Atornado may be simulated as a two-part circulating flow in cylindrical coordinates, with vr = vz = 0. vtheta = ωr if r ≤ r and vtheta = ωr2 / r if r ≥ r. determine the vorticity and the strain rates in each part of the flow.

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.