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Revision Tutorial

1. An engine working on the air standard Dual Combustion Cycle has a single cylinder whose bore is 10cm and stroke is 20 cm. The clearance volume of the cylinder is 6 % of the swept volume. The suction

conditions are 1 bar and 30 oC. The maximum cycle pressure is 75 bar. The volume cut-off ratio,β, is

1.80. Sketch the p-V and T-s diagrams for this cycle and determine the:

(a) compression ratio,(b) heat supplied (in kJ/kg),

(c) heat rejected (in kJ/kg),(d) nett work done (in kJ/kg),

(e) thermal efficiency of the cycle. (Ans: 17.67,1270.9,449,821.9,64.7%.)

2. An engine operating on the dual combustion cycle has a compression ratio of 18:1. At the beginning of the cycle,

the pressure and temperature are 1.01 bar and 30 oC. The maximum cycle pressure and temperature are 70 bar 

and 1500 oC. Sketch the p-V and T-s diagrams of this cycle and determine the:

(a) cut off ratio,

(b) heat supplied in kJ/kg,

(c) heat rejected in kJ/kg,(d) nett work done in kJ/kg,

(e) thermal efficiency. (Ans: 1.52, 755.9, 256.1, 499.8, 0.661)

3. Superheated steam at 50 bar absolute and 400o C (point 1) expands isentropically to 2 bar absolute in a high

 pressure stage turbine. The steam is then reheated at constant pressure to 300o C before passing through the

low-pressure stage turbine to a condenser pressure of 0.05 bar absolute. The low pressure stage turbine has an

isentropic efficiency 90%. Neglect the feedpump work and calculate the:

(a) work output in kJ/kg,

(b) heat supplied in kJ/kg,

(c) thermal efficiency of the cycle,

(d) specific steam consumption in kg/kwh. (Ans: 1276, 3612, 0.353, 2.82)

4. A 200 MW steam plant operates on the Rankine cycle with superheat and reheat. The steam enters the

high-pressure turbine at 110 bar absolute and 500 oC. After isentropic expansion, the steam leaves thehigh-pressure turbine at 10 bar absolute. The steam is then reheated at constant pressure to 500 oC

 before it expands to a pressure of 0.05 bar absolute in the low-pressure turbine. The low-pressure

turbine has an isentropic efficiency of 80 %. Sketch the T-s diagram for the cycle and neglecting thefeed pump work, find the:

(a) dryness fraction of the steam leaving the high pressure turbine, b (b) thermal efficiency of the cycle,

c (c) specific steam consumption,(d) mass flow rate of steam in kg/s. (Ans: 0.9894, 0.378, 2.41, 134)

5. A single stage, single acting air compressor operates at 800 rpm. It has a bore of 120 mm and a stroke

of 150 mm. The clearance volume is 3 % of the swept volume. The intake conditions are 1.01 bar and

32 oC and the delivery pressure is 8 bar. The index of compression and expansion (n)is 1.3. Sketch the p-V diagram for the cycle and calculate the:

(a) induced volume (in m3/s),(b) mass flow rate (in kg/s),

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(c) volumetric efficiency at inlet conditions

(d) indicated power (in kW). (Ans: 01996,.02303,0.8827,5.347)

6. A single stage air compressor has a bore of 50 mm and a stroke of 60 mm. The clearance volume is 8% of the

swept volume. The intake conditions are 110 kN/m2 and 32oC and the delivery pressure is 400 kN/m2. Draw the

 p-V diagram for this compressor cycle. The compression and expansion processes are polytropic with n = 1.3.

The compressor speed is 2900 rpm. Take atmospheric conditions to be 101.3 kN/m2 and 27 oC and calculate the

following:

(a) induced volume in m3,

(b) F.A.D. per sec.,

(c) volumetric efficiency at atmospheric conditions,

(d) volumetric efficiency at inlet conditions,

(e) indicated power (kW). ( Ans: 0.1018 x 10-3 m3, 5.25 x 10-3 m3/s, 92.3%, 86.4%, 0.814 kW)

7. A pipe has an inlet diameter of 0.2 m and an outlet diameter of 0.4 m. Water enters the pipe at 2 mabove the ground with a velocity of 2.8 m/s and a pressure of 150 kN/m2. It leaves the pipe at 6 m

above the ground. Determine the:

(a) potential head, velocity head, pressure head and total head at the inlet,

(b) velocity head and pressure head at the outlet,

(c) volume flow rate of the water.(Ans:2,0.4,15.29,17.69,0.025,11.66,0.088)

8. Water is flowing inside a pipe inclined at an angle to the ground. Section (1) of this pipe is 4 m abovethe ground. It has a diameter of 0.2 m, a pressure of 125.57 kN/m 2 and a velocity of 5.85 m/s. Section

(2) of the pipe is 8 m above the ground and has a diameter of 0.3 m. Determine the:

(a) volumetric flowrate of the water,(b) total head at section (1),

(c) velocity and pressure at section (2). (Ans:0.184m3/s, 18.544m,2.60m/s,100kN/m2)

9. Water flowing from left to right (x-axis) out of a nozzle hits a flat plate placed on the right side. If the

diameter of the water jet is 25 mm and the velocity is 10.18 m/s, calculate the magnitude and direction

(angle measured from the x-axis) of the resultant force on the plate. Take the density of water as 1000kg/m3 and the acceleration due to gravity (g) as 9.81m/s 2.

(Ans:50.93N, 0o)

10. A fixed curved vane deflects a jet of water through an angle of 60 o. The jet enters the vanetangentially with a velocity of 35 m/s and leaves it with a velocity of 30 m/s. If the jet has a mass flow

rate of 2 kg/s, calculate the magnitude and direction of the resultant force on the vane. Take the

density of water as 1000 kg/m3 and the acceleration due to gravity (g) as 9.81m/s2.(Ans:65.57N at 52.41o)