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Continuity equation can take the form (where A = Area, V = Volume, ρ = Density and P = Pressure)
Question

Continuity equation can take the form
(where A = Area, V = Volume, ρ = Density and P = Pressure)

A.

P1A1V1=P2A2V2P_1A_1V_1 = P_2A_2V_2

B.

ρ1A1=ρ2A2\rho_1 A_1 = \rho_2 A_2​​

C.

A1V1=A2V2A_1V_1 = A_2V_2

D.

P1V1=P2V2P_1V_1 = P_2V_2

Correct option is C

The continuity equation in fluid dynamics expresses the conservation of mass in a flowing fluid. For an compressible fluid (where density can vary ), the mass flow rate must remain the same from one cross-section to another. This can be represented by the equation: ρ1A1V1=ρ2A2V2\rho_1 A_1 V_1 = \rho_2 A_2 V_2​​

For an incompressible fluid, the density (ρ)cancels out, simplifying the equation to:
A1V1=A2V2A_1V_1 = A_2V_2
This form of the equation relates the product of area and velocity (volume flow rate) at two different cross-sections of a pipe or duct.

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