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A single stage reciprocating air compressor takes in 8m3/min of air at 1 bar and 300 C and delivers it at 6 bar. The clearance is 5% of the stroke. The expansion and compression are polytropic with the value of n=1.3. Calculate: (a) the temperature of delivered air; (b) volumetric efficiency, and (c) Power of the compressor Given that v1-v4 = 8 m3/min?
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A single stage reciprocating air compressor takes in 8m3/min of air at...
Solution:
Given data:
Qin = 8 m3/min
P1 = 1 bar
T1 = 30°C = 303 K
P2 = 6 bar
n = 1.3
Clearance volume = 5% of stroke volume
v1 - v4 = 8 m3/min
(a) Temperature of delivered air:
Using the formula of polytropic process, we can find the temperature of delivered air.
P1V1^n = P2V2^n
V1/V2 = (P2/P1)^1/n
V1/V2 = (6/1)^1.3
V1/V2 = 4.213
Let V1 = 1 m3
V2 = V1/4.213 = 0.237 m3
Also, we know that
T1V1^(n-1) = T2V2^(n-1)
T2 = T1(V1/V2)^(n-1)
T2 = 303(4.213)^(1.3-1)
T2 = 572.28 K
T2 = 299.28°C
Therefore, the temperature of delivered air is 299.28°C.
(b) Volumetric efficiency:
Volumetric efficiency is defined as the ratio of actual volume of air delivered to the compressor cylinder to the swept volume of the piston.
Volumetric efficiency, ηv = (Volume of air delivered)/(Swept volume)
Swept volume, Vs = π/4 × (bore)2 × (stroke)
Let the bore = B
Stroke = S
Vs = π/4 × B2 × S
Clearance volume, Vc = 5% of Vs
Vc = 0.05 × Vs
Total volume of cylinder, V = Vc + Vs
Volume of air delivered, Vd = v1 - v4
Volumetric efficiency, ηv = Vd/V
ηv = (v1 - v4)/(Vc + Vs)
Substituting the given values, we get
ηv = (8)/(0.05 × π/4 × B2 × S + π/4 × B2 × S)
ηv = 0.8/(0.05 + 1)
ηv = 0.42 or 42%
Therefore, the volumetric efficiency of the compressor is 42%.
(c) Power of the compressor:
Power of the compressor, P = (Wp × N)/(60 × ηm)
Where,
Wp = work done per cycle
N = speed of the compressor
ηm = mechanical efficiency
Work done per cycle, Wp = P2V2 - P1V1/(n-1)
Wp = 6 × 0.237 - 1 × 1/(1.3-1)
Wp = 1.26 kJ/cycle
Mechanical efficiency, ηm = 0.85
Speed of the compressor, N = 800 rpm
Power of the compressor, P = (1.26 × 800)/(60 × 0.85)
P = 14.82 kW
Therefore, the power of the compressor is 14.82 kW.
Given data:
Qin = 8 m3/min
P1 = 1 bar
T1 = 30°C = 303 K
P2 = 6 bar
n = 1.3
Clearance volume = 5% of stroke volume
v1 - v4 = 8 m3/min
(a) Temperature of delivered air:
Using the formula of polytropic process, we can find the temperature of delivered air.
P1V1^n = P2V2^n
V1/V2 = (P2/P1)^1/n
V1/V2 = (6/1)^1.3
V1/V2 = 4.213
Let V1 = 1 m3
V2 = V1/4.213 = 0.237 m3
Also, we know that
T1V1^(n-1) = T2V2^(n-1)
T2 = T1(V1/V2)^(n-1)
T2 = 303(4.213)^(1.3-1)
T2 = 572.28 K
T2 = 299.28°C
Therefore, the temperature of delivered air is 299.28°C.
(b) Volumetric efficiency:
Volumetric efficiency is defined as the ratio of actual volume of air delivered to the compressor cylinder to the swept volume of the piston.
Volumetric efficiency, ηv = (Volume of air delivered)/(Swept volume)
Swept volume, Vs = π/4 × (bore)2 × (stroke)
Let the bore = B
Stroke = S
Vs = π/4 × B2 × S
Clearance volume, Vc = 5% of Vs
Vc = 0.05 × Vs
Total volume of cylinder, V = Vc + Vs
Volume of air delivered, Vd = v1 - v4
Volumetric efficiency, ηv = Vd/V
ηv = (v1 - v4)/(Vc + Vs)
Substituting the given values, we get
ηv = (8)/(0.05 × π/4 × B2 × S + π/4 × B2 × S)
ηv = 0.8/(0.05 + 1)
ηv = 0.42 or 42%
Therefore, the volumetric efficiency of the compressor is 42%.
(c) Power of the compressor:
Power of the compressor, P = (Wp × N)/(60 × ηm)
Where,
Wp = work done per cycle
N = speed of the compressor
ηm = mechanical efficiency
Work done per cycle, Wp = P2V2 - P1V1/(n-1)
Wp = 6 × 0.237 - 1 × 1/(1.3-1)
Wp = 1.26 kJ/cycle
Mechanical efficiency, ηm = 0.85
Speed of the compressor, N = 800 rpm
Power of the compressor, P = (1.26 × 800)/(60 × 0.85)
P = 14.82 kW
Therefore, the power of the compressor is 14.82 kW.
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A single stage reciprocating air compressor takes in 8m3/min of air at 1 bar and 300 C and delivers it at 6 bar. The clearance is 5% of the stroke. The expansion and compression are polytropic with the value of n=1.3. Calculate: (a) the temperature of delivered air; (b) volumetric efficiency, and (c) Power of the compressor Given that v1-v4 = 8 m3/min?
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A single stage reciprocating air compressor takes in 8m3/min of air at 1 bar and 300 C and delivers it at 6 bar. The clearance is 5% of the stroke. The expansion and compression are polytropic with the value of n=1.3. Calculate: (a) the temperature of delivered air; (b) volumetric efficiency, and (c) Power of the compressor Given that v1-v4 = 8 m3/min? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A single stage reciprocating air compressor takes in 8m3/min of air at 1 bar and 300 C and delivers it at 6 bar. The clearance is 5% of the stroke. The expansion and compression are polytropic with the value of n=1.3. Calculate: (a) the temperature of delivered air; (b) volumetric efficiency, and (c) Power of the compressor Given that v1-v4 = 8 m3/min? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single stage reciprocating air compressor takes in 8m3/min of air at 1 bar and 300 C and delivers it at 6 bar. The clearance is 5% of the stroke. The expansion and compression are polytropic with the value of n=1.3. Calculate: (a) the temperature of delivered air; (b) volumetric efficiency, and (c) Power of the compressor Given that v1-v4 = 8 m3/min?.
A single stage reciprocating air compressor takes in 8m3/min of air at 1 bar and 300 C and delivers it at 6 bar. The clearance is 5% of the stroke. The expansion and compression are polytropic with the value of n=1.3. Calculate: (a) the temperature of delivered air; (b) volumetric efficiency, and (c) Power of the compressor Given that v1-v4 = 8 m3/min? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A single stage reciprocating air compressor takes in 8m3/min of air at 1 bar and 300 C and delivers it at 6 bar. The clearance is 5% of the stroke. The expansion and compression are polytropic with the value of n=1.3. Calculate: (a) the temperature of delivered air; (b) volumetric efficiency, and (c) Power of the compressor Given that v1-v4 = 8 m3/min? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single stage reciprocating air compressor takes in 8m3/min of air at 1 bar and 300 C and delivers it at 6 bar. The clearance is 5% of the stroke. The expansion and compression are polytropic with the value of n=1.3. Calculate: (a) the temperature of delivered air; (b) volumetric efficiency, and (c) Power of the compressor Given that v1-v4 = 8 m3/min?.
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