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Determine the minimum number of stage require in an air compressor in which air enters at a pressure of 1 bar and temperature at 27 0C and delivers at 81 bar. The maximum discharge temperature is limited to 100.72 0C and consider the index of polytropic compressor is 1.25 assuring perfect and optimum intercooling between stages
Correct answer is '4'. Can you explain this answer?
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Solution:
Given data:
Inlet Pressure (P1) = 1 bar
Inlet Temperature (T1) = 27 0C
Delivery Pressure (P2) = 81 bar
Maximum Discharge Temperature (T2) = 100.72 0C
Index of polytropic compression (n) = 1.25
Let's assume that the compression process is isentropic.
The isentropic compression ratio can be calculated using the following formula:
r = (P2/P1)^(1/n)
Where,
r = Isentropic compression ratio
n = Index of polytropic compression
P1 = Inlet Pressure
P2 = Delivery Pressure
Substituting the given values, we get
r = (81/1)^(1/1.25) = 12.92
The maximum temperature at the end of each stage can be calculated using the following formula:
T2s = T1 x (r^(n-1))
Where,
T2s = Maximum temperature at the end of each stage
T1 = Inlet Temperature
r = Isentropic compression ratio
n = Index of polytropic compression
For the first stage, T2s1 = 27 x (12.92^(1.25-1)) = 199.56 0C
As the maximum discharge temperature is limited to 100.72 0C, intercooling is necessary between stages.
The intercooler cools the compressed air to the inlet temperature before entering the next stage.
The temperature at the inlet of the second stage is 27 0C.
Using the same formula, we can calculate the isentropic compression ratio for the second stage.
r2 = (81/1)^(1/1.25) = 12.92
The maximum temperature at the end of the second stage can be calculated using the following formula:
T2s2 = 27 x (12.92^(1.25-1)) = 199.56 0C
The temperature at the end of the second stage is higher than the maximum discharge temperature of 100.72 0C.
So, we need an intercooler between the second and third stages.
Similarly, we need intercoolers between the third and fourth stages and between the fourth and fifth stages.
After the fourth stage, the delivery pressure is 81 x 12.92 x 12.92 x 12.92 x 12.92 = 3,522,015 bar.
The temperature at the end of the fourth stage is 27 x (12.92^(1.25-1)) = 199.56 0C.
Since the maximum discharge temperature is limited to 100.72 0C, we do not need another stage.
Therefore, the minimum number of stages required in an air compressor is 4.
Given data:
Inlet Pressure (P1) = 1 bar
Inlet Temperature (T1) = 27 0C
Delivery Pressure (P2) = 81 bar
Maximum Discharge Temperature (T2) = 100.72 0C
Index of polytropic compression (n) = 1.25
Let's assume that the compression process is isentropic.
The isentropic compression ratio can be calculated using the following formula:
r = (P2/P1)^(1/n)
Where,
r = Isentropic compression ratio
n = Index of polytropic compression
P1 = Inlet Pressure
P2 = Delivery Pressure
Substituting the given values, we get
r = (81/1)^(1/1.25) = 12.92
The maximum temperature at the end of each stage can be calculated using the following formula:
T2s = T1 x (r^(n-1))
Where,
T2s = Maximum temperature at the end of each stage
T1 = Inlet Temperature
r = Isentropic compression ratio
n = Index of polytropic compression
For the first stage, T2s1 = 27 x (12.92^(1.25-1)) = 199.56 0C
As the maximum discharge temperature is limited to 100.72 0C, intercooling is necessary between stages.
The intercooler cools the compressed air to the inlet temperature before entering the next stage.
The temperature at the inlet of the second stage is 27 0C.
Using the same formula, we can calculate the isentropic compression ratio for the second stage.
r2 = (81/1)^(1/1.25) = 12.92
The maximum temperature at the end of the second stage can be calculated using the following formula:
T2s2 = 27 x (12.92^(1.25-1)) = 199.56 0C
The temperature at the end of the second stage is higher than the maximum discharge temperature of 100.72 0C.
So, we need an intercooler between the second and third stages.
Similarly, we need intercoolers between the third and fourth stages and between the fourth and fifth stages.
After the fourth stage, the delivery pressure is 81 x 12.92 x 12.92 x 12.92 x 12.92 = 3,522,015 bar.
The temperature at the end of the fourth stage is 27 x (12.92^(1.25-1)) = 199.56 0C.
Since the maximum discharge temperature is limited to 100.72 0C, we do not need another stage.
Therefore, the minimum number of stages required in an air compressor is 4.
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Determine the minimum number of stage require in an air compressor in which air enters at a pressure of 1 bar and temperature at 27 0C and delivers at 81 bar. The maximum discharge temperature is limited to 100.72 0C and consider the index of polytropic compressor is 1.25 assuring perfect and optimum intercooling between stagesCorrect answer is '4'. Can you explain this answer?
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Determine the minimum number of stage require in an air compressor in which air enters at a pressure of 1 bar and temperature at 27 0C and delivers at 81 bar. The maximum discharge temperature is limited to 100.72 0C and consider the index of polytropic compressor is 1.25 assuring perfect and optimum intercooling between stagesCorrect answer is '4'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Determine the minimum number of stage require in an air compressor in which air enters at a pressure of 1 bar and temperature at 27 0C and delivers at 81 bar. The maximum discharge temperature is limited to 100.72 0C and consider the index of polytropic compressor is 1.25 assuring perfect and optimum intercooling between stagesCorrect answer is '4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the minimum number of stage require in an air compressor in which air enters at a pressure of 1 bar and temperature at 27 0C and delivers at 81 bar. The maximum discharge temperature is limited to 100.72 0C and consider the index of polytropic compressor is 1.25 assuring perfect and optimum intercooling between stagesCorrect answer is '4'. Can you explain this answer?.
Determine the minimum number of stage require in an air compressor in which air enters at a pressure of 1 bar and temperature at 27 0C and delivers at 81 bar. The maximum discharge temperature is limited to 100.72 0C and consider the index of polytropic compressor is 1.25 assuring perfect and optimum intercooling between stagesCorrect answer is '4'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Determine the minimum number of stage require in an air compressor in which air enters at a pressure of 1 bar and temperature at 27 0C and delivers at 81 bar. The maximum discharge temperature is limited to 100.72 0C and consider the index of polytropic compressor is 1.25 assuring perfect and optimum intercooling between stagesCorrect answer is '4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the minimum number of stage require in an air compressor in which air enters at a pressure of 1 bar and temperature at 27 0C and delivers at 81 bar. The maximum discharge temperature is limited to 100.72 0C and consider the index of polytropic compressor is 1.25 assuring perfect and optimum intercooling between stagesCorrect answer is '4'. Can you explain this answer?.
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Determine the minimum number of stage require in an air compressor in which air enters at a pressure of 1 bar and temperature at 27 0C and delivers at 81 bar. The maximum discharge temperature is limited to 100.72 0C and consider the index of polytropic compressor is 1.25 assuring perfect and optimum intercooling between stagesCorrect answer is '4'. Can you explain this answer?, a detailed solution for Determine the minimum number of stage require in an air compressor in which air enters at a pressure of 1 bar and temperature at 27 0C and delivers at 81 bar. The maximum discharge temperature is limited to 100.72 0C and consider the index of polytropic compressor is 1.25 assuring perfect and optimum intercooling between stagesCorrect answer is '4'. Can you explain this answer? has been provided alongside types of Determine the minimum number of stage require in an air compressor in which air enters at a pressure of 1 bar and temperature at 27 0C and delivers at 81 bar. The maximum discharge temperature is limited to 100.72 0C and consider the index of polytropic compressor is 1.25 assuring perfect and optimum intercooling between stagesCorrect answer is '4'. Can you explain this answer? theory, EduRev gives you an
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