y Q1 As illustrated in left figure, given the H uo steady shear flow for two layers of fluids, a constant Fluid 1 velocity uo is maintained for fluid 2 @ y = H with "no h slip" boundary condition at stationary plate for fluid 1 @ Fluid 2 x y = 0. If fluid 1 is shear thinning (I1 = C1D1//1) while fluid 2 is shear thickening (I2 = C2/2D2), where C1,2 are constants and /1,2 = dux1,2/dy are steady shear rates), representative. Please determine steady shear rate of fluid 2 /2 @ interface with y = h. Q2 Knowing the description on the velocity of a flow ux = - tx, uy =t(y+1), please determine the pathline and the streamline function. Q3 Given the velocity of a steady flow ux = x -4y, uy =- y -4x, please determine whether the flow is incompressible and/or irrotational. If so, please calculate the stream function y and potential function ¢ for the flow. Q4 Please determine the pressure distribution for the irrotational 2D flow (with fluid density of p) by superposing flow of free vortex (ue = c/r in polar coordinates, c is a constant) with constant speed flow (ux = A, uy = B in Cartesian coordinates, A, B are constants).