Hydrodynamics: Pressure of water coming out of a glass

[qnney]

"What pressure do you need to get water to flow at 2 m/sec coming out of a hole?"

Here is the visual of a container sitting on top of a glass of water with a hole poked through the bottom: http://i96.photobucket.com/albums/l168/synovial/fluids.jpg

Given: A₁, A₂, V₂, (y₁-y₂)

Find: p_atm

Useful equations:
Bernoulli's Equation:
p₁ +[tex]\rho[/tex] [tex]\cdot[/tex] g [tex]\cdot[/tex] y₁ + 0.5 [tex]\rho[/tex][tex]\cdot[/tex] V₁² = p₁ +[tex]\rho[/tex] [tex]\cdot[/tex] g [tex]\cdot[/tex] y₂ + 0.5 [tex]\rho[/tex][tex]\cdot[/tex] V₂²

A₁V₁ = A₂V₂


I'm not sure how to modify the Bernoulli's equation to combine the y₁ and y₂ into (y₁ - y₂) and to also combine the pressures into p_atm. Can someone please help me?

 

[denverdoc]

Bernoullis is just a statement of conservation of energy.

The potential energy is the static pressure = rho*g*h where rho is density and the
kinetic energy =1/2pho*v^2.

Look familiar? So we convert from one form to the other.

Almost like a kinematics problem.

 

[qnney]

I'm not sure I understand. Is the pho supposed to be rho or p*rho?

 

[denverdoc]

rho throughout. But as it turns out it is a common factor leaving 2gh=v^2. As I said, does this look familiar?

 

[qnney]

Yes it does... especially the 2gh=v^2.

One last question: do I need the v^1, or can I find it from what is given?

 

[denverdoc]

Well if you mean v^1 is velocity, yes that is what we are trying to solve for as in equal to 2m/second. So yes you need to take the square root if that is what you are asking.

 

[qnney]

Yes... thank you!