JEE Mains · Physics · STD 11 - Fluid mechanics
- JEE Mains 2020
- Medium
- MCQ
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
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(\sqrt{\frac{ P }{\rho}+ v ^{2}}\)
Step-by-step Solution
Detailed explanation
Applying Bernoulli's Equation
\(P _{1}+\frac{1}{2} \rho v _{1}^{2}+\rho gy _{1}= P _{2}+\frac{1}{2} \rho v _{2}^{2}+\rho gy _{2}\)
\(P +\frac{1}{2} \rho v ^{2}=\frac{ P }{2}+\frac{1}{2} \rho V ^{2}\)
\(\frac{2 P }{2 \rho}+\frac{1}{2} \frac{\rho v ^{2}}{\rho} \times 2= V ^{2}\)
\(\sqrt{\frac{P}{\rho}+v^{2}}=V\)
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