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
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
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