Consider a steady incompressible flow through a channel as shown below.

The velocity profile is uniform with a value of $${u_0}$$ at the inlet section $$A$$. The velocity profile at section B down stream is

$$$u\left\{ {\matrix{ {{V_m}{y \over \delta },} & {0 \le y \le \delta } \cr {{V_m},} & {\delta \le y \le H - \delta } \cr {{V_m}{{H - y} \over \delta },} & {H - \delta \le y \le H} \cr } } \right.$$$

The ratio $${{{P_A} - {P_B}} \over {{1 \over 2}\rho {u_0}^2}}$$ (where $${{P_A}}$$ and $${{P_B}}$$ are the pressure at section $$A$$ and $$B$$ respectively and $$\rho $$ is the density of the fluid ) is

Consider an incompressible laminar boundary layer flow over a flat plate of length $$L$$, aligned with the direction of an incoming uniform free stream. If $$F$$ is the ratio of the drag force on the front half of the plate to the drag force on the rear half, then

Oil flows through a $$200mm$$ diameter horizontal cast iron pipe (friction factor, $$f=0.0225$$) of length $$500m.$$ The volumetric flow rate is $$0.2{m^3}/s.$$ The head loss (in $$m$$) due to friction is (assume $$g=9.81$$ $$m/{s^2}$$)

Consider steady laminar incompressible axi-symmetric fully developed viscous flow through a straight circular pipe of constant cross - sectional area at a Reynolds number of $$5.$$ The ratio of inertia force to viscous force on a fluid particle is