# Homework Help: Need Help Transposing the pressure drop formula

1. Feb 25, 2017

### Jack Mc

1. The problem statement, all variables and given/known data

Hi, Iv got to find the minimum diameter of a pipe if the pressure drops in a system is to be limited to 0.3bar. when delivered through a pipe of equivalent length 160m

I have to use the formula

Pressure Drop = 800lQ^2/Rd^5.31

I belive I have to transpose this to find the min diameter.

2. Relevant equations

compressor delivers 300 l s–1 of free air into a pipe at a pressure of 6 bar gauge.

Using the pressure drop formula: pressure drop = 800lQ2 Rd 5.31

calculate the minimum diameter of pipe if the pressure drop in a system is to be limited to 0.3 bar when is delivered through a pipe of equivalent length 160 m .

3. The attempt at a solution

d^5.31=800lQ^2/R

2. Feb 28, 2017

### CWatters

Ok so far then take the 5.31th root of both sides.

If your calculator can't do that perhaps logarithms will help..

log(mn) = n * log(m)

3. Feb 28, 2017

### CWatters

Actually I see you forgot to put the pressure drop on the right hand side. If ΔP is the pressure drop it should read..

d5.31=800lQ2/RΔP

4. Feb 28, 2017

### Jack Mc

I see thank you. Ill give this a go.

5. Mar 1, 2017

### Jack Mc

d^5.31=800x160x300^2/6.94x0.3
= d^5.31 = 55.331412.1
Is this the right lines?

6. Mar 1, 2017

### CWatters

Looks right to me although I don't have my calculator to hand.

7. Mar 2, 2017

### CWatters

I get..
d5.31 = 800x160x300^2/6.94x0.3 = 5.5 * 106
then
5.31*log(d) = Log(5.5 * 106)
so
d = 10(Log(5.5 * 106)/5.31)
= 68m
which is very large for a pipe!

Where did the equation come from?
Is the value of R correct?
Should the pressure drop be in bar or some other units?

8. Mar 2, 2017

### Jack Mc

I got R by...

R=p2/p1

R=6+1.01/1.01

R=6.94

9. Mar 2, 2017

### CWatters

Should the flow rate Q be in L/s or m3/s ?

10. Mar 2, 2017

### Jack Mc

l = the equivalent length of pipe in metres
Q = the flow through the pipe in ℓs−1 free air
R = p2/p1 = the ratio of compression at the start of the pipe
d = the internal diameter of the pipe in mm

11. Mar 2, 2017

### CWatters

Ah OK 68mm makes more sense than meters.

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