Question

The velocity distribution in the boundary layer is given by $\frac{u}{U}=\frac{y}{\delta },$ where u is the velocity at a distance of y from the boundary and u=U at y=$\delta ,\delta$ being boundary layer thickness. Then the value of momentum thickness will be

• A. $\frac{\delta }{2}$
• B. $\frac{\delta }{4}$
• C. $\frac{\delta }{6}$
• D. $\frac{\delta }{8}$

Answer 1

The correct option is C $\frac{\delta }{6}$

$\frac{u}{U}=\frac{y}{\delta }\theta ={\int }_0^{\delta }\frac{u}{U}[1-\frac{u}{U}]dy{\int }_0^{\delta }\frac{y}{\delta }[1-\frac{y}{\delta }]dy\frac{\delta }{2}-\frac{\delta }{3}=\frac{\delta }{6}$