The velocity profile inside the boundary layer for flow over a flat plate is given as $${u \over {{U_\infty }}} = \sin \left( {{\pi \over 2}\,{y \over \delta }} \right),$$ where $${U_\infty }$$ is the free stream velocity and $$'\delta '$$ is the local boundary layer thickness. If $${\delta ^ * }$$ is the local displacement thickness, the value of $${{{\delta ^ * }} \over \delta }$$ is

A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is $${U_0}.$$ The velocity profile at the inlet $$a$$-$$b$$ is uniform, while that at a downstream location $$c$$-$$d$$ is
given by $$u = {U_0}\left[ {2\left( {{y \over \delta }} \right) - {{\left( {{y \over \delta }} \right)}^2}} \right]$$

The ratio of the mass flow rate, $$\mathop {m{}_{bd}}\limits^ \bullet ,$$ leaving through the horizontal section $$b$$-$$d$$ to that entering through the vertical section $$a$$-$$b$$ is

Air ( $${\rho = 1.2\,\,kg/{m^3}}$$ and kinematic viscosity, $${v = 2 \times {{10}^{ - 5}}{m^2}/s}$$ ) with a velocity of $$2m/s$$ flows over the top surface of a flat plate of length $$2.5m.$$ If the average value of friction coefficient is $${C_f} = {{1.328} \over {\sqrt {{{{\mathop{\rm Re}\nolimits} }_x}} }},\,\,$$ the total drag force (in $$N$$) per unit width of the plate is ____________

An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is $$1mm$$ at a location where the Reynolds number is $$1000$$. If the velocity of the fluid alone is increased by a factor of $$4,$$ then the boundary layer thickness sat the same location, in $$mm$$ will be