Evaluation of velocity based on Thrust information

[geg1633]

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

 

[rb1957]

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

 

[rb1957]

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)

 

[EricZhao]

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.

 

[Sparweb]

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