
Concept explainers
The given relation in a dimensionless form using Ipsen’s method.

Answer to Problem 5.40P
Explanation of Solution
Given information:
The time
Hole diameter
Initial volume
Initial depth
Density
Viscosity
Ipsen’s method is a way to find all pi products at once.
We have to use either multiplication or division to eliminate each dimension in a function.
Usually we eliminate mass
Then
By doing this, finally we get a dimensionless relation between the variables.
Calculation:
Write the function with respective dimensions,
First of all,
Eliminate mass
For that, select density
Therefore, we can rewrite the equation as,
Now, discard
Select
Therefore, we can rewrite the equation as,
Now, finally eliminate
Now discard
Conclusion:
The relation between the given variables can be written as,
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