1. An oil of density p and viscosity µ, drains steadily down the side of a vertical wall, as shown. After a development region near the top of the wall, the oil film becomes independent of z and flows with a constant thickness 8. Note that the wall is very large, extending "infinitely" (compared to the thickness 8) in y and z directions. The vertical velocity can be assumed to be the only component of flow velocity. The whole flow is taking place out in the atmosphere and the atmosphere offers no shear resistance to the film. Plate Oil film Air First, reduce the continuity equation to its simplest formfor this problem by justifying each reduction/simplification. Then, using the information obtained from the continuity and other assumptions/information about the flow, reduce the remaining Navier-Stokes equations reduction/simplification. What would you obtain if you solved the reduced equations? Do not solve the reduced equations. to their simplest forms by justifying each

The block of weight W = 50 N is pulled by a weight W0 = 60 N along the surface of a table by means of an inextensible cable and a pulley. Between the block and the table there is a uniform layer of oil of viscosity m = 0.1 Pa-s and clearance h = 2 mm. The contact area is 0.01 m2. Find the terminal velocity U if the table is very long.

A smooth square cylinder is put in 15 °C  flowing water. The flow direction is perpendicular to the long axis of the cylinder (parallel to the square section). The edge length of the square is s=2.0m. The long axis length is L=5.0m.  The flow velocity is v=0.046 m/s.  The density of water is ρ=1000kg/m3.  T he dynamic viscosity is η=1.15×10-3kg/m·s. (3) Calculate the drag force FD_________N (2 decimal places)

Oil Coating: A long, continuous belt is pulled upwards through a chemical oil bath at velocity V0. The belt has rectangular cross-section and has length (L), width into the paper (W). The belt picks up a film of oil of thickness h, density ρ, and dynamic viscosity μ. Gravity g tends to make the oil drain down, but the movement of the belt keeps the fluid from running off completely. Assume fully developed, steady, laminar, incompressible and two-dimensional flow of oil to answer the following questions. Assume that no pressure gradient is needed in the vertical direction to drive the film flow. Also assume that the shear stress at the air-oil interface is zero (free shear condition). Assume no-slip condition for the fluid in contact with the moving belt. Justify any other assumptions you may make. Show all steps. (a) Derive an expression for the two-dimensional velocity field inside the oil film in terms of the known parameters. Clearly indicate your co-ordinates and origin. You must…

Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational.

1.A) A fluid of density ρ=850 kg/m3 and viscosity µ=0,8 Pa s is completely filling the spacing h= 2 cm between two parallel horizontal plates of length 2,5 m and width 1 m . The upper plate is pulled at a speed of U while lower plate is fixed . In order to generate a laminar steady incompressible flow of fluid in the spacing at a rate of 0,85 kg/s determine total shearing force in the field.ANSWER:10 N 1.B) A fluid of density ρ=850 kg/m3 and viscosity µ=0,8 Pa s is completely filling the spacing h= 2 cm between two parallel horizontal plates of length 2,5 m and width 1 m . The upper plate is pulled at a speed of U while lower plate is fixed . In order to generate a laminar steady incompressible flow of fluid in the spacing at a rate of 0,85 kg/s determine Reynolds Number of flow using the spacing as the characteristic dimension.ANSWER: 2,125 1.C) A fluid of density ρ=850 kg/m3 and viscosity µ=0,8 Pa s is completely filling the spacing h= 2 cm between two parallel horizontal plates of…