Question

Derive the equation of continuity of flow​

Answer 1

Answer:

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The equation proves the law of conservation of mass in fluid dynamics. Also, if the fluid is incompressible, the density will remain constant for steady flow. So, ρ1 =ρ2. This was the derivation of continuity equation.

Answer 2

According to the equation of continuity Av = constant. Where A =cross-sectional area and v=velocity with which the fluid flows.

It means that if any liquid is flowing in streamline flow in a pipe of non-uniform cross-section area, then rate of flow of liquid across any cross-section remains constant.

Consider a fluid flowing through a tube of varying thickness.

Let the cross-sectional area at one end (I) = A1 and cross-sectional area of other end (II)= A2.

The velocity and density of the fluid at one end (I)=v1,ρ1respectively, velocity and densityof fluid at other end (II)= v2,ρ2

Volume covered by the fluid in a small interval of time ∆t,across left cross-sectional is Area (I) =A1xv1x∆t

Volume covered by the fluid in a small interval of time ∆tacrossright cross-sectional Area(II) = A2x v2x∆t

Fluid inside is incompressible(volume of fluid does not change by applying pressure) that is density remains sameρ1=ρ2. (equation 1)

Along(I) mass=ρ1 A1 v1∆t and along second point (II) mass = ρ2A2 v2∆t

By using equation (1). We can conclude that A1 v1 = A2 v2.This is the equation of continuity.

From Equation of continuity we can say that Av=constant.

This equation is also termed as “Conservation of mass of incompressible fluids”.