## Turbo Machines - May 2016

### Mechanical Engg. (Semester 5)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1(a)** Explain any six major differences between turbomachines and positive displacement machines.(6 marks)
**1(b)** What are unit quantites? Derive the expressions to each of them.(6 marks)
**1(c)** The following data were obtained from the main characteristics of a Kaplan turbine of runner diameter 1 m. P_{u}=30.695,

Q_{u}=108.6,

N_{u}=63.6. Estimate

i) The runner diameter

ii) The discharge

iii) The speed of a simlilar runner working under a head of 30 m and developing 2000kW. Also

iv) determine the specific speed of the runner.(8 marks)
**2(a)** Define the polytropic efficiencyof a turbine. Draw the T-S diagram and show that the polytropic efficiency is given by$$\eta _{p}=\left [ \frac{n-1}{n} \right ]\left [ \frac{\gamma }{\gamma -1} \right ],$$ when n=Index of polytropic process,γ=Ratio of specific heats.(10 marks)
**2(b)** Air flows through an air turbine where its stagnation pressure is reduced in the ratio 5:1. The total-to-total efficiency is 80%. The air flow is 5 kg/s. If the total power output is 500kW, find

i) inlet total temperature

ii) actual exit total temperature

iii) actual exit static temperature if the flow velocity is 100m/s

iv) total-to-static efficiency.(10 marks)
**3(a)** Obtain an expression as shown below for energy transfer and degree of reaction as a function of discharge blade angleβ_{2} for a turbomachine. Make the following assumptions:

i) u_{2}=2u_{1},

ii) Constant radial velocity,

iii) No whirl velocity at inlet and inlet blade angle 45°.$$R=\frac{2+cot{\beta_2}}{4}$$(10 marks)
**3(b)** In an axial flow turbine, the discharge blade angles are 20° each, for both the stator and the rotor.The steam speed at the exit of the fixed blade is 140m/s. The ration of $$\frac{V_a}{u}=0.7$$ at the entry and 0.76 at the exit of the rotor blade. Find

i) the inlet rotor blade angle,

ii) the power developedby the blade ring for a mass flow rate 2.6kg/s,

iii) Degree of reaction.(10 marks)
**4(a)** With the help of inlet and outlet velocity diagrams, show that the degree of reaction for an axial flow compressor is given by

$$R=\frac{V_a}{2U}\left [ cot\beta _1+cot\beta _2 \right ]$$ where, V_{a}=axial flow velocity,

u = blade velocity,

β<sub<1< sub=""> and β_{2} are the vanes angles of inlet and outlet.</sub<1<><>(10 marks)
**4(b)** A centrifugal pump delivers water against a head of 25m. The radial velocity of flow is 3.5m/s and is constant, the flow rate of water is 0.05m^{3}/s . The blades are radial at tip and pump runs at 1500 rpm. Determine

i) Diameter at tip,

ii) Width of blade at tip,

iii) Inlet diffuser angle at impeller exit.(10 marks)
**5(a)** With a neat sketch, explain the pressure-velocity compounding of steam turbine.(8 marks)
**5(b)** In a Curtis stage with two rows of moving blades the rotor are equiangular. The first rotor has angle of 29° each while second rotor has angle of 32°each. The velocity of steam at the exit of nozzle is 530m/s and the blade coefficients are 0.9 in the first,0.95 in the stator and in the second rotor. If the absolute velocityat the stage exit should be axial, find

i) Mean blade speed

ii) The rotor efficiency

iii) The power output for a flow rate of 32kg/s.(12 marks)
**6(a)** Show that for a Pelton turbine the maximum hydraulic efficiency is given by

$$\eta _{max}=\frac{1=C_bcos\beta _2}{2}$$ where C_{b} is blade velocity co-efficient and β/_{2} is blade discharge angle.(8 marks)
**6(b)** Explain the function of a draft tube and mention its types.(4 marks)
**6(c)** In a Francis turbine, the discharge is radial, the blade speed at inlet is 25m/s .At the inlet tangential component of velocity is 18m/s. The radial velocity of flow is constant and equal to 2.5m/s. Water flows at the rate 0.8m^{3}/s . The utilization factor is 0.82. Find

i) Euler's head

ii) Power developed

iii) Inlet blade angle

iv) Degree of reaction(R). Draw the velocity triangles.(8 marks)
**7(a)** What are the applications of multi-stage centrifugal pumps? With a neat sketch, explain centrifugal pumps in series and parallel.(8 marks)
**7(b)** Explain the phenomenon of cavitation in centrifugal pump.(4 marks)
**7(c)** A centrifugal pump impeller has radial vanes from inner radius of 8 cm to outer radius 24cm. The width of the impeller is consatnt and id 6 cm between the shrouds. If the speed is 1500 rpm and the discharge is 250 lit/s. Find

i) change in enthalpy

ii) The outlet pressure if inlet pressure is 0.8kPa and water flow is outword.(8 marks)
**8(a)** Define the following terms of centrifugal compressor:

i) Slip factor

ii) Power factor

iii) Pressure coefficient.(6 marks)
**8(b)** Explain the phenomenon of surging in centrifugal compressor.(4 marks)
**8(c)** The speed of an axial flow compressor is 15,000rpm. The mean diameter is 0.6m. The axial velocity is constant and is 225m/s. The velocity of whirl at inlet is 85m/s. The work done is 45kJ/kg of air. The inlet conditions are 1 bar and 300 K. Assume a stage efficiency of 0.89. Calculate

i) Fluid deflection angle,

ii) Pressure ratio,

iii) Degree of reaction,

iv) Mass flow rate of air. Power developed is 425kW.(10 marks)