If a spherical drop of liquid evaporates at a rate proportional to its area, if initially its radius is 1/20 inches, and if in 15 minutes the radius is 1/40 inches, find the radius r in terms of the time t.

Suppose that in a coating process a solid sheet immersed in a liquid is pulled steadily at velocity U through a slot in a die, as shown in the figure. The die dimensions are such that there is a liquid gap of thickness H on each side of the sheet. Far downstream from the die the coating has a final thickness H... The pressure in the upstream liquid is ambient (P = Po) and gravitational and surface tension effects are negligible. The die length is L and the system width is W. The liquid is Newtonian and Re is such that the flow is laminar. Liquid P = Po X Die Liquid Solid Sheet Liquid Die H Gas P = Po Width = W Hoo U (a) Assuming fully developed flow, determine vx(y) for the liquid in the upper gap. Be sure to use the coordinates shown. (b) Determine the force required to pull the sheet through the die. You may assume that the shear force on the sheet in the upstream liquid (x < 0) is negligible. (c) Assuming that H is given, determine H...

In planar flow of an incompressible fluid, the x component of the velocity is given by u = ½ x² + 2x – 4y. Use the equation of continuity to derive the expression for v. %3D

A pair of concentric glass cylinders, with diameters of 1 and 1.05 cm, respectively are held together in such a way that both annular ends are open to the flow of fluids. The pair of cylinders with its axis vertical are so placed that the open end is slightly below the surface of a reservoir of silicone oil at 25 deg. C. What is the expected height of the oil into the annular space between the cylinders? Take o=0.019 N/m and p=900 kg/m³.