Consider flow through the sudden expansion shown. If the flow is incompressible and friction is neglected, show that the pressure rise, \(\Delta p=p_{2}-p_{1}\), is given by

\[\frac{\Delta p}{\frac{1}{2} ho \bar{V}_{1}^{2}}=2\left(\frac{d}{D}\right)^{2}\left[1-\left(\frac{d}{D}\right)^{2}\right]\]

Plot the nondimensional pressure rise versus diameter ratio to determine the optimum value of \(d / D\) and the corresponding value of the nondimensional pressure rise.

Transcribed Image Text:

d P4.77 (2 D