Chapter 8, Problem 8.10P

Interpretation Introduction

Interpretation: The relation for the pressure gradient between two parallel plates is to be determined for the zero shear stress at lower wall.

Concept introduction:

The differential equation governing the motion of the fluid between the two horizontal plates is,

  $\frac{{\text{d(τ}}_{\text{yx}}\text{)}}{\text{dy}}\text{-}\frac{\text{dP}}{\text{dx}}\text{=}\text{0}$ ....... (1)

  ${\text{τ}}_{\text{yx}}$ = Shear stress developed

P = Pressure around the plates due to fluid

The shear stress developed is given as,

  ${\text{τ}}_{\text{yx}}\text{=}\text{μ}\frac{{\text{dv}}_{\text{x}}}{\text{dy}}$ ....... (2)

  $\text{μ}$ = Viscosity of the fluid

  $\frac{{\text{dv}}_{\text{x}}}{\text{dy}}$ = Shear rate

Here, v_x is the velocity in the x direction and y is the distance from the interface.