Water flows over a dam at Q = 40 m^3/s through a spillway that is 65m wide. The important parameters in this problem are the water height (h) as it goes over the spillway, the velocity (v) of the water over the spillway, the flow rate (Q), the width of the spillway (w), the density of the water (p), ad the gravity (g). (a) Are there any of the parameters above that may be eliminated from a dimensional analysis? (b) Determine the Product groups for this problem. (c) Find the flow rate required for a 0.9m-wide model.

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.

At steady state, air at 200 kpa, 325 k, and mass flow rate of 0.5 kg/s enters an insulated duct having differing inlet and exit cross-sectional areas. the inlet cross-sectional area is 6 cm2. at the duct exit, the pressure of the air is 100 kpa and the velocity is 250 m/s. neglecting potential energy effects and modeling air as an 1.008 kj/kg k, determine ideal gas with constant cp = (a) the velocity of the air at the inlet, in m/s. (b) the temperature of the air at the exit, in k. (c) the exit cross-sectional area, in cm2

The power source in a certain welding setup generates 3500w that is transferred to the low carbon steel work with a heat transfer factor of 0.85. the melting factor in the operation is 0.45. a continuous fillet weld is to be made with a cross-sectional area of 23 mm2 determine the travel speed at which the welding can be accomplished.