Question

Consider a laminar flow at zero incidence over a flat plate.The shear stress at the wall is denoted by ${\tau }_w$. The axial position $x_1$ and$x_2$ on the plate are measured from the leading edge in the direction of flow.If $x_2>x_1$,then

• A. ${\tau }_w{|{}_{x_1}={\tau }_w|}_{x_2}=0$
• B. ${\tau }_w{|{}_{x_1}={\tau }_w|}_{x_2}\ne 0$
• C. ${\tau }_w{|{}_{x_1}>{\tau }_w|}_{x_2}$
• D. ${\tau }_w{|{}_{x_1}<{\tau }_w|}_{x_2}$

Answer 1

The correct option is C ${\tau }_w{|{}_{x_1}>{\tau }_w|}_{x_2}$

Laminar flow over plate
As per Blasius equation

$C_{fx}=\frac{0.664}{\sqrt{R_{ex}}}$
and

$C_{fx}=\frac{{\tau }_w}{\frac{1}{2}\rho u_{\infty }^2}$

$\frac{0.664}{\sqrt{\frac{u_{\infty }x}{v}}}=\frac{{\tau }_w}{\frac{1}{2}\rho u_{\infty }^2}$

${\tau }_w\propto \frac{1}{\sqrt{x}}$

as $x_2>x_1$

${\tau }_{w2}<{\tau }_{w1}$