Fluid Mechanics

JEE Main level, single correct, medium

63 of 192

Question 63 of 192

A fluid is flowing through a horizontal pipe of varying cross-section, with vms−1v {ms}^{-1} at a point where the pressure is PP Pascal. At another point where pressure P2\dfrac{P}{2} Pascal its speed is Vms−1V{ms}^{-1}. If the density of the fluid is ρkg−m−3\rho kg-{m}^{-3} and the flow is streamline, then VV is equal to

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Answer: (D) Pρ+υ2\sqrt{\dfrac{P}{\rho }+{υ}^{2}}

P+12ρv2=P2+12ρV2P+\dfrac{1}{2}{\rho v}^{2}=\dfrac{P}{2}+\dfrac{1}{2}{\rho V}^{2}
P2+12ρv2=12ρV2\dfrac{P}{2}+\dfrac{1}{2}{\rho v}^{2}=\dfrac{1}{2}{\rho V}^{2} ;
V=v2+PρV=\sqrt{{v}^{2}+\dfrac{P}{\rho }}

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