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A single stage double acting air compressor delivers 5 m3 of free air per minute at 1 ata and 200 C to 7.5 bar with the following data; R.P.M. = 300; Mechanical efficiency = 0.9; Pressure loss in passing through intake valves = 0.04 bar; Temperature rise of air during suction stroke = 120 C ; Clearance volume = 5% of stroke volume; Index of compression and expansion, n=1.3; Length of the stroke = 1.3 times the cylinder diameter.?
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A single stage double acting air compressor delivers 5 m3 of free air ...
Calculation of Free Air Delivery (FAD)
The free air delivery (FAD) is the actual volume of air delivered by the compressor under the given conditions. The FAD can be calculated using the following formula:
FAD = V x n x rpm x eff / (P1 + p1 - P2)
Where,
V = Swept volume of the cylinder
n = Index of compression and expansion
rpm = Revolutions per minute of the compressor
eff = Mechanical efficiency of the compressor
P1 = Intake pressure (1 ata)
p1 = Pressure loss in passing through intake valves
P2 = Discharge pressure (7.5 bar)
Given data:
Swept volume (V) = (π/4) x D^2 x L
D = Diameter of the cylinder
L = Length of the stroke = 1.3 x D
n = 1.3
rpm = 300
eff = 0.9
P1 = 1 ata = 1.013 bar
p1 = 0.04 bar
P2 = 7.5 bar
Using the above formula, the FAD can be calculated as follows:
V = (π/4) x D^2 x L
L = 1.3 x D
V = (π/4) x D^2 x 1.3D
V = 1.208 D^3
FAD = V x n x rpm x eff / (P1 + p1 - P2)
FAD = (1.208 D^3) x 1.3 x 300 x 0.9 / (1.013 + 0.04 - 7.5)
FAD = 16.89 D^3 m^3/min
Given that FAD = 5 m^3/min
5 = 16.89 D^3
D = 0.864 m
Therefore, the diameter of the cylinder is 0.864 m.
Calculation of Temperature Rise during Compression
The temperature rise during compression can be calculated using the following formula:
T2 = T1 x (P2/P1)^((n-1)/n)
Where,
T1 = Inlet air temperature = 20°C + 273 = 293 K
P1 = Inlet pressure = 1.013 bar
P2 = Discharge pressure = 7.5 bar
n = Index of compression and expansion = 1.3
Using the above formula, the temperature rise can be calculated as follows:
T2 = T1 x (P2/P1)^((n-1)/n)
T2 = 293 x (7.5/1.013)^((1.3-1)/1.3)
T2 = 616 K
Therefore, the temperature rise during compression is 616 - 293 = 323°C.
Calculation of Clearance Volume
The clearance volume is the volume of the cylinder that remains filled with compressed air at the end of the compression stroke. The clearance volume can be calculated using the following formula:
Vc = Vd x (1/cr - 1)
Where,
Vd = Swept volume of the cylinder
cr = Compression ratio = P2/P1
Using the above formula, the clearance volume can be calculated as follows:
cr = P2/P1 = 7.5/
The free air delivery (FAD) is the actual volume of air delivered by the compressor under the given conditions. The FAD can be calculated using the following formula:
FAD = V x n x rpm x eff / (P1 + p1 - P2)
Where,
V = Swept volume of the cylinder
n = Index of compression and expansion
rpm = Revolutions per minute of the compressor
eff = Mechanical efficiency of the compressor
P1 = Intake pressure (1 ata)
p1 = Pressure loss in passing through intake valves
P2 = Discharge pressure (7.5 bar)
Given data:
Swept volume (V) = (π/4) x D^2 x L
D = Diameter of the cylinder
L = Length of the stroke = 1.3 x D
n = 1.3
rpm = 300
eff = 0.9
P1 = 1 ata = 1.013 bar
p1 = 0.04 bar
P2 = 7.5 bar
Using the above formula, the FAD can be calculated as follows:
V = (π/4) x D^2 x L
L = 1.3 x D
V = (π/4) x D^2 x 1.3D
V = 1.208 D^3
FAD = V x n x rpm x eff / (P1 + p1 - P2)
FAD = (1.208 D^3) x 1.3 x 300 x 0.9 / (1.013 + 0.04 - 7.5)
FAD = 16.89 D^3 m^3/min
Given that FAD = 5 m^3/min
5 = 16.89 D^3
D = 0.864 m
Therefore, the diameter of the cylinder is 0.864 m.
Calculation of Temperature Rise during Compression
The temperature rise during compression can be calculated using the following formula:
T2 = T1 x (P2/P1)^((n-1)/n)
Where,
T1 = Inlet air temperature = 20°C + 273 = 293 K
P1 = Inlet pressure = 1.013 bar
P2 = Discharge pressure = 7.5 bar
n = Index of compression and expansion = 1.3
Using the above formula, the temperature rise can be calculated as follows:
T2 = T1 x (P2/P1)^((n-1)/n)
T2 = 293 x (7.5/1.013)^((1.3-1)/1.3)
T2 = 616 K
Therefore, the temperature rise during compression is 616 - 293 = 323°C.
Calculation of Clearance Volume
The clearance volume is the volume of the cylinder that remains filled with compressed air at the end of the compression stroke. The clearance volume can be calculated using the following formula:
Vc = Vd x (1/cr - 1)
Where,
Vd = Swept volume of the cylinder
cr = Compression ratio = P2/P1
Using the above formula, the clearance volume can be calculated as follows:
cr = P2/P1 = 7.5/
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A single stage double acting air compressor delivers 5 m3 of free air per minute at 1 ata and 200 C to 7.5 bar with the following data; R.P.M. = 300; Mechanical efficiency = 0.9; Pressure loss in passing through intake valves = 0.04 bar; Temperature rise of air during suction stroke = 120 C ; Clearance volume = 5% of stroke volume; Index of compression and expansion, n=1.3; Length of the stroke = 1.3 times the cylinder diameter.?
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A single stage double acting air compressor delivers 5 m3 of free air per minute at 1 ata and 200 C to 7.5 bar with the following data; R.P.M. = 300; Mechanical efficiency = 0.9; Pressure loss in passing through intake valves = 0.04 bar; Temperature rise of air during suction stroke = 120 C ; Clearance volume = 5% of stroke volume; Index of compression and expansion, n=1.3; Length of the stroke = 1.3 times the cylinder diameter.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single stage double acting air compressor delivers 5 m3 of free air per minute at 1 ata and 200 C to 7.5 bar with the following data; R.P.M. = 300; Mechanical efficiency = 0.9; Pressure loss in passing through intake valves = 0.04 bar; Temperature rise of air during suction stroke = 120 C ; Clearance volume = 5% of stroke volume; Index of compression and expansion, n=1.3; Length of the stroke = 1.3 times the cylinder diameter.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single stage double acting air compressor delivers 5 m3 of free air per minute at 1 ata and 200 C to 7.5 bar with the following data; R.P.M. = 300; Mechanical efficiency = 0.9; Pressure loss in passing through intake valves = 0.04 bar; Temperature rise of air during suction stroke = 120 C ; Clearance volume = 5% of stroke volume; Index of compression and expansion, n=1.3; Length of the stroke = 1.3 times the cylinder diameter.?.
A single stage double acting air compressor delivers 5 m3 of free air per minute at 1 ata and 200 C to 7.5 bar with the following data; R.P.M. = 300; Mechanical efficiency = 0.9; Pressure loss in passing through intake valves = 0.04 bar; Temperature rise of air during suction stroke = 120 C ; Clearance volume = 5% of stroke volume; Index of compression and expansion, n=1.3; Length of the stroke = 1.3 times the cylinder diameter.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single stage double acting air compressor delivers 5 m3 of free air per minute at 1 ata and 200 C to 7.5 bar with the following data; R.P.M. = 300; Mechanical efficiency = 0.9; Pressure loss in passing through intake valves = 0.04 bar; Temperature rise of air during suction stroke = 120 C ; Clearance volume = 5% of stroke volume; Index of compression and expansion, n=1.3; Length of the stroke = 1.3 times the cylinder diameter.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single stage double acting air compressor delivers 5 m3 of free air per minute at 1 ata and 200 C to 7.5 bar with the following data; R.P.M. = 300; Mechanical efficiency = 0.9; Pressure loss in passing through intake valves = 0.04 bar; Temperature rise of air during suction stroke = 120 C ; Clearance volume = 5% of stroke volume; Index of compression and expansion, n=1.3; Length of the stroke = 1.3 times the cylinder diameter.?.
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