# Relationship between volumetric flow rate and pressure

## Main Question or Discussion Point

Hello everybody,

This is my first post. I've been working on a liquid rocket engine for a while, but I have never gotten to work on its feed system (fluid mechanics), until recently. We are using a very simple pressure fed system, and its main goal is to deliver the propellants at a specific flow and pressure to the engine. I know that Q = v*A, but this doesn't help me that much since I can't "set" the velocity of the pressurized propellants. Nevertheless, I do know their pressures and the cross sectional area of the pipes. I tried to derivate that formula to come up with another one that includes pressure, but even though the units are correct, I don't think it is correct. This is the other formula I know: Q = Cd * A * sqrt(2 dP / rho), where Cd is the discharge coefficient, dP the pressure drop, and rho, the fluid density. Sadly, dP is not very useful here neither.

So in summary, my question is: if I have a pipe of x diameter coming out from a tank with a pressure of y (assuming I know the physical properties of this fluid), what would it be its resulting flow, and how can I change it?

Best,

Roy S. Ramirez

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JBA
Gold Member
The last equation you gave is for flow through a nozzle or orifice, it does not apply for a piping loss. Regardless of that, you must know the pipe inlet pressure and discharge point backpressure to determine the flow with all piping loss analyses as well. The basic starting point for general piping systems if the backpressure at the piping discharge point is not known is to assume atmospheric pressure; although, if you are designing piping for a rocket motor fuel line then that will not get you very far because your backpressure is going to be determined by either the fuel discharge nozzle or the engine chamber operating pressure.

JBA
Gold Member
Roy, for a basic reference on piping loss analysis I recommend that, if possible, you locate a copy of the "Standard Handbook For Mechanical Engineers" by Baumeister & Marks which has a section covering this type of analysis including a sample calculation.

Roy, for a basic reference on piping loss analysis I recommend that, if possible, you locate a copy of the "Standard Handbook For Mechanical Engineers" by Baumeister & Marks which has a section covering this type of analysis including a sample calculation.
Thank you very much JBA!