Problem 4. The velocity of a shearing flow is given by = 2 , and , = 0. The dynamic viscosity of the fluid is = 1. Compute the viscous force (x- and y- components) that the fluid acts on a control surface that is an upper-half cylinder with radius = 1. Assume the depth of the flow and cylinder in z-direction is 1.

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Problem 5. For the parabolic shearing flow shown in Problem 1.65 in the textbook, if U=2, h=0.1, the dynamic viscosity of the fluid = 1, and the angle of the river bed is 30 degree with respect to the ground. Compute the viscous force acted on a vertical surface facing right (as shown in red color). The surface starts from the river bottom and ends at the free surface. Assume the depth of the flow in z-direction is 1.