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Evaluation of velocity based on Thrust information

Evaluation of velocity based on Thrust information

Evaluation of velocity based on Thrust information

(OP)
Hello,
I'm trying to determine the flow velocity at the exit of an axial flow jet pump.  The pumps create a thrust of 900 lbs, and have a 80 mm exit diameter, 160 HP.  Flow at the exit has a pressure of approx 120-130 psi.

I first evaluated the velocity by computing the head associated with the pressure, but then I was wondering if i could also use the thrust to compute velocity. Flow rate is a function of velocity and area, so if Thrust is a function of flow rate, I would be able to determine velocity, right? So what is the relationship between thrust and velocity?

Thanks!
Greg

RE: Evaluation of velocity based on Thrust information

this may not be correct, but it's what you get for free !

p = 1/2*rho*V^2
so you need to know the fluid (i'm sure you do)
but ...

Force = integral p dA

assuming your pressure 120 psi is constant over your area 31sq.in, you get a force of >3000 lbs; so either
pressure isn't constant across the cross-section, or
your pressure isn't dynamic, or
i'm doing something wrong (see preface remarks !)

if you knew the mass flow rate (by running the pump from a reservior) you'd get a better idea as to the average velocity of the jet.

good luck

RE: Evaluation of velocity based on Thrust information

oops,
area = 8sq.in
so that makes force = 120*8 = 960 lbs (much like your thrust !!)

so if you know the fliud density then its ...
p = 1/2*rho*V^2
so that V = sqrt(2p/rho)

RE: Evaluation of velocity based on Thrust information

I don’t think the above post gives the correct formula.
According to the momentum equation:

F = flow rate*V = rou*V*A*V = rou*A*V^2.

This formula can be found in any jet propulsion book.

RE: Evaluation of velocity based on Thrust information

You can relate the mass flow rate to the area, velocity, and density, but that doesn't give you thrust.

M = rho*V*A

Since you don't know V yet, you must solve the equation simultaneously with the Thrust equation:

T = M * ( Ve - Vo) + (Pe - Po)*A       (Ref. Anderson)

My answer came out around 800 ft/sec exit velocity.

Make sure you're using STATIC pressure in the equation, not dynamic pressure, nor stagnation pressure.

Steven Fahey, CET

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