The velocity profile for a steady laminar flow in a circular pipe of radius R is given by u=u0(1−r2R2) . If the fluid density varies with radial distance r from the centerline as rho=rho0(1+rR)14 , where rho0 is the fluid density at the pipe center, obtain and choose the correct relation for the bulk fluid density in the tube.

What is the heat treatment of metals? what is the benefit of it? why and how it's useful? answer in details, do not write by hand.

Water vapor initially at 10 bar and 400 °c is contained within a piston-cylinder assembly. the water lost heat to the surrounding according to isochoric (iso-volumetric) process until its temperature is 150 °c. the water is then condensed isothermally to saturated liquid. for the water as a system, calculate the work in kj/kg

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