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JEE Main 20206 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Evening Shift
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2020 · 6 September · Evening Shift · Physics · Mechanical Properties of Fluids

A fluid is flowing through a horizontal pipe of varying...

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−3ρkg - {m}^{- 3} and the flow is streamline, then VV is equal to

Options

  1. APρ+υ\sqrt{\dfrac{P}{ρ} + υ}
  2. B2Pρ+υ2\sqrt{\dfrac{2P}{ρ} + {υ}^{2}}
  3. CP2ρ+υ2\sqrt{\dfrac{P}{2ρ} + {υ}^{2}}
  4. DPρ+υ2\sqrt{\dfrac{P}{ρ} + {υ}^{2}}

Correct answer

D. Pρ+υ2\sqrt{\dfrac{P}{ρ} + {υ}^{2}}

Step-by-step solution

P+12ρv2=P2+12ρV2P + \dfrac{1}{2}{ρv}^{2} = \dfrac{P}{2} + \dfrac{1}{2}{ρV}^{2}

P2+12ρv2=12ρV2\dfrac{P}{2} + \dfrac{1}{2}{ρv}^{2} = \dfrac{1}{2}{ρV}^{2} ;

V=v2+PρV = \sqrt{{v}^{2} + \dfrac{P}{ρ}}

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