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Tuesday, 16 June 2015

Fluid Mechanics and thermodynamics of turbomachinary- Model question paper for B.E/B.Tech Engineering



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 m3/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 500, the exit flow angle is measured as 15.80. 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 CL=0.8 with CD=0.045. The inlet guide vanes produce a flow angle of 200 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 450 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 m3/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 900 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 m3/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 m3/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 (R2) and far downstream of the disc (R3) compared with the radius far upstream (R1). (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 = 2.50. 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 CL is 0.1 × angle of incidence, what is the final value of the lift co-efficient? ( 6 Marks)

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