Concept explainers
The relationship in dimensionless form.
Answer to Problem 5.37P
Explanation of Solution
Given information:
Volume flow
Pipe diameter
To find the relation between these variables,
Basically we have some steps to follow,
1. Find the number of variables
2. Find the dimensions of the given variables.
3. Find
4. In other words
5. Find the number of desired pi products
6. Finally write the dimensionless function obtained.
Calculation:
Write the function,
Count the number of variables
Find dimension of each variable,
Find
Find the number of pi products,
To obtain the equation,
To find the first pi group combine
Equate exponents,
Length:
Mass:
Time:
Therefore, we get
Therefore, the expression will be,
To find the second pi group combine
Equate exponents,
Length:
Mass:
Time:
Therefore, we get
Therefore, the expression will be,
To find the third pi group combine
Equate exponents,
Length:
Mass:
Time:
Therefore, we get
Therefore, the expression will be,
The original relation between 6 variables can be reduced in to 3 dimensionless groups as below,
Conclusion:
The expression between the given variables can be written as,
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Chapter 5 Solutions
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