A shower is fed through two pipes that merge together to feed the shower head. Cold water at temperature T1 is carried through pipe 1 of diameter D1 at a flow rate Q1, while hot water at temperature T2 flows at an average velocity U2 through pipe 2 of diameter D2. Knowing that the shower head has N holes each of diameter dh, determine the expression of the temperature of the water coming through the shower head as well as the average velocity of the shower head jets through each hole. Assume that all physical properties are constant and independent of temperature