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At a sudden contraction in a pipe the diameter changes fromD1toD2. The pressure drop,Δp, which develops across the contraction is a function ofD1andD2, as well as the velocity,V, in the larger pipe, and the fluid density, rho, and viscosity,μ. UseD1,V, andμas repeating variables to determine a suitable set of dimensionless parameters. Why would it be incorrect to include the velocity in the smaller pipe as an additional variable?

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Answer: The working and answer can be viewed from the screenshots below. Thanks

At a sudden contraction in a pipe the diameter changes fromD1toD2. The pressure drop-example-1
At a sudden contraction in a pipe the diameter changes fromD1toD2. The pressure drop-example-2
At a sudden contraction in a pipe the diameter changes fromD1toD2. The pressure drop-example-3
At a sudden contraction in a pipe the diameter changes fromD1toD2. The pressure drop-example-4
At a sudden contraction in a pipe the diameter changes fromD1toD2. The pressure drop-example-5
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