# What pressure drop is needed to get 15-20 gpm?

Scenario: There's a 1 inch, rubber hose, with fluid flowing in it at 75 psi. The density of the fluid changes (but I'll just be calculating with a specific known density, 8.35). So, I want to get the flowrate to 15-20 gpm. The initial flowrate is unknown (unless we can calculate it based off the pressure and hose diameter).

I'm thinking of using the pressure drop equation, but 1) the formula requires a flowrate. I don't know if I'm supposed to use the initial flowrate or somehow calculate the original and 2) to get the friction coefficient, I'd need Reynold's number, which again, requires the flowrate or velocity.

Anyone have any idea about which flowrate I'm supposed to use & whether I'm using the right equations? Thanks.

• What is the interior diameter of the hose? – Jasper Aug 15 '19 at 2:06

So you have the pressure drop equation which gives you the pressure drop if you give it a flow rate.

And you have a pressure drop and you want to know the flow rate.

I assume the pressure drop equation cannot be solved algebraically, or at least that you find it too intimidating.

So -- iteratively solve the pressure drop equation with different guesses at the correct flow rate. Refine your estimated flow rate until the calculated pressure drop is accurate enough for you. That is your answer.

If you generalize this -- "I have a function $$y = f(x)$$, I want to know $$x$$ given $$y$$", then for any such problem the approach is to first try to find an exact solution algebraically, and, if you can't do that, solve it iteratively.

The iterative solution is so common that any math package (Matlab, Scilab, Octave, Numpy, MathCad, Mathmatica, etc.) will have a solver. It'll have a collection of built-in functions that solve the equation $$f(x) = 0$$. You write your $$f(x)$$, hand it to the solver with an initial guess $$x_0$$, and then usually before you lift your finger from the "enter" key you have an answer.

In your case, your $$f(x)$$ would be the pressure drop from the pressure drop equation minus the pressure drop you have.

• Thanks for the response, but I'm still confused on which flowrate I"m supposed to use. Am I supposed to use my target flowrate or the initial flowrate (which I don't have but I assume I can calculate from knowing pressure and diameter). PS: I'm basically just trying to make sure that I don't need more than a 5 psi pressure drop to achieve a 15-20 gpm flowrate. – carsof Jul 15 '19 at 20:35
• Then please edit your question to show that you want that flow rate at that maximum pressure drop. "What result will I get" is very different from "will my result fit within these bounds?" – TimWescott Jul 15 '19 at 21:11
• just want to add that excel also has a solver – mart Aug 16 '19 at 10:14