# Tapered Sprues and Bernoulli's Eqn

• ACE_99
In summary, the conversation discusses the importance of using a tapered sprue in sand casting to prevent aspiration. The relationship between the areas of the top and bottom of the sprue must follow A1/A2 = √(h1/h2) to avoid defects in the resulting casting. The attempt at a solution includes using Bernoulli's and continuity equations to find the velocity of the molten metal, but further information is needed to accurately solve the problem. A diagram and detailed steps would be helpful in finding the solution.
ACE_99

## 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.

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

## Homework Equations

Bernoulli's Equation = h + $$\frac{v2}{2g}$$ +$$\frac{P}{\rho}$$ + 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 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?

The OP is dated Dec 20, 2009

ACE_99 said:
h2 = 0
If one is to obtain a ratio with h2 as the denominator, then it should not be 0.

Is A1 > A2? Or rather what is the relationship between top and bottom cross sections?

It would help to provide a diagram and show the steps in solving the problem.

## 1. What is the purpose of a tapered sprue in casting?

A tapered sprue is used in casting to control the flow of molten metal into the mold. It helps to regulate the amount of metal entering the mold and prevent defects such as porosity and shrinkage in the final product.

## 2. How does Bernoulli's equation relate to tapered sprues in casting?

Bernoulli's equation, which describes the relationship between fluid velocity and pressure, is used to calculate the velocity of molten metal as it flows through a tapered sprue. This is important in determining the optimal size and shape of the sprue to achieve the desired flow rate and prevent turbulence.

## 3. Can tapered sprues improve the quality of a casting?

Yes, tapered sprues can greatly improve the quality of a casting by reducing defects and ensuring a consistent flow of molten metal into the mold. They also help to increase the yield of usable castings and reduce production costs.

## 4. Are there different types of tapered sprues?

Yes, there are several types of tapered sprues including straight, conical, and stepped sprues. The type used depends on the shape and size of the mold, as well as the type of metal being cast.

## 5. How do you determine the optimal size and shape of a tapered sprue?

The optimal size and shape of a tapered sprue can be determined through a combination of experience and mathematical calculations. Factors such as mold design, metal type, and casting temperature all play a role in determining the ideal sprue dimensions for a specific casting process.

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