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  • A fluid is flowing through a horizontal pipe of varying cross-section, with speed at a point where the pressure is P Pascal. At another point where pre

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 \sqrt{\frac{P}{\rho }+v}
 
Option: 2 \sqrt{\frac{2P}{\rho }+v^{2}}
Option: 3 \sqrt{\frac{P}{2\rho }+v^{2}}  
Option: 4 \sqrt{\frac{P}{\rho }+v^{2}}

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\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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Deependra Verma

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