# Homework Help: Tapered Sprues and Bernoulli's Eqn

1. Dec 20, 2009

### ACE_99

1. The problem statement, all variables and given/known data

In sand casting, the sprue should be tapered. If a sprue with a constant cross-sectional area is used, aspiration may take place whereby air will be sucked in or entrapped in the molten metal, causing defects in the resulting casting. To avoid aspiration, show that the areas of the top and bottom of the sprue must obey the following relationship.

A1/A2 = $$\sqrt{\frac{h1}{h2}}$$

2. Relevant equations

Bernoulli's Equation = h + $$\frac{v2}{2g}$$ +$$\frac{P}{\rho}$$ + F = Constant
Continuity Equation = Q = vA

3. The attempt at a solution

So if we take the bottom of the sprue to be the reference point then h2 = 0 and v1 = 0 then we get v2 = $$\sqrt{2gh1}$$. Now if I sub the velocity into the continuity equation I get

A1/A2 = $$\sqrt{\frac{h1}{h2}}$$

which is not correct. What am I missing?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution