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
uniform flow
incompressible flow
steady flow

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Hydraulics & Fluid Mechanics
According to Bernoulli’s equation for steady ideal fluid flow

total energy is constant throughout
velocity and pressure are inversely proportional
the energy is constant along a stream-line but may vary across streamlines
principle of conservation of mass holds

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