Bernoulli's Equation (Water Outflow Speed of Tank)

1. Jan 18, 2013

Von Neumann

Problem:

Suppose the top of a tank is sealed and pressurized to twice atmospheric pressure. What is the speed of the liquid emerging from a small hole at the base of the tank?

My Solution:

Using Bernoulli's Equation, and assuming v_top ≈ 0,

P_top + 1/2*ρ*v_top^2 + ρgh = P_hole + 1/2*ρ*v_hole^2 + ρg*0

2*P_a + ρgh = P_a + 1/2*ρ*v_hole^2

Solving for v_hole I get,

$\sqrt{\frac{2(P_{a}+ρgh)}{ρ}}$

While my book has,

$\sqrt{\frac{2P_{a}}{ρ+gh}}$

Anyone know where I went wrong? Or, less likely, if my text is incorrect? Thank you in advance.

2. Jan 19, 2013

voko

The text is incorrect. The sum in the denominator is impossible, the units of the addends do not match.

3. Jan 19, 2013

Von Neumann

Oh wow, I'm foolish for not thinking of that myself. My units come out to be the correct units of velocity.