To rewrite:
This function in dimensionless form, using dimensional analysis.
Answer to Problem 5.2CP
The dimensionless function is
Explanation of Solution
Given Information:
For fluid exiting a nozzle which is a gas instead of water, upstream pressure p1is large and d2,the exit diameter is small. The difference
Ref Fig 3.49:
Concept Used:
The number of pi groups are to be calculated:
Where, k is the number of variables and r is the number of fundamental references.
On substituting 5 for k and 4 for r ,
Calculation:
Dimensional analysis is applied to find the pi groups.
Where
On substituting
On equating M coefficients:
On equating
On equating T coefficients:
On equating L coefficients:
Therefore, the following values are obtained:
Therefore, the pi group is as follows:
Hence, the pi group is:
Conclusion:
The dimensionless function is
To plot:
Data using the dimensionless form obtained, a curve fit formula and a single value of a range.
Answer to Problem 5.2CP
The data is plotted as above and the measured value of
Explanation of Solution
Given Information:
For fluid exiting a nozzle which is a gas instead of water, upstream pressure p1 is large and d2, the exit diameter is small. The difference
Ref Fig 3.49:
Diameter of pipe, d2 = 1 cm
The following values of mass flow through the nozzle are shown by the measurements for flow of air:
Concept Used:
The value of
T( K) | |
300 | 0.543 |
300 | 0.54 |
300 | 0.538 |
500 | 0.543 |
800 | 0.543 |
Calculation:
The pi value is calculated by substituting 0.037 kg/s for
And
The values obtained are plotted on the graph as follows:
Hence, the measured value of
Conclusion:
The data is plotted as above and the measured value of
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Chapter 5 Solutions
Fluid Mechanics
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