# 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 : Option: 1   Option: 2 Option: 3   Option: 4

Answers (1)

\begin{aligned} &\text { Applying Bernoulli's Equation }\\ &P_{1}+\frac{1}{2} \rho v_{1}^{2}+\rho g y_{1}=P_{2}+\frac{1}{2} \rho v_{2}^{2}+\rho g y_{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{\mathrm{P}}{\rho}+\mathrm{v}^{2}}=\mathrm{V} \end{aligned}

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