For a very rough pipe wall the friction factor is constant at high Reynolds numbers. For a pipe of diameter D1 the pressure drop over the length is capital delta P subscript 1. If he diameter of the pipe is then reduced to one-half the original value what is the relation of the new pressure drop capital delta P subscript 2 to the original pressure drop capital delta P subscript 1 at the same mass flow rate?

Agas contained within a piston-cylinder assembly e end nation about same energy states, 1 and 2, where pi 10 bar, v undergoes two processes, a and b, between the sam 0.1 m3, ui-400 kj and p2 1 bar, v2 1.0 m2, u2 200 kj: process a: process from 1 to 2 during which the pressure- volume relation is pv constant process b: constant-volume process from state 1 to a pressure of 2 bar, followed by a linear pressure-volume process to +20 0 state 2 kinetic and potential energy effects can be ignored. for each of the processes a and b, (a) sketch the process on p-v coordinates, (b) evaluate the work, in kj, and (c) evaluate process the heat transfer, in kj