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Water is flowing in streamline motion through a horizontal tube. The pressure at a point in the tube is $p$ where the velocity of flow is $v$. At another point, where the pressure is $p / 2,$ the velocity of flow is [density of water $=\rho]$
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The correct answer is:
$\sqrt{v^{2}+\frac{p}{\rho}}$
As the water is flowing through the horizontal tube, so in the streamline flow of water, the sun of static pressure and dynamic pressure is constant $i, e$
$$
P+\frac{1}{2} \rho v^{2}=\frac{P}{2}+\frac{1}{2} \rho v_{1}^{2}
$$
$\Rightarrow \quad v_{1}=\sqrt{\frac{P}{\rho}+v^{2}}$
$$
P+\frac{1}{2} \rho v^{2}=\frac{P}{2}+\frac{1}{2} \rho v_{1}^{2}
$$
$\Rightarrow \quad v_{1}=\sqrt{\frac{P}{\rho}+v^{2}}$
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