Physics Question for you Brains

[JustinONE]

Ok, it's not aircraft related, but I need a formula for the speed of a liquid exiting from a fuel injector, with about 40 psi behind the injector, pressure always being constant.
Does anyone know how to figure this out???? :confused:

[erikhaha]

It involves summing the forces that act on the fluid stream as it exits the injector, also:

1)Fuel properties, specific weight or specific gravity.

2) Area of the hole that the fuel exits the injector.

There isn't a general equation that you could use to determine the velocity, It is more of a process.

[Ollie]

It depends what you mean by velocity of the jet. If you want to measure the average velocity across the nozzle it is simple. If you want to know the velocity changes from wall to center of the nozzle it is complex.

Collect the volume (measure) of the fluid and the time (measure) collected. The volume divided by the crossection area of the nozzel multiplied by time, equals average velocity.

Average Velocity=(volume/area) x t.

Use velocity, foot per second.
Use area, per foot squared.
Use volume, per cubed foot.

[vintage1]

Do a google on 'fluid mecahnics nozzle'

I found a site that had the formula, but netscape crashed on me.

[Berdie]

I think you probably want bernoulli's equation and the continuity equation. These work if you assume that the fluid is inviscid. If not then you have to start adding pressure losses and such. Variations involving boundary layer make it horribly complicated.
PS are u sure the pressure is constant? no pressure difference mean there's no drive for the fluid to move.

P1 +0.5*p*v1^2=P2+0.5*p*v2^2 (bernoulli)

P1, P2 - starting/finishing pressures
p - density
v1, v2 - starting/finishing velocities

A1v1=A2v2 (continuity)

A1, A2 - cross-sectional area

[erikhaha]

I like Ollies method the best. It is so simple I can't believe that I didn't think about it.

Velocity = [(Volume collected)/time] * cross sectional area of hole in injector.

Be carefull of units, Area in inches^2, volume should also be in inches^3

[markdrela]

If you have a positive displacement pump, you have to use Ollie's volume rate formula.
If you have a pressure-providing pump, you have to use Berdie's Bernoulli formula.

The latter gives
Vexit = sqrt( 2 delta_p / rho )
where delta_p is the gauge pressure provided by the pump.

For delta_p = 40 psi = 2.7e5 Pa, and rho = 850 kg/m^3 (hydrocarbon fuel), I get V = 25 m/s

[erikhaha]

Mark a few questions:

You can see the attached word document that I attached, as to the application of bernoulli's equation to this problem.
Did you assume that the initial fluid velocity was zero?

I guess I am curious as to how you solved it?

Erik