Concept explainers
(a)
The dimensional parameter generated by the given quantities.
Explanation of Solution
Given information:
In the given question,
We use the method of variable to find the dimensionless quantity from the given data.
Total number of parameters given,
n = 5 |
We define the function as,
Primary dimensions of all the given parameters,
The number of primary dimensions is (L, M, t).
Since the value of n is 5.
So,
J = 3,
And,
k = (N − J)
k = (5 − 3) = 2.
So, the number of pi-terms is two.
For further calculation we need to choose any three repeating quantities,
I choose
Thus, by using repeating variables, first independent pi- term is formed.
So, the substituting the values of variables to get a dimensionless relationship.
Thus, the required relationship is,
On simplifying,
(b)
The change in
Answer to Problem 97P
Explanation of Solution
Given information:
From subpart a,
On simplifying,
When h is doubled,
(c)
The change in
Answer to Problem 97P
Explanation of Solution
Given information:
From subpart a,
On simplifying,
When
(d)
The number of experiments required to describe complete relationship.
Answer to Problem 97P
The number of experiments required is 2.
Explanation of Solution
Given information:
From previous problem,
There exist two pi-terms in the given question,
So, we need to perform two experiment for generation complete relationship between the given parameters.
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Chapter 7 Solutions
Fluid Mechanics: Fundamentals and Applications
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