Hydraulics & Fluid Mechanics
The continuity equation pi V,A,= p2V2A2 is based on the following assumption regarding flow of fluid (where pi and p2 are mass densities.)

incompressible flow
frictionless flow
uniform flow
steady flow

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Hydraulics & Fluid Mechanics
The shear stress distribution for a fluid flowing in between the parallel plates, both at rest, is

parabolic distribution across the section
zero at the mid plane and varies linearly with distance from mid plane
zero at plates and increases linearly to midpoint
constant over the cross section

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