The pressure drop, Δpp, along a straight pipe of diameter D has been experimentally studied and it is observed that for laminar flow of a given fluid and pipe, the pressure drop varies directly with the distance, l, between pressure taps. Assume that Δpp is a function of D, and l, the velocity, V, and the fluid viscosity, µµ. Use dimensional analysis to deduce how the pressure drop varies with pipe diameter.

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.

Afluid flows with a velocity field given by v=(x/t)i.. determine the local and convective accelerations when x=3 and t=1.

Determine whether or not it is possible to compress air adiabatically from k to 140 kpa and 400 k. what is the entropy change during this process?