4. Fluid Mechanics

By using Bernoulli and mass balance equations, velocity at the point 2 (\(v_2\)) is obtained as \[v_2 = \frac{1}{\sqrt{1-\beta^4}}\sqrt{\frac{2(P_1-P_2)}{\rho}}\] where \(\beta=D_2/D_1\). The above equation applies strictly to the frictionless flow of non-compressible fluids. To account for the small friction loss between locations 1 and 2, the above equation is corrected by introducing an empirical factor \(C_f\), known as the flow coefficient.