Concept explainers
The profile of sprue diameter as function of its height.
Answer to Problem 5.71P
The profile of sprue diameter as function of its height is shown in Figure-A.
Explanation of Solution
Given data:
The diameter at top of the sprue is
The height of the sprue is
The diameter at bottom of the sprue is
Formula used:
The expression for the area is given as,
Here,
Calculation:
The relation between area and height can be given as,
Here,
Evaluate the above equation further,
In equation 1, take
Here, equation 1 becomes,
As the reference location for the height is not known, take
So, the location of surface at height from top surface is
Substitute the value in equation 2,
Further applying the boundary conditions,
At
Substitute the values in equation 3,
At
Substitute the values in equation 3,
Solve equation 4 and 5,
Substitute the value in equation 4,
Substitute the values in equation 3,
The graph further can be plotted between the diameter and sprue height using the above equation.
Figure- A Graph between diameter and height of the sprue
Conclusion:
Therefore, the profile of sprue diameter as function of its height is shown in Figure-A.
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