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Physics Assignment Help With Continuity Equation for fluid

8.8 Continuity Equation for fluid

This is a mathematical expression for the conservation of fluid mass following in a region. Consider a streamline fluid entering in a pipe at P and leave it at point Q. If P be the density of fluid at a point where velocity v then mass of fluid enter a region of cross-section area A is

fluid statics1

m = rvA

Since there is no distribution of mass while flowing from P to Q, so mass entering per second is equal to mass learning at Q per second, i.e.

mp = mQ

or rpvpAp = rQvQAQ

In general rvA = constant

This is the equation of continuity. If the fluid is compressible, then r = constant at each point in fluid. Thus, the equation of continuity reduces to

vA= constant

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