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ACE_99

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## Homework Statement

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.

A

_{1}/A

_{2}= [tex]\sqrt{\frac{h1}{h2}}[/tex]

## Homework Equations

Bernoulli's Equation = h + [tex]\frac{v2}{2g}[/tex] +[tex]\frac{P}{\rho}[/tex] + F = Constant

Continuity Equation = Q = vA

## The Attempt at a Solution

So if we take the bottom of the sprue to be the reference point then h

_{2}= 0 and v

_{1}= 0 then we get v

_{2}= [tex]\sqrt{2gh1}[/tex]. Now if I sub the velocity into the continuity equation I get

A

_{1}/A

_{2}= [tex]\sqrt{\frac{h1}{h2}}[/tex]

which is not correct. What am I missing?