maximum power transmission is given by 𝑑
=(
𝐷5
0.25
)
8𝑓𝑙
8) Explain the phenomena of Water hammer. Obtain an expression for the rise of pressure when the
flowing water in pipe is brought to rest by closing the valve gradually.
9) Obtain an expression for the rise of pressure when the flowing water in pipe is brought to rest by
closing the valve suddenly closure (i) pipe is rigid and (ii) Elastic .
10) What is syphon? Explain it.
11) A pipe of diameter 300 mm and length 1000 m connects two reservoir, having difference of water
levels as 15 m. determine the discharge through the pipe. If an additional pipe of diameter 300 mm
and length 600 m is attached to the last 600 m length of the existing pipe, find the increase in the
discharged.
12) A pipe line of length 2100 m is used for transmitting 103 kW. The pressure at inlet of the pipe is
392.4 N/cm2. if the efficiency of transmission is 80 %, find the diameter of pipe. Take f = 0.005
13) Three reservoir A,B and C are connected by a pipe system having length 700 m ,1200 m, and 500
m and diameters 400 mm, 300 mm, and 200 mm respectively. The water levels in reservoir A and B
from a datum line are 50 m and 45 m respectively. The level of water in reservoir C is below the
level of water in reservoir B. find the discharge into or from the reservoir B and C if the rate of flow
from reservoir A is 150 litres per sec. find the height of water level in the reservoir C. Take f = 0.005
14) A horizontal pipe line 50 m long is connected to a water tank at one end and discharges freely into
the atmosphere at the end. For the first 30 m of its length from the tank, the pipe is 200 mm diameter
and its diameter is suddenly enlarged to 400 mm. The height of water level in the tank is 10 m above
the centre of the pipe. Considering all minor losses, determine the rate of flow. Take f = 0.01 for
both sections. Also draw the H.G.L and T.E.L.
15) Three pipes of lengths 800 m, 600 m and 300 m and of diameters 400 mm, 300 mm, and 200 mm
respectively are connected in series. The ends of the compound pipe is connected to two tanks,
whose water surface levels are maintained at a difference of 15 m. determine the rate of flow of
water through the pipe if f = 0.005 what will be diameter of a single pipes of length 1700 m and f =
0.005 which replace the three pipes.
16) Two sharp ended pipes of diameters 60 mm and 100 mm respectively, each of length 150 m are
connected in parallel between two reservoir which have a difference of level of 15 m. if co-efficient
of friction for each pipe is 0.08, calculate the rate of flow for each pipe and also the diameter of a
single pipe 150 m long which would give the same discharged if it were substituted for the original
two pipes.
ASSINGNMENT – 2
IMPACT OF JET AND JET PROPULSION
1) Define the terms (a) Impact of jet (b) Jet propulsion.
2) Obtain the expression for force exerted by jet of water on a fixed vertical plate and inclined plate in
the direction of jet.
3) Show that the angle of swing of vertical hinge plate is given by sin 𝜃 =
𝜌𝑎𝑉 2
𝑊
4) Prove that the work done per second on series of moving curved vane by a jet of water striking at one
of the tips of the vane is given by
𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒/ sec = 𝜌𝑎𝑉1 [𝑉𝑤1 ± 𝑉𝑤2 ] × 𝑢
5) Find the expression for efficiency of series of the moving curved vanes when a jet of water strikes the
vane at the one of the its tips. prove the maximum efficiency is when u = V and the value of the
maximum efficiency is 50%
6) Show that the curved redial vane, the work done per sec is given by
𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒/ sec = 𝜌𝑎𝑉1 [𝑉𝑤1 𝑢1 ± 𝑉𝑤2 𝑢2 ]
7) Find the expression for the propelling force and work done per sec on a tank which is provided with
orifice through which jet of water is coming out and tank is free to move.
8) Show that the efficiency of free jet striking normally on a series of flat plate mounted on a periphery
of wheel can never exceed 50%.
9) Derive the equation of force exerted by jet of water on moving inclined plate in the direction of jet.
10) Jet of water having a velocity of 30 m/s , strikes a series of radial curved vane mounted on wheel
which is rotating at 300 r.p.m. jet makes an angle of 300 with tangent to wheel at inlet and leave the
wheel with velocity of 4 m/s at angle of 1200 to the tangent to the wheel at outlet. Water is flowing
from outward in radial direction. The outer and inner radii of the wheel are 0.6 m and 0.3 m
respectively. Determine (a) Vane angle at inlet and outlet (b) Work done/ Sec per kg of water (c)
Efficiency of wheel.
11) A jet of water strikes at the centre of a curved vane. The jet speed is ‘V’ m/s and the vane
moves at ‘u’ m/s in the direction of the jet. If the outgoing jet makes an angle ‘θ’ with the
entering jet. Prove that (a) For maximum efficiency u=V/3 (b) Maximum
efficiency=8/27*(1+cos θ)
12) An oil jet of Specific gravity 0.8 of 40 mm diameter strikes a stationary plate inclined at an angle 30 0
with the axis of jet at a velocity of 30 m/s. Find the force exerted by the jet on the plate in the
direction (1) Normal to plate. (2) Along the X-axis and Y-axis.
13) Water in a jet propelled boat is drawn mid ship and is discharge at back with an absolute velocity 30
m/s. The cross-section area of the jet at the back is 0.04 m2 and boat is moving in sea water with a
speed of 30 km/hr. Determine (a) propelling force of the boat. (b) Power (c) Efficiency of jet
propulsion.
14) The water in a jet propelled boat is drawn through inlet opening facing the direction of motion of the
ship. The boat is moving in sea water with speed of 40 km/ hr. The Absolute velocity of jet of the
water discharge at the back is the 40 m/s area of jet of water is 0.04 m2. Determine (a) propelling
force of the boat. (b) Power (c) Efficiency of jet propulsion.
ASSINGNMENT – 3
Hydraulic turbine
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Explain the essential element of hydroelectric power plant with neat sketch.
What are advantages and disadvantages of hydroelectric power plant?
What is a draft tube? Why is it used in a reaction turbine? What are the various types of it?
Define specific speed of a turbine and derive an expression for the same.
Define the term “Governing of a turbine”. Explain with neat sketch governing mechanism of
Francis Turbine.
Explain: Hydraulic efficiency, Mechanical efficiency, Overall efficiency with reference to
water turbines. Give expressions of each efficiencies
Derive the equations of theoretical power developed by a Pelton wheel and its hydraulic
efficiency. Obtain the condition for maximum hydraulic efficiency.
Explain difference between impulse and reaction turbine
Derive the equations of the hydraulic efficiency for a Francis turbine having velocity of flow
through runner as constant is given by
1
𝜂ℎ =
tan 𝛼 2
1+
tan 𝛼
2 (1 − tan 𝜃 )
where
θ= Runner vane angle at inlet
α=guide blade angle at inlet
10. The penstock supplies water from a reservoir to the pelton wheel with a gross head of 500m.
one third of the gross head is lost I friction in the penstock. The rate of flow of water
through the nozzle fitted at the end of the penstock is 2.0m3/s. The angle of deflection of the
jet is 1650. Determine the power given by the water to the runner and hydraulic efficiency of
the pelton wheel. Take speed ratio = 0.45 and Cv = 1.0
11. A pelton wheel is to be designed for the following specification. Shaft power = 11,772kw;
Head = 380m; Speed = 750 r.p.m; Over efficiency = 86%; jet diameter is not to exceed onesixth of the wheel diameter. Determine (1) The wheel diameter (2) the number of jets
required (3) Diameter of jet Take CV = 0.985 and Ku = 0.45
12. The following data is related to a pelton wheel turbine.
(I) Head at the base of the nozzle = 80 m
(II) Diameter of the jet = 100 mm
(III) Discharge of the nozzle = 0.30 m3/s
(IV) Power at the shaft = 206 KW
(V) Power absorbed in mechanical resistance = 4.5 KW
Determine power lost in nozzle and power lost due to hydraulic resistance in the runner.
13. As inward flow reaction turbine has external and internal diameters as 1.0 m and 0.6 m
respectively. The hydraulic efficiency of the turbine is 90% when the head on the turbine is
36 m. The velocity of flow at outlet is 2.5m/s and discharge at outlet is radial. If the vane
angle at outlet is 150 and width of the wheel is 100 mm at inlet and outlet, determine: (1) the
guide blade angle (2) speed of the turbine (3) vane angle of the runner at inlet (4) volume
flow rate (5) power developed.
ASSINGNMENT – 4
Pump
1. Explain the working of centrifugal pump with neat sketch.
2. Define& expression the following terms.
(1)Suction head (2) delivery head (3) static head (4) manometric head (5) mechanical
efficiency (6) manometric efficiency (7) volumetric efficiency (8) overall efficiency
3. Obtain the expression for pressure rise in impeller of Centrifugal (C. F.)Pump.
4. Prove that the manometric head of Centrifugal pump running at speed N and giving a
discharge Q is given by Hmano = AN2 + BNQ + CQ2.
5. Derive an expression for minimum speed of C.F. pump for delivery to commence.
6. Explain the characteristic curve of C.F. pump
7. Explain the working of submersible pump with neat sketch.
8. Explain the working of deep well pump with neat sketch.
9. During a performance test of C. F. pump following reading are taken
Vaccum gauge reading on suction side
250 mm of Hg
Pressure gauge reading on delivery side
15 m of water
Vertical distance between the gauge
50 cm
Output of electric motor
15 KW
Diameter of delivery pipe
15 cm
Diameter of Suction pipe
20 cm
Discharge
60 LPS
Find the overall efficiency of the C. F. pump.
10. A C. F. pump having outer diameter equal to two times inner diameter and running at 1200
rpm work against net head of 75 m. The velocity of flow through the impeller is constant
and equal to 3 m/s. The vanes are set back at the angle of 300 at the outlet. If outer diameter
of impeller is 600 mm and width of outlet is 50 mm find (1) Vane angle at inlet (2) Work
done by impeller (3)Manometric efficiency (4)Discharge.
11. A centrifugal pump is running at 500 rpm and discharge 8 m3/ min against a head of 10 m. It
has an impeller of 50 cm outer diameter and 25 cm inner diameter. Vanes are set back at
angle of 45o .The constant velocity of flow is 2 m/s. calculate (1) the manometric efficiency
(2) vane angle at inlet (3) width of impeller at inlet & outlet (4) water power .
12. Find the power required to drive a centrifugal pump which delivers 0.04m3/s of water to a
height of 20 m through a 15 cm diameter pipe and 100 m long. The overall efficiency of the
pump is 70 % and co-efficient of friction f = 0.015 in the formulae hf = 4flV2 / 2gd
ASSINGNMENT – 5
Compressor
1. Prove that the work done / kg of air in single stage reciprocating air Compressor without
clearance is given by
Where notations have their usual meaning.
2. What is pre-whirl? Sketch the velocity diagrams with and without pre whirl for a centrifugal
compressor.
3. Explain the phenomenon of surging and stalling in an axial flow air compressor and
centrifugal compressor.
4. Sketch the possible compressor on P-V and T-S diagram of reciprocating air compressor.
5. Define (1)FAD (2) Clearance ratio (3) Isothermal efficiency (4) Volumetric efficiency (5)
Adiabatic efficiency
6. Show that for a two stage air compressor with perfect intercooling , total work of
compression become minimum when pressure ratio in each stage is equal.
7. Describe with neat sketch the working of centrifugal compressor. State it’s advantages and
application.
8. Explain slip factor , power input factor , pressure co-efficient of centrifugal compressor
9. With the help of velocity diagram and head capacity curve, discuss salient features of radial,
back ward and forward curve vanes in centrifugal compressor.
Chapter 6 : Miscellaneous Machines
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Explain with the help of a neat sketch the working and principle of hydraulic press.
Draw a neat sketch, and explain the working of a hydraulic accumulator.
Explain working of differential hydraulic accumulator.
Explain with line diagram the construction and working of hydraulic intensifier.
What is function of hydraulic jack? Where it is used? Explain with neat sketch the working
of hydraulic jack.
6. Explain working of hydraulic ram with neat sketch.
7. Explain the fluid torque convertor with neat sketch