Question

The velocity distribution for flow between two fixed parallel plates

• A. is constant over the cross-section
• B. is zero at the plates and increases linearly to the mid-plane
• C. varies parabolically across the section
• D. is zero in middle and increases linearly towards the plates

Answer 1

The correct option is C varies parabolically across the section

• The expression for velocity of flow between two parallel plates is given by :

$u=\frac{1}{2\mu }\left(\frac{-\partial P}{\partial x}\right)(\text{By}-y^2)$

$\text{where,}$

$B=\text{Distance between the plates}$

$y=\text{Distance of point from one of the plate}$

$\mu =\text{Dynamic viscosity of flowing fluid}$

$\left(\frac{-\partial P}{\partial x}\right)=\text{Pressure gradient along the flow}$

• It is clear from the expression that the velocity distribution between two plates is parabolic with max. value at the centre and minimum (zero) at the boundary/plate surface.

Note:

• $u_{\text{max}}(\text{at}y=\frac{B}{2})=\frac{1}{8\mu }\left(\frac{-\partial P}{\partial x}\right)B^2$
• $u_{\text{avg}}$$=\frac{2}{3}{u}_{\text{max}}$
• If one of the plate is moving with velocity V and other is at rest, then expression for velocity is as following:

$u=\frac{Vy}{B}+\frac{1}{2\mu }\left(\frac{-\partial P}{\partial x}\right)(\text{By}-y^2)$