Help with pressure drop/transposing formula to get pipe diameter

In summary, pressure drop is the decrease in fluid pressure that occurs as a fluid flows through a pipe or other conduit, caused by factors such as friction, changes in elevation, and restrictions in the pipe. It is important because it affects the flow rate and efficiency of a system, and can be calculated using various formulas such as the Darcy-Weisbach equation. Transposing a formula is the process of rearranging the variables in an equation to solve for a different variable, and can be useful in determining the required pipe diameter for a specific pressure drop. However, not all equations are easily transposable.
  • #1
mrose94
1
0
Homework Statement
A compressor delivers 300 s–1 of free air into a pipe at a pressure of
6 bar gauge. Using the pressure drop formula: Pressure drop = 800lQ^2/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 .
Relevant Equations
pressure drop = 800lQ^2/Rd^5.31
Hello.

My attempt at the solution is as follows:

l = 160m
Q= 300 ls-1
R= p2/p1= 6+1.01/1.01 = 6.94 (2dp)
d = Unknown
Pressure drop = 0.3 Bar

0.3 = 800*160*300^2/6.94*d^5.31

0.3 = 1.152x10^10/6.94*d^5.31

0.3 ( 6.94*d^5.31) = 1.152x10^10

6.94*d^5.31 = 1.152x10^10/0.3

d^5.31 = (1.152x10^10/0.3)/6.94

d= 5.31 root (1.152x10^10/0.3)/6.94

d= 394984.81 mm (I think mm is correct?)

d= 394.98 M

I'm struggling to see how this answer can be correct as an internal diameter of a pipe being so large seems ridiculous to me. Any help as to where I've gone wrong would be appreciated. Thank you!
 
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  • #2
In the pressure drop formula what are the units of the various parameters supposed to be?
 

Related to Help with pressure drop/transposing formula to get pipe diameter

1. What is pressure drop?

Pressure drop refers to the decrease in pressure that occurs as a fluid (such as air or water) flows through a pipe or other conduit. It is caused by factors such as friction, changes in elevation, and obstructions in the pipe.

2. How is pressure drop calculated?

The pressure drop in a pipe can be calculated using the Darcy-Weisbach equation, which takes into account factors such as flow rate, pipe diameter, and fluid properties. There are also various online calculators and software programs available to help with these calculations.

3. What is the relationship between pressure drop and pipe diameter?

As a general rule, a larger pipe diameter will result in a lower pressure drop. This is because a larger diameter pipe allows for a larger volume of fluid to flow through, which reduces friction and therefore decreases the pressure drop.

4. How do you transpose the formula to get pipe diameter?

To transpose the Darcy-Weisbach equation to solve for pipe diameter, you would need to rearrange the equation and solve for the diameter variable. This can be done by dividing both sides of the equation by the other variables (flow rate, fluid properties, etc.) and then taking the square root of both sides.

5. Are there any other factors that affect pressure drop besides pipe diameter?

Yes, there are many other factors that can affect pressure drop, including fluid viscosity, pipe roughness, and the presence of bends or other obstructions in the pipe. These factors should be taken into account when calculating pressure drop and determining the appropriate pipe diameter for a given application.

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