This set of Thermal Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Rotary Compressor”.

1. A roots blower compressor compresses 0.08m^{3} of air from 1bar to 1.8bar per revolution. Which of the following is the actual work done per revolution?

a) 6.25kJ

b) 5.6kJ

c) 5.4kJ

d) 6.4kJ

View Answer

Explanation:

Given: v

_{1}= 0.08m

^{3}; p

_{1}= 1bar = 1 × 10

^{5}N/m

^{2}; p

_{2}= 1.8bar = 1.8 × 10

^{5}N/m

^{2};

We know that the actual work done per revolution is given by,

W

_{act}= v

_{1}(p

_{2}– p

_{1})

W

_{act}= 0.08(1.8 × 10

^{5}– 1 × 10

^{5})

W

_{act}= 0.08 × 0.8 × 10

^{5}

W

_{act}= 6400J or W

_{act}= 6.4kJ

2. A roots blower compressor compresses 0.06m^{3} of air from 1bar to 1.6bar per revolution. Which of the following is the ideal work done per revolution?

a) 3288.59J

b) 3000.13J

c) 1518.13J

d) 3018.13J

View Answer

Explanation:

Given: v

_{1}= 0.06m

^{3}; p

_{1}= 1bar = 1 × 10

^{5}N/m

^{2}; p

_{2}= 1.6bar = 1.6 × 10

^{5}N/m

^{2};

We know that the ideal work done per revolution is given by,

W

_{ideal}= \(\frac{\gamma}{\gamma – 1}\) × p

_{1}v

_{1}\(\bigg[(\frac{p_2}{p_1} )^{\frac{\gamma – 1}{\gamma}} – 1\bigg] \)

= \(\frac{1.4}{1.4-1}\) × 1 × 10

^{5}× 0.06\(\bigg[(\frac{1.6}{1})^{\frac{1.4-1}{1.4}} – 1\bigg] \)

= 21000 × [1.143 – 1]

W

_{ideal}= 3018.13J

3. A roots blower compressor consumes 4386N-m of actual work done. The required ideal work done is 3500N-m. Which of the following is the efficiency of the compressor in percentage?

a) 79.79%

b) 72.52%

c) 40.79%

d) 100%

View Answer

Explanation:

Given: W

_{act}= 4386J; W

_{ideal}= 3500J;

We know that the efficiency of the compressor is given by,

η = \(\frac{W_ideal}{W_act}\)

η = \(\frac{3500}{4386}\)

η = 0.7979 or 79.79%

4. A centrifugal compressor delivers 45kg per minute of air at a pressure of 3.2bar and 83°C. The intake pressure and temperature of the air is 1bar and 27°C. Which of the following is the index of compression? Consider R = 287J/kg-K.

a) 1.171

b) 1.4

c) 1.2

d) 2

View Answer

Explanation:

Given: m = 45kg/min; p

_{1}= 1bar; T

_{1}= 27°C = 273 + 27 = 300K;

p

_{2}= 3.2bar; T

_{2}= 83°C = 83 + 273 = 356K; R = 287J/kg-K;

Let n = index of compression,

We know that, \(\frac{T_2}{T_1} = (\frac{p_2}{p_1})^{\frac{n-1}{n}}\)

\(\frac{356}{300} = (\frac{3.2}{1})^{\frac{n-1}{n}}\)

1.186 = (3.2)\(^{\frac{n-1}{n}}\)

log(1.186) = \(\frac{n-1}{n}\) log(3.2)

0.074 = \(\frac{n-1}{n}\) × 0.505

0.074n = 0.505n – 0.505

0.431n = 0.505

n = 1.171

5. A centrifugal compressor delivers 32kg per minute of air at a pressure of 2.75bar and 87°C. The intake pressure and temperature of the air is 1bar and 15°C. Which of the following is the power required, if the compression is isothermal? Consider R = 287J/kg-K.

a) 44.56kW

b) 40.39kW

c) 56.85kW

d) 26.73kW

View Answer

Explanation:

Given: m = 32kg/min; p

_{1}= 1bar; T

_{1}= 15°C = 273 + 15 = 288K;

p

_{2}= 2.75bar; T

_{2}= 87°C = 87 + 273 = 360K; R = 287J/kg-K;

We know that work done by the compressor if the compression is isothermal,

W = 2.3 mRT

_{1}log(r)

Where, r = \(\frac{p_2}{p_1}\) = \(\frac{2.75}{1}\) = 2.75

W = 2.3 × 32 × 287 × 288 × log(2.75)

W = 6083481.6 × 0.4395

W = 2673690.163J/min = 2673.69kJ/min

∴ Power required, P = \(\frac{2673.69}{60}\) = 44.56kW

6. A centrifugal air compressor having a pressure compression ratio of 4.75 compresses air at the rate of 7.5kg/s. If the initial pressure and temperature of the air is 1bar and 17°C, then which of the following is the final temperature of the gas? Consider γ = 1.4 and c_{p} = 1kJ/kg-K.

a) 259.62°C

b) 279.62°C

c) 179.62°C

d) 156.25°C

View Answer

Explanation:

Given: \(\frac{p_2}{p_1}\) = 4.75; m = 7.5kg/sec; p

_{1}= 1bar; T

_{1}= 17°C = 17 + 273 = 290K;

γ = 1.4; c

_{p}= 1kJ/kg-K;

Let T

_{2}= Final temperature of the gas,

We know that, \(\frac{T_2}{T_1} = (\frac{P_2}{P_1})^{\frac{\gamma – 1}{\gamma}}\)

\(\frac{T_2}{T_1}\) = (4.75)\(^{\frac{1.4-1}{1.4}}\) = 1.56

∴ T

_{2}= T

_{1}× 1.56

= 290 × 1.56

T

_{2}= 452.62K = 179.62°C

7. In a rotary air compressor the work done by the compressor is 358kJ. Which of the following is the heat exchanged with the jacket water? The compression follows the relation pv^{1.6} = constant.

a) -179kJ

b) +179kJ

c) -259kJ

d) +259kJ

View Answer

Explanation:

Given: W = 358kJ; n = 1.6;

We know that the heat exchanged in a polytropic process,

Q = \(\frac{\gamma – n}{\gamma – 1}\) × W

Q = \(\frac{1.4-1.6}{1.4-1}\) × 358

Q = -179kJ

8. A centrifugal compressor running at 1500r.p.m. the outer diameter of the blade tip is 540mm. Which of the following is the tangential velocity of the outer blade tip?

a) 72.41m/s

b) 65.75m/s

c) 49.29m/s

d) 42.41m/s

View Answer

Explanation:

Given: N = 1500r.p.m.; D

_{1}= 540mm = 0.54m;

We know that tangential velocity of the outer blade tip,

V

_{b1}= \(\frac{\pi × D_1 × N}{60}\)

= \(\frac{\pi × 0.54 × 1500}{60}\)

= 42.41m/s

9. A centrifugal compressor running at 1200r.p.m. the tangential velocity of the outer blade tip is 52m/sec. Which of the following is the work done per kg of air?

a) 2704kW

b) 27.04kW

c) 4504kW

d) 2.704kW

View Answer

Explanation:

Given: N = 1200r.p.m.; V

_{b1}= 52m/s;

We know that work done per kg of air is given by,

W = m(V

_{b1})

^{2}

= 1 × (52)

^{2}

= 2704W

= 2.704kW

10. A centrifugal compressor running at 1000r.p.m. receives air at 25°C. If the work done per kg of air is 5.675kW, then which of the following is the temperature of the air leaving the compressor? Consider c_{p} =1kJ/kg K.

a) 303.675°C

b) 30.675°C

c) 306.75°C

d) 3.0675°C

View Answer

Explanation:

Given: N = 1000r.p.m.; T

_{1}= 25°C = 25 + 273 = 298K; W = 5.675kW;

We know that work done is given by,

W = mc

_{p}(T

_{2}– T

_{1})

5.675 = 1 × 1 × (T

_{2}– 298)

T

_{2}= 5.675 + 298

T

_{2}= 303.675K

T

_{2}= 30.675°C

**Sanfoundry Global Education & Learning Series – Thermal Engineering**

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