Velocity and temperature profiles for laminar flow in a tube of radius ro=10 mm have the form u(r)=0.1[1−(rro⁄)2] T(r)=344.8+75.0(rro⁄)2−18.8(rro⁄)4 With units of m/s and K, respectively. Determine the corresponding value of the mean (or bulk) temperature, Tm, at this axial position.

Liquid flows at steady state at a rate of 2 lb/'s through a pump, which operates to raise the elevation of the liquid 100 ft from control volume inlet to exit. the liquid specific enthalpy at the inlet is 40.09 btu/lb and at the exit is 40.94 btub. the pump requires 3 btu/s of power to operate. if kinetic energy effects are negligible and gravitational acceleration is 32.174 tt/s, the heat transfer rate associated with this steady state process is most closely 1)-2,02 btu/s from the liquid to the surroundings 2)-3.98 btu/s from the surroundings to the liquid. 3)-4.96 btu/s from the surroundings to the liquid. 4)-1.04 btu/s from the liquid to the surroundings.