A thin layer of an incompressible fluid flows steadily over a horizontal smooth plate as shown in

Question:

A thin layer of an incompressible fluid flows steadily over a horizontal smooth plate as shown in Fig. P7.55. The fluid surface is open to the atmosphere, and an obstruction having a square cross section is placed on the plate as shown. A model with a length scale of \(\frac{1}{4}\) and a fluid density scale of 1.0 is to be designed to predict the depth of fluid, \(y\), along the plate. Assume that inertial, gravitational, surface tension, and viscous effects are all important. What are the required viscosity and surface tension scales?

Figure P7.55