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Find the minimum number of stages required when air enters at 1 bar and 270C and delivers at 260 bar. The maximum temperature at the outlet of compressor is limited to 3270C . Take the perfect intercooling in between stages and γ = 1.3.
- a)2
- b)3
- c)4
- d)5
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Find the minimum number of stages required when air enters at 1 bar an...
In multistage compression, if there are N stages then pressure ratio in each stage will be equal for perfect intercooling.
From this we can write ,
Now, for perfect intercooling the inlet temperature for each compressor will be same. And as we know that pressure ratio will be same for each stage. So for perfect intercooling case we can write:
From this we can write ,
Now, for perfect intercooling the inlet temperature for each compressor will be same. And as we know that pressure ratio will be same for each stage. So for perfect intercooling case we can write:
Solving , we get N = 1.85 ~ 2
So, the correct option is (a).
So, the correct option is (a).
Most Upvoted Answer
Find the minimum number of stages required when air enters at 1 bar an...
Adiabatic compression in each stage.
To solve this problem, we can use the equation for the polytropic process:
P2/P1 = (T2/T1)^(n/(n-1))
where P1 and T1 are the initial pressure and temperature, P2 and T2 are the final pressure and temperature, and n is the polytropic exponent. For an adiabatic process, n = k, where k is the ratio of specific heats.
Let's assume that we have n stages, each with a pressure ratio of R = P2/P1^(1/n). The temperature at the outlet of each stage will be T2 = T1*R^((k-1)/k). We want to find the minimum number of stages required to reach a final pressure of 260 bar while keeping the temperature below 3270C.
Starting with the initial conditions of P1 = 1 bar and T1 = 270C, we can calculate the pressure ratio for each stage:
R = (260/1)^(1/n) = 3.778^(1/n)
The temperature at the outlet of each stage will be:
T2 = 270*(3.778^(1/n))^((k-1)/k)
We want to find the minimum number of stages required to reach a final pressure of 260 bar while keeping the temperature below 3270C. So we can set up the following inequality:
T2 < />
270*(3.778^(1/n))^((k-1)/k) < />
Taking the logarithm of both sides:
log(270) + ((k-1)/k)*log(3.778^(1/n)) < />
Simplifying:
((k-1)/k)*log(3.778^(1/n)) < log(3270)="" -="" />
((k-1)/k)*log(3.778^(1/n)) < />
((k-1)/k)*(1/n)*log(3.778) < />
Solving for n:
n > (k*log(3.778))/log((k-1)*log(3.778)/log(12.111))
For air, k = 1.4. Plugging this in, we get:
n > 6.14
Therefore, we need at least 7 stages to compress the air from 1 bar to 260 bar while keeping the temperature below 3270C.
To solve this problem, we can use the equation for the polytropic process:
P2/P1 = (T2/T1)^(n/(n-1))
where P1 and T1 are the initial pressure and temperature, P2 and T2 are the final pressure and temperature, and n is the polytropic exponent. For an adiabatic process, n = k, where k is the ratio of specific heats.
Let's assume that we have n stages, each with a pressure ratio of R = P2/P1^(1/n). The temperature at the outlet of each stage will be T2 = T1*R^((k-1)/k). We want to find the minimum number of stages required to reach a final pressure of 260 bar while keeping the temperature below 3270C.
Starting with the initial conditions of P1 = 1 bar and T1 = 270C, we can calculate the pressure ratio for each stage:
R = (260/1)^(1/n) = 3.778^(1/n)
The temperature at the outlet of each stage will be:
T2 = 270*(3.778^(1/n))^((k-1)/k)
We want to find the minimum number of stages required to reach a final pressure of 260 bar while keeping the temperature below 3270C. So we can set up the following inequality:
T2 < />
270*(3.778^(1/n))^((k-1)/k) < />
Taking the logarithm of both sides:
log(270) + ((k-1)/k)*log(3.778^(1/n)) < />
Simplifying:
((k-1)/k)*log(3.778^(1/n)) < log(3270)="" -="" />
((k-1)/k)*log(3.778^(1/n)) < />
((k-1)/k)*(1/n)*log(3.778) < />
Solving for n:
n > (k*log(3.778))/log((k-1)*log(3.778)/log(12.111))
For air, k = 1.4. Plugging this in, we get:
n > 6.14
Therefore, we need at least 7 stages to compress the air from 1 bar to 260 bar while keeping the temperature below 3270C.
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Find the minimum number of stages required when air enters at 1 bar and 270Cand delivers at 260 bar. The maximum temperature at the outlet of compressor is limited to 3270C. Take the perfect intercooling in between stages and γ = 1.3.a)2b)3c)4d)5Correct answer is option 'A'. Can you explain this answer?
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