For a flow in the xy plane, the x component of velocity is given by u = Ax2y2, where A = 0.4 m-3 · s-1, and x and y are measured in meters. (a) Find a possible y component for steady, incompressible flow. (b) Is it also valid for unsteady, incompressible flow? (c) How many possible y components are there? (d) Determine the equation of the streamline for the simplest y component of velocity (use C as constant).

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.