Concept explainers
Prove that the flow field specified in Example 2.1 is not incompressible; i.e., it is a compressible flow as stated without proof in Example 2.1.
To prove:
The flow in example 2.1 is compressible.
Explanation of Solution
Calculation:
Velocity field for the subsonic flow is expressed as follows:
Differentiate the equation (1) with respect to x as follows:
Differentiate the equation (2) with respect toy as follows:
The divergence of a vector field is calculated as follows:
Rate of change of volume is calculated as follows:
Substitute the values in the above equation as follows:
Apply the control volume equation as follows:
This shows that the given flow is compressible by 73.37%.
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