Question

Velocity distribution in a boundary layer flow over a plate is given by
$\left(u/u_m\right)=1.5\eta$
where, $\eta =y/\delta ,$ y is the distance measured normal to the plate, $\delta$ is the boundary layer thickness, and $u_m$ is the maximum velocity at $y=\delta$. If the shear stress $\tau$, acting on the plate is given by
$\tau =K\left(\mu u_m\right)/\delta$.
Where $\mu$ is the dynamic viscosity of the fluid, K takes the value of

• A. 0
• B. 1
• C. 1.5
• D. None of these

Answer 1

The correct option is C 1.5

$Given,\frac{u}{u_m}=1.5\eta ;\eta =\frac{y}{\delta }$

$\therefore u=1.5u_m\times \frac{y}{\delta }$

$\frac{du}{dy}=1.5\frac{u_m}{\delta }$

$Now,\tau =\mu \frac{du}{dy}=1.5\mu \frac{u_m}{\delta }$
$\therefore$ $K=1.5$