- #1

Von Neumann

- 101

- 4

**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,

[itex]\sqrt{\frac{2(P_{a}+ρgh)}{ρ}}[/itex]

While my book has,

[itex]\sqrt{\frac{2P_{a}}{ρ+gh}}[/itex]

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