A piston having a diameter of 9in. and a length of 995in. slides downward with a velocity V through a vertical pipe. The downward motion is resisted by an oil film between the piston and the pipe wall. The film thickness is 90000 in., and the cylinder weighs 7836lb. Estimate V if the oil kinematic viscosity is 7800 ft/s and its density 432 slugs/ft.Assume the velocity distribution in the gap is linear.

An inner radius of an artery is 4.00×103 m. Blood flows through the artery at the rate of 1.00 x 10-6 m³ s'. The blood has a dimensional relative viscosity of 5.2 and viscosity of continuous phase with 10.84x103 Pås and a density of 1.06 × 10 kg m³. Compute the kinematic viscosity and åverage blood velocity in the artery.

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…

6. A hydraulic lift (see below) of the type commonly used for greasing automobiles consists of a 280.00 mm diameter ram which slides in a 280.18 mm-diameter cylinder, the annular space being filled with oil film of thickness t = 0.09 mm, having a viscosity 0.3612 kg/(m s). If the rate of travel of the ram is v= 0.22 m/s, find the frictional resistance when 2 m of the ram is engaged in the cylinder. Take the weight of ram as 500 N. Ram Oil film -Fixed cylinder