Problem 2 Fomts) By applying 5 N force, glycerin is sheared between two parallel plates, as shown in Fig. 2. The gap between the plates (h) is 1.5 mm. The plates measure 10 cm in length and 5 cm in width. The bottom plate is stationary. Calculate: a) the velocity of the upper plate ( b) the Reynolds number (1 c) the power required to pull the plate Fig. 2 Flow between parallel plates Viscosity of Fluids Fluid Hydrogen Air F = 5 N Gasoline Water Ethyl alcohol Mercury SAE 30 oil P. kg/(ms) 8.8 E-6 1.8 E-5 2.9 E-4 1.0 E-3 1.2 E-3 1.5 E-3 0.29 1.5

A cylindrical machine part moves within a surrounding cylinder. The centrelines of the part and the surrounding cylinder are coincident. The cylinder is full of an oil (viscosity 0.25kg/ms) that is not flowing i.e. no pressure gradient is applied. What is the value of the viscous force exerted on the machine part as it moves along the cylinder at a speed of 9m/s? • The machine part is 0.06m long and has a radius of 0.041m. • The ratio of the machine part radius to the cylinder radius is 0.98. • Assume that the flow is dominated by viscous forces. • Give your answer as an absolute value i.e. no negative sign, in Newtons to one decimal place.

Problem 2 The apparatus sketched in the figure below serves as a viscometer i.e. it can be used to measure the viscosity of a liquid. In the drawing, D is a large reservoir containing a viscous liquid A and E is a cylindrical tube of radius R, open at both ends, surrounding and coaxial with B, which is a cylindrical "bob" of radius êR that is dragged up through the fluid by a frictionless pulley system (C) utilizing a weight W. Determine a design equation that relates the viscosity of the liquid to the geometry of the system and the weight W. Hint: you can assume that the length of the cylindrical tube is sufficiently long for the flow to reach steady state. W E D B

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…