(adsbygoogle = window.adsbygoogle || []).push({}); 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.

A_{1}/A_{2}= [tex]\sqrt{\frac{h1}{h2}}[/tex]

2. Relevant equations

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

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

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Tapered Sprues and Bernoulli's Eqn

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