Given the extended darcy-weisbach eq. for an open channel g v r l h f h l major 4 2 2 , = where f – friction factor, l – pipe length, rh – hydraulic radius, g – gravity, v—average cross section velocity. derive chezy eq. as follow q = ca rh s and determine c. in the equation, q is flow rate, and s is the channel bottom slope. you will score only if you do the derivation step by step, correctly in logic, and clearly state your assumption, if any (10 pts).

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.