Understanding Pressure Drop in Pipes

[BigBob]

Hi,

This isn't actually a homework problem, but rather I'm just trying to understand a few things. It's pretty simple though, so I thought this would be the best place to post. I don't care so much that I'm getting the correct answer, as much as I care that I'm understanding the situation correctly. So any advice is appreciated.

Homework Statement

There is a very large water tower (infinity wide, let's say). The pressure measured at the bottom of the tower is 100 PSIG (i.e. the tower is about 230 foot tall).

At the base of the tower, a pipe is connected. The pipe has a cross sectional area of 1 square inch (i.e. 1.128 inch diameter). The flow in the pipe is 19.25 inches per second (5 gallon per minute). Neglecting friction, what would the measured pressure in the pipe be?

Homework Equations

Pressure Drop = 1/2 d v^2 where d is density and v is velocity
Density of water = 0.03605 lb/in^3

The Attempt at a Solution

I believe the velocity of the water flowing would be 19.25 inches per second. Then, using the formula above for pressure drop, I get a pressure drop of about 6.68 PSI. So the pressured measured would be 93.3 PSIG.

If possible, I would like someone to double check my work. Also, am I using the proper formula for this situation? Am I using the correct units (density in lb/in^3, pressure in lb/in^2, velocity in in/sec)? Would my result be a reasonable outcome in real life, or would friction dominate the answer?

And, one thing I don't understand. If I am applying the formula correctly, then wouldn't a very small pipe, with a very great flow, yield a negative pressure? Isn't that impossible?

Thanks!

 

[jbsteele]

Yes, you are using the correct formula for this situation, and the correct units. This result is a reasonable outcome in real life, however, friction would play a role in the pressure drop. The pressure drop due to friction is dependent on the type of pipe being used, the length of the pipe, as well as the flow rate of the water. In regard to the last question, it is not impossible to have negative pressure in a pipe. This can happen when the flow rate of the water is much greater than the capacity of the pipe. In such cases, the pressure in the pipe can drop below atmospheric pressure, resulting in a negative pressure.