Chapter 8, Problem 8.13P

Interpretation Introduction

Interpretation:

The pressure rise and the efficiency for the given device as a function of the flow per unit depth are to be determined.

Concept Introduction:

Equation for the pressure drop for a Newtonian and continuous fluid which flows through a pipe with incompressible, steady, laminar, and fully developed flow is:

  $\frac{dP}{dx}=\frac{d\tau }{dy}$ ................ (1)

Here, $dP/dx$ is the pressure gradient along the length of the pipe and $d\tau /dy$ is the rate of shear stress.

The relationship between the viscosity $\left(\mu \right)$ , rate of shear strain $\left(d{v}_x/dy\right)$ , and stress $\left(\tau \right)$ is:

  $\tau =\mu \frac{d{v}_x}{dy}$ ................ (2)