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(C) According to Bernoulli's equation for a fluid in motion,the sum of pressure energy,kinetic energy,and potential energy per unit volume remains con

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$\left[\frac{2(P_1-P_2)}{\rho}\right]^{1/2}$

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(C) According to Bernoulli's equation for a fluid in motion,the sum of pressure energy,kinetic energy,and potential energy per unit volume remains constant along a streamline.Assuming the pipe is horizontal and the initial velocity $v_1$ inside the pipe is negligible $(v_1 \approx 0)$:$P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2$Since $v_1 = 0$,the equation simplifies to:$P_1 = P_2 + \frac{1}{2} \rho v_2^2$Rearranging for $v_2$:$P_1 - P_2 = \frac{1}{2} \rho v_2^2$$v_2^2 = \frac{2(P_1 - P_2)}{\rho}$$v_2 = \sqrt{\frac{2(P_1 - P_2)}{\rho}}$

$A$ closed pipe containing a liquid showed a pressure $P_1$ by gauge. When the valve was opened,the pressure was reduced to $P_2$. The speed of water flowing out of the pipe is ( $\rho=$ density of water )

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