Part -1: PRIME MOVERS AND FLUID MACHINES                               

Q1. Derive the dimensionless terms using Buckingham's π-theorem for analysis of different turbo-machines and discuss the physical significance of these dimensionless terms.  In addition, also discuss how the formula for specific speed for a hydraulic turbine can be derived.

Q2. Derive the condition for maximum efficiency of a flat plate based turbine and find the value for its maximum efficiency. Also discuss the ways for increasing the efficiency of such a turbine.

Q.3 A radial flow hydraulic turbine produces 32 kW under a head of 16 m and running at 100 rpm. A geometrically similar turbine producing 42kW under a head of 6m is to be developed. If the efficiency of both the turbines is assumed to be 92 percent, find the diameter ratio between the turbines, the volume flow rate through the new turbine and speed of the new turbine.

Q.4 A Pelton turbine develops 12900kW at 425rpm under a head of 505m. The overall efficiency of the machine is 84 percent. Find the discharge required through the turbine, diameter of the turbine wheel, and diameter of the nozzle. Assume the jet velocity coefficient as 0.98 and the ratio of blade speed to jet speed as 0.46.

Q.5 A Kaplan turbine develops 40 MW while running at 240 rpm and consumes 2.18 m³/s of water. The specific-speed is 800 and ψ is 0.7. Find the available head. The hub to outer diameter ratio for the wheel is 0.35. The wheel is designed so that the fluid leaves it axially. Find the speed ratio (based on outer diameter), the moving blade angles and guide blade angles at hub as well as at tip.

Q6. What purpose is served when we put centrifugal pumps in series or in parallel? Discuss with the help of performance characteristic curves, the limitations of installing different capacity centrifugal pumps in series or parallel.  Also explain the shift in point of operation when two similar centrifugal pumps are put in series as well as parallel.

Q7.   A centrifugal pump impeller runs at 950rpm. Its external and internal diameters are 500 mm and 250 mm. The vanes are set back at an angle of 35^o to the outer rim. If the radial velocity of the water through the impeller be maintained constant at 2 m/s, find the angle of the vanes at inlet, the angle of the guide vanes and the work done by the impeller per kg of water.

Q8.   A single acting reciprocating pump has a plunger diameter of 250 mm and stroke length of 450 mm. the suction pipe is 125 mm diameter and 12 m long with a suction lift of 3 m. An air vessel is fitted to the suction pipe at a distance of 1.5 m from the cylinder and 10.5 m from the sump water level. If the atmospheric pressure is 10 m of water and separation takes place at 7.5 m vacuum, find the speed at which the crank can operate without separation to occur when Darcy's friction factor is 0.04.            

Q.9 A centrifugal compressor running at 10000 rpm delivers 660 m³/min of free air. The air is compressed from 1 bar and 20^oC to a pressure of 4 bar with an isentropic efficiency of 82%. The blades are radial at the outlet of impeller and flow velocity of 62 m/s is constant throughout. The outer radius of impeller is twice the inner and the slip factor is 0.9. Calculate (i) the final temperature of air (ii) power required to drive the compressor (iii) impeller diameters at inlet and outlet (iv) Impeller blade angle at inlet (v) diffuser blade angle at inlet.    A Pelton turbine develops 12900kW at 425rpm under a head of 505m. The overall efficiency of the machine is 84 percent. Find the discharge required through the turbine, diameter of the turbine wheel, and diameter of the nozzle. Assume the jet velocity coefficient as 0.98 and the ratio of blade speed to jet speed as 0.46.                                                           

Q.10 An axial flow compressor with an isentropic efficiency of 85% draws air at 20^oC and compresses it through a pressure ratio of 4:1. The mean blade speed and flow velocity are constant throughout the compressor. Assuming 50% degree of reaction and taking blade velocity as 180 m/s and work input factor 0.82, determine (i) flow velocity (ii) number of stages if work requirement is equal in all stages. Take α₁ = 12^o and β₁ = 42^o.

Part -2: Power Generation

Q.1. Explain with neat sketch the effect of super heat on Rankine cycle efficiency. 

Q.2. Draw a line diagram and T-S diagram for Ideal regenerative cycle, obtain the expression of its efficiency and turbine work. State the limitations of the Ideal regenerative cycle.

Q.3. In a cogeneration plant, the power load is 5.6 MW and the heating load is 1.163 MW. Steam is generated at 40 bar and 500^oC and is expanded isentropically through a turbine to a condenser at 0.06 bar. The heating load is supplied by extracting steam from the turbine at 2 bar, which condensed in the process heater to saturated liquid at 2 bar and then pumped back to the boiler.

Compute (a) the steam generation capacity of the boiler in t/h, (b) the heat input to the boiler in kW, (c) the fuel burning rate of the boiler in t/h if a calorific value 25 MJ/kg is burned and the boiler efficiency is 88%, (d) the heat rejected to the condenser, (e) the rate of flow of cooling water in the condenser if the temperature rise of water is 6^oC.

 Q.4. Obtain the expression overall efficiency in terms of boiler efficiency for Brayton - Rankine combined cycle plant.

 Q.5. Obtain the expression for slip ratio (S) in terms of quality, void fraction, and specific volume for two phase flow in a riser.

 Q.6. A furnace wall riser 18 m long, 76.2 mm OD, and 6.1 mm thick receives saturated water at 80 bar and 1.5 m/s velocity. Assuming a circulation ratio is 12.5 and slip ratio of 1.2. Determine (i) Pressure head developed, (ii) void fraction at riser exit, (iii) rate of steam formation in the riser tube.