Explain briefly how the continuity equation in the form A1v1 = A2v2 arises when the cross sectional area changes from A1 to A2 (and the fluid velocity changes from v1 to v2) for flow in an incompressible fluid.
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As the fluid is incompressible, at any cross-section, its volumetric flow rate is constant.
=> If v1 = velocity at cross-section A1, volumetric flow rate = A1v1
and If v2 = velocity at cross-section A2, volumetric flow rate = A2v2
Since volumetric flow rate is the same
A1v1 = A2v2 which is called the equation of continuity.
=> If v1 = velocity at cross-section A1, volumetric flow rate = A1v1
and If v2 = velocity at cross-section A2, volumetric flow rate = A2v2
Since volumetric flow rate is the same
A1v1 = A2v2 which is called the equation of continuity.