1. The pressure drop p for steady, incompressible, viscous flow through a straight horizontal pipe depends on the pipe length l the average velocity V, the fluid viscosity , the pipe diameter D, the fluid density , the average roughness height e Determine a set of dimensionless groups that can be used to correlate data
3.  We put a plate with a weight of Mg on a drop with a volume of V on a substrate, so that the plate is supported by the sandwiched droplet, as shown in the figure The surface tension of the liquid is, and the contact angle is 180 (super hydrophobic) on the surfaces of the plate and the substrates Assuming the thickness of the droplet at the final equilibrium state is thin, find the thickness in terms of the given parameters

5. Consider a control volume (CV) of the half of a soap bubble, as shown figure. (a) Draw free body diagram' with forces acting on the CV and (b) deduce the Laplace pressure, the pressure difference across the soap film. Assume the thickness of the soap bubble is greatly thin compared with the diameter. Control volume side view