This equation is based on the principle of conservation of mass, according to this - If an incompressible or viscosity-less fluid is flowing through a tube having an area of a cross-section in a streamlined flow, then the product of the velocity of the fluid at any point in the tube and the area of the cross-section of the tube remains constant.
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Proof that Equation
Suppose a liquid is flowing in a linear flow in a tube xy of the area of the cross-section. Let velocity at the x and y ends be v1 and v2 respectively and density (ρ) and area be A1 and A2, then the volume of liquid entering the tube from the x end is Avρ.
Mass of fluid entering from end X in 1 second = A1v1(ρ)
Mass of fluid coming out of end y in 1 second = A2v2(ρ)
The one who enters from the x end will exit from the y end.
Mass input = Mass output
A1v1(ρ) = A2v2(ρ)
A1v1 = A2v2
Av = Constant
Conditions of Continuity Equation
1. Reverse flow of fluids.
2. The flow should be incompressible, that is, there should be no change in the density of the liquid under the flow.
3. Take the equivalent speed of the fluid at each cut.
4. There should be no means of fluid entering or exiting the pump between the bites in question.
Also Read: Reynolds Experiment Theory and Reynolds Number
Bernoulli's Theorem Definition, Derivation, and Applications
Uses of Continuity Equation
Following are the primary uses of the continuity equation.
With the help of this equation, problems related to fluid flow are solved, and the cross-section or velocity of the fluid is determined at some point in the path.
This equation helps establish and use the experimental formulas of liquid flow meters.
These help solve problems related to fluid flow in all fluid machines (pumps, turbines).