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.)

frictionless flow
steady flow
incompressible flow
uniform flow

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Hydraulics & Fluid Mechanics
The horizontal component of force on a curved surface is equal to the

weight of liquid vertically above the curved surface
force on the horizontal projection of the curved surface
product of pressure intensity at its centroid and area
force on a vertical projection of the curved surface

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