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JEE Mains · Physics · STD 11 - 9.1 fluid mechanics

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

  1. A \(\sqrt{\frac{ P }{2 \rho}+ v ^{2}}\)
  2. B \(\sqrt{\frac{ P }{\rho}+ v ^{2}}\)
  3. C \(\sqrt{\frac{2 P }{\rho}+ v ^{2}}\)
  4. D \(\sqrt{\frac{ P }{\rho}+ v }\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\sqrt{\frac{ P }{\rho}+ v ^{2}}\)

Step-by-step Solution

Detailed explanation

Applying Bernoulli's Equation \(P _{1}+\frac{1}{2} \rho v _{1}^{2}+\rho gy _{1}= P _{2}+\frac{1}{2} \rho v _{2}^{2}+\rho gy _{2}\) \(P +\frac{1}{2} \rho v ^{2}=\frac{ P }{2}+\frac{1}{2} \rho V ^{2}\) \(\frac{2 P }{2 \rho}+\frac{1}{2} \frac{\rho v ^{2}}{\rho} \times 2= V ^{2}\)…
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