Question

Figure shows how the stream of water emerging from a faucet "necks down" as it falls. Figure shown two levels separated by a vertical distance $h$. The cross-sectional areas $A_0$ and $A$ are marked in the figure. At what rate does water flow from the tap?

• A. $A_{0}A\sqrt{\frac{2gh}{A^2-A_0^2}}$
• B. $A_0\sqrt{\frac{2ghA}{A^2-A_0^2}}$
• C. $A\sqrt{\frac{2gh{A}_0}{A^2-A_0^2}}$
• D. $A_{0}A\sqrt{\frac{2gh}{A_0^2-A^2}}$

Answer 1

The correct option is D $A_{0}A\sqrt{\frac{2gh}{A_0^2-A^2}}$

$\text{Acc. to bernouli theorem}$

$P_0+\rho gh+\frac{1}{2}\rho v^2=P_0+0+\frac{1}{2}\rho {\left(\frac{A_0}{A}v\right)}^2$

$V^2\left(\frac{A^2-A_0^2}{A^2}\right)=-2gh$

$V=\sqrt{\frac{2gh{A}^2}{A_0^2-A^2}}$

vol. flowing $=A_{0}v=A{A}_0\sqrt{\frac{2gh}{A_0^2-A^2}}$

Answer. (D)