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A fluid of density ρ\rho is flowing in a pipe of varying cross-sectional area as shown in the figure. Bernoulli's equation for the motion becomes:

A

p+12ρv2+ρgh=constantp+\frac{1}{2}\rho v^2+\rho gh = \text{constant}

B

p+12ρv2=constantp+\frac{1}{2}\rho v^2 = \text{constant}

C

12ρv2+ρgh=constant\frac{1}{2}\rho v^2+\rho gh = \text{constant}

D

p+ρgh=constantp+\rho gh = \text{constant}

Step-by-Step Solution

Bernoulli's principle states that for the streamline flow of an ideal (incompressible and non-viscous) fluid, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant at every point along a streamline.

Mathematical Expression: P+12ρv2+ρgh=constantP + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}

Where: PP is the static pressure. 12ρv2\frac{1}{2}\rho v^2 is the kinetic energy per unit volume.

  • ρgh\rho gh is the potential energy per unit volume.
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