The drag force d that a fluid exerts of a thin vertical rectangular plate is function of the plate height h, plate width w, the fluid dynamic viscosityp, the fluid density p, and the fluid flow velocity v. using buckingham pi theorem, determine all the dimensionless products (ls) of the problem.

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 the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct.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.