Given below are two statements:Statement I: W | vedclass

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(D) For Statement $I$: When the liquid is at rest $(v_1=v_2=0)$,the pressure difference between two points at heights $h_1$ and $h_2$ is given by the

Vedclass · Accepted Answer

Statement $I$ is correct but Statement $II$ is incorrect.

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(D) For Statement $I$: When the liquid is at rest $(v_1=v_2=0)$,the pressure difference between two points at heights $h_1$ and $h_2$ is given by the hydrostatic pressure formula: $P_1-P_2=\rho g(h_2-h_1)$. Thus,Statement $I$ is correct.For Statement $II$: Applying Bernoulli's equation for a horizontal venturi tube $(h_1=h_2)$: $P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$$P_1 - P_2 = \frac{1}{2}\rho(v_2^2 - v_1^2)$From the manometer,the pressure difference is $P_1 - P_2 = \rho gh$.Equating the two expressions: $\rho gh = \frac{1}{2}\rho(v_2^2 - v_1^2)$,which simplifies to $2gh = v_2^2 - v_1^2$.Since the statement says $2gh = v_1^2 - v_2^2$,it is incorrect.Therefore,Statement $I$ is correct but Statement $II$ is incorrect.

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