Initial velocity of air from tank

1. Aug 13, 2010

macum

Hi all,

I am trying to work out the initial velocity of dry air, through a 3" opening in a pressurized tank (150 psi).

I thought I should use Bernoulli's eq. as a start: P=1/2*rho*V^2 by changing the formula to give velocity, V = sqrt(P*2/rho)

Then I realized there was no time value in the result.

I'm sure this is a pretty lame question but any help would be appreciated.

Thanks

2. Aug 13, 2010

Staff: Mentor

Welcome to PF. You're thinking and process is good here - you wouldn't believe how many people simply ignore units altogether and get wrong results because of it.

There is a neat little trick you can do to units: you can apply an equation to them without even using any numbers. So try writing out the units of the equation f=ma then substiting those units into the "force" part of the pressure units. You should find your final units are the proper units for velocity.

What this means is that the numerical answer won't change from what you already calculated. But you'll find that the answer you got is above the speed of sound. This basic form of Bernoulli's equation is only valid for incompressible flow, which is to say only below about 220 mph. Beyond that, the rules change completely when you get to the speed of sound: the shock waves that form actually prevent the air from going above the speed of sound. This is called "choked flow": http://en.wikipedia.org/wiki/Choked_flow

So what this means for your situation is that the velocity through the orifice of the opening will be exactly the speed of sound. This will tell you the max possible mass flow rate through the opening. And assuming there is no well-shaped diverging duct at the end of this opening, it'll quickly spread out and drop below the speed of sound.

3. Aug 13, 2010

macum

Thanks Russ,
I see what you're saying now. It really had me stumped but now I can proceed with the rest of my calcs.
And thanks for pointing out the "choke", it makes perfect sense and actually simplifies things.

Again, thanks!