Problem 12.1 = Assume the temperature of the exhaust in an exhaust pipe can be approximated by T = To(1 + ae-b)[1 + c cos(wt)], where To 100 C, a = 3, b = 0.03 m, c = 0.05, and w = 100 rad/s. If the exhaust speed is a constant 2 m/s, determine the time rate of change of temperature of the fluid particles at x = 0 and x = 4 m when t = 0. Is the flow steady or unsteady? If unsteady what causes it? Problem 12.2 A fluid flows past a sphere with an upstream velocity of Vo = 40 m/s as shown in the fiqure. From a more advanced theory it is found that the speed of the fluid along the front part of the sphere is V = Vo sin 8. Determine the streamwise and normal components of acceleration at point A if the radius of the sphere is a = 0.20 m. Vo Problem 12.3 40 Compute the acceleration vector for the following 2-D cylindrical flows: wree a) Rigid body rotation: = wri b) Radial in-flow:= -Q/2re,