Moving plate и, (a) General picture Ton plate Moving plate - y = D At y = D: u = uT = T_ T on fluid Parallel streamlines T, on fluid At y = 0:u = 0,T = T,, Чw y = 0 Fixed surface T„ on surface (b) Detailed model Figure 16.2 Model for Couette flow.

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…

7. Consider a fluid flow between two parallel fixed plates 5 cm apart. The velocity distribution of the flow is given by u(y) =120(0.05-y²) m/s where y is in meters. The fluid is water at 10°C. Calculate the magnitude of the shear stress along each of the plates.

Problem 1 – A laminar flow fluid of known density (ρ) and viscosity (μ) flows between twoparallel plates with different velocities in the same direction. The top plate has a velocity Utop inthe positive x direction. The bottom plate has a velocity Ubot in the positive x direction. The twoplates are a distance of “a” apart. There is a pressure gradient in the x direction ( ). Derivean expression of the velocity and shear stress profiles between the two plates

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.