Mechanical Engineering - Compressors, Gas Dynamics and Gas Turbines - Discussion

To determine the delivery pressure at the fourth stage, let's assume the compression ratio is the same for each stage. This is a common approach in multi-stage compression.

Given:
- Stage 1 pressure (P1) = 1 bar.
- Stage 3 pressure (P3) = 16 bar.

Let's find the compression ratio per stage (R). If P1 is the suction pressure of the first stage and P2 is the discharge pressure of the first stage (which becomes the suction pressure for the second stage), and so on:

P2 = P1 * R.
P3 = P2 * R = P1 * R^2,
16 = 1 * R^2.
R^2 = 16.
R = 4.

Now, let's find P4 (discharge pressure of the fourth stage):

P4 = P3 * R = 16 * 4 = 64 bar.

So, the delivery pressure at the fourth stage would be 64 bar.

The first two values given are delivery pressures at 1st and 3rd stage compressors, we have to find delivery pressure at 4th compressor.

We have p3/p2 = p4/p3 = p5/p4.
p2 = 1, p4 = 16, p5 = ?

=> p3 = (1*16)^(1%2),=> p3 = 4.
Similarly p4 = (p3*p5)^(1%2) => p5 = 64.

Let r be the pressure ratio.
P2 =P1 x r.
P3 = P1 x r^2 (P3 and P1 are given, we can find r).

r^2 = P3/P1 = 16/1 = 16,
r = 4.

Delivery pressure at fourth stage P4 = P1 x r^3
= 1 x 4^3 = 64.

When we know that for multistage compressor p2/p1 = p3/p2 = p4/p3.

Since p3 = 16, p1 = 1 so p2/p1 = p3/p2 then p2 = 4 also p3/p2 = p4/p3.

16/4 = p4/16.

p4 = 64.

We know in multistage compressor:
P2/P1 = P3/P2 = P4/P3.

Since,
P3 = 16.
P1 = 1.

So from,
P2/P1 = P3/p2.

Hence,
P2 = 4.

Now P3/P2 = P4/P3.
P4 = 64.

Four stage compressor 3rd stage me intercooler hota so its temperature and pressure is constant 4 stage compressed so increased delivery pressure.

In multistage compressor the pressure in each stage follows geometric progression:

For 2nd stage: SQRT (1*16) = 4.

For fourth stage: 4*4*4 = 64.

@All.

The pressure mentioned in the question are the Delivery pressure. If we assume P2 as 1 bar and P4 as 16 bar, then only P5 comes as 64 bar.

Since pressure ratio is constant for a compressor. So firstly found pressure ratio. And then make dual like p2/p1=p3/p2=p4/p3 and solve this.

The delivery pressure at the fourth stage means p5.

So p1 is 1.
P2 is 4.
P3 is 16.
P4 is 64.
P5 is 256.

So option D. 256 should be correct.