For turbulent flow in a smooth, circular tube with a radius R, the velocity profile varies according to the following expression at a Reynolds number of 105: = 56.(1 − ⁄)A/C, where r is the radial distance from the center and 56. the maximum velocity at the center. Show that, for an incompressible fluid, the average velocity 68 is related to 56. through: 68 = (49⁄60)56.. If the fluid is water at 25 ℃ flowing through a 30 cm-diameter steel pipe, calculate: (i) 56., (ii) the mass velocity, (iii) the volumetric flow rate, and (iv) the mass flow rate.

Apiston-cylinder with a volume of 0.25 m3 holds 1 kg of air (r 0.287 k/kgk) at a temperature of 100 c. heat transfer to the cylinder causes an isothermal expansion of the piston until the volume triples. how much heat is added to the piston-cylinder?

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.

Refrigerant 134a enters an insulated compressor operating at steady state as saturated vapor at -26°c with a volumetric flow rate of 0.18 m3/s. refrigerant exits at 9 bar, 70°c. changes in kinetic and potential energy from inlet to exit can be ignored. determine the volumetric flow rate at the exit, in m3/s, and the compressor power, in kw.