Which combination of the following statements about steady incompressible forced vortex flow is correct?

P: Shear stress is zero at all points in the flow.
Q: Velocity is directly proportional to the radius from the centre of the vortex.
R: Total mechanical energy per unit mass is constant in the entire flow field.
S: Total mechanical energy per unit mass is constant in the entire flow field.

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

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 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