Question

Laminar flows takes place between two parallel plates. The distance between the plates is $B$. The minimum depth of flow from the bottom plate where local velocity is equal to $3/4^{th}$ the average velocity of flow is kB. The value of k (correct upto two decimal place) is ____.

• A. 0.14

Answer 1

The correct option is A 0.14
The velocity at a distance from bottom plate between two parallel plates is given by,
$u=\frac{1}{2\mu }(-\frac{\partial p}{\partial x})(By-y^2)$
Average velocity, $u_{avg}=\frac{1}{12\mu }(-\frac{\partial p}{\partial x})B^2$
As per question,
$\frac{3}{4}\left(\frac{1}{12\mu }\right)(-\frac{\partial p}{\partial x})B^2=\frac{1}{2\mu }(-\frac{\partial p}{\partial x})(By-y^2)$
$\frac{B^2}{8}=By-y^2$
$B^2=8By-8y^2$
$8y^2-8By+B^2=0$
$y=\left[\frac{8\pm \sqrt{8^2-(4\times 8\times 1)}}{16}\right]\times B$
$=0.146B,0.854B$
$\therefore$ Minimum depth from the bottom plate $=kB=1.146B$