Please Help Me Find the Flow Rate

[npc214]

Hey everyone,

I have a fluid system of water coming from a pressure source. Then there is a converging nozzle, which I have calculated the resistance coefficient using Crane's Manual and it has an outlet to the atmosphere.
I have tried to simplify the system. The full system is a pressure source, converging nozzle which has outlet into original diameter at converging nozzle inlet followed by hose to outlet to atmosphere. (this is like a fire hose system - slightly different for my actual application)
The pressure of the pressure source is my independent variable, I am doing a sweep in excel. So if it helps for simplicity, you can assume the pressure is 100 psi.

How do I calculate the flow rate (in GPM)? Do I need to take away the outlet of the system?

Currently I am thinking using:

hL = [k(v)^2]/(2g)
ΔP = (ρ*hL)/144
then what for q??

Or I am thinking q = K*A*(2*144*g*ΔP/ρ)
but then what is ΔP?? is it the pressure drop across the converging nozzle or is it the pressure drop from the inlet to outlet at atmospheric?

 

[npc214]

Hey, sorry I cant find how to edit a post.

Wanted to include a picture of the system:

 

[msquared48]

There is no way to edit a post after you post it. You have to check it before you post.

Mike McCann, PE, SE (WA)

 

[Spoonful]

I would think Q before nozzle is equal to Q after nozzle? Maybe I didn't understand your question clear?

 

[npc214]

Yes, you are correct. I didn't pose the question too well. I do need the Q of the system.

Maybe this can help clarify the problem:

http://www.physicsforums.com/showthread.php?t=764003

 

[lhwingking]

FYI, you can re-post and "red flag" your old one for deletion. Or, if it is a small edit/typo you can red flag it and a change will be made.

 

[npc214]

Corrected logic:

Here is the attachment of the excel I'm working on. As you can see I have a table of variable inputs to calculate K values for varying nozzle designs. Then I have a sweep of pressures vs. the nozzle designs. What I am trying to complete is the Q (gpm) calculations for the given P and K values (based on nozzle design). The idea is that if we are given a system, we can use this table to find an appropriate nozzle design that will satisfy the job. It's not in the picture or the post, but this is a water jet eductor educting dry powder fire suppression agent.

 

[katmar]

It looks to me as though you are on the right track, but you need to take into account the K value of the sudden expansion from the outlet of your nozzle into the hose. This K value is likely to be larger than that for the converging part of the nozzle. Once you have the total K value, you can use the Darcy-Weisbach formula to solve for the flowrate. Remember to add one velocity head ( i.e. K=1) for the eventual pipe outlet - usually this is negligible with liquids, but in a high velocity situation like this it might be important.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"