1(a) Write a note on the equation
of continuity. (4 Marks)

(b) Explain the terms turbine
polytropic efficiency and reheat factor. (4 Marks)

(c) Describe with the aid of sketches, the
relationship between geometry and specific speed for pumps. (8 Marks)

(d) A fan operating at 1750
rev/min at a volume flow rate of 4.25 m

^{3}/s develops a head of 153 mm measured on a water-filled U-tube manometer. It is required to build a larger, geometrically similar fan that will deliver the same head at the same efficiency as the existing fan but at a speed of 1440 rev/min. Calculate the volume flow rate of the larger fan. (4 Marks)
2(a) Write a note on cascade
performance parameters. (6 Marks)

(b) Explain Mollier diagram for
an impulse turbine stage. (6 Marks)

(c) Derive an approximate
expression for the total-to-total efficiency of a turbine stage in terms of the
enthalpy loss coefficients for the stator and rotor when the absolute
velocities at inlet and outlet are not equal. (4 Marks)

(d) A two-dimensional compressor
cascade is tested in air with an inlet stagnation pressure of 1 bar and an
inlet stagnation temperature of 300 K. For an inlet Mach number of 0.75 and an
inlet flow angle of 50

^{0}, the exit flow angle is measured as 15.8^{0}. Determine the mass flow rate per unit frontal area. Assuming the flow is isentropic; calculate the exit Mach number and the static pressure ratio across the cascade. (4 Marks)
3(a) Explain the velocity
diagrams for a compressor stage. (6 Marks)

(b) Derive an expression for the
degree of reaction of an axial compressor stage in terms of the flow angles
relative to the rotor and the flow coefficient. (6 Marks)

(c) The rotational speeds of a four-bladed axial
flow fan is 2900 rev/min. At the mean radius of 16.5 cm the rotor blades
operate at C

_{L}=0.8 with C_{D}=0.045. The inlet guide vanes produce a flow angle of 20^{0}to the axial direction and the axial velocity through the stage is constant at 20 m/s. For the mean radius, determine
(i) the rotor relative flow
angles, (ii) the stage efficiency, (iii) the rotor static pressure increase and
(iv) the size of the blade chord needed for this duty. (8 Marks)

4(a) Prove that in a
turbomachine, equal work is delivered at all radii and the total pressure
losses across a row are uniform with radius. (8 Marks)

(b) Derive the radial equilibrium
equation for an incompressible fluid flowing with axisymmetic swirl through an
annular duct. (8 Marks)

(c) Gas leaves an untwisted
turbine nozzle at an angle 45

^{0}to the axial direction and in radial equilibrium. Determine the axial velocity at a radius of 0.6 m when the axial velocity is 100 m/s at a radius of 0.3 m. (4 Marks)
5(a) Define slip factor. Write a
note on slip factor correlations. (6 Marks)

(b) Distinguish between symmetric
volute and overhung volute. (4 Marks)

(c) Using the performance chart
given by Sovran and Klomp, determine the efficiency of a conical low speed
diffuser to give maximum pressure recovery with a prescribed non-dimensional
length of 8.0 and evaluate the included angle of the cone. (6 marks)

(d) A model low speed centrifugal
compressor runs at 430 rpm and delivers 10 m

^{3}/s of air against pressure head of 60 mm of water. If the pump efficiency is estimated to be 80%, how much power is required to drive the compressor? (4 Marks)
6(a) Distinguish between
Cantilever turbine and 90

^{0}IFR turbine. (4 Marks)
(b) Define spouting velocity. (3
Marks)

(c) Several decisions need to be
made regarding the design of the rotor exit. Explain. (5 Marks)

(d) An IFR turbine is required
with a power output of 300 kW driven by a supply of gas at a stagnation
pressure of 222 kPa, at a stagnation temperature of 1100 K, and at a flow rate
of 1.5 kg/s. The turbine selected by the engineer has 13 vanes and preliminary
tests indicate it should have a total –to-static efficiency of 0.86. Based on
the optimum efficiency design method sketch the appropriate velocity diagrams
for the turbine and determine (i) the absolute and relative flow angles at
rotor inlet, (ii) the overall pressure ratio and (iii) the rotor tip speed. ( 8
Marks)

7(a) With a neat figure, explain
the working of Pelton turbine. (6 Marks)

(b) Write a note on effect of
size on turbomachine efficiency. (4 marks)

(c) A model of Francis turbine is
built to a scale of one fifth of full size and when tested it developed a power
output of 3 kW under a head of 1.8 m of water, at a rotational speed of 360
rev/min and a flow rate of 0.215 m

^{3}/s. Estimate the speed, flow rate and power of the full-scale turbine when working under dynamically similar conditions with a head of 60 m of water. (6Marks)
(d) A model of a Kaplan turbine,
built to a scale of 1/6 of the full scale prototype, develops an output of 5kW
from a net head of 1.2 m of water at a rotational speed of 300 rev/min and a
flow rate of 0.5 m

^{3}/s. Determine the efficiency of the model. (4 Marks)
8(a) What is the role of tower
height in the design of horizontal axis wind turbine? (4 Marks)

(b) Determine the radii of the
unmixed slipstream at the disc (R

_{2}) and far downstream of the disc (R_{3}) compared with the radius far upstream (R_{1}). (4 Marks)
(c) Explain Aileron control and
blade pitch control. (6 Marks)

(d) A three-bladed HAWT with a
rotor of 60 m diameter operates with a tip-seed ratio, J=5.5. At a radius of
25m, the blade chord is 1.5 m and the blade pitch angle, β = 2.5

^{0}. Assuming negligible drag and using an iterative method of calculation, determine values for the axial and tangential induction factors a and a^{’}at that section. Assuming that C_{L}is 0.1 × angle of incidence, what is the final value of the lift co-efficient? ( 6 Marks)
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