Bernoulli's Equation (Water Outflow Speed of Tank)

[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.

 

[voko]

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

 

[Von Neumann]

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