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  • A U-tube has uniform cross section and has a lower portion in shape of a quarter circle of radius <img alt="0.1 \mathrm{~m}" src="https://entrancecorner.oncodecogs.com/gif.latex?0.1%20%5Cmathrm%7B%

A U-tube has uniform cross section and has a lower portion in shape of a quarter circle of radius 0.1 \mathrm{~m}. A valve is provided at the right tube as shown. Water is filled such that the height of the liquid column in the left tube is 0.2 \mathrm{~m} and water is filled upto the closed valve in the right tube. The valve is suddenly opened. The pressure at the lowest point (A) immediately after opening the valve is

Option: 1

\mathrm{P_a+\rho_w g \times 0.2}


Option: 2

\mathrm{P_a+\rho_w g\left(1-\frac{2}{\pi}\right) \times 0.2}


Option: 3

\mathrm{P_a+\rho_w g\left(\frac{2+\pi}{4+\pi}\right) \times 0.2}


Option: 4

\mathrm{P_a+\rho_w g\left(1+\frac{2}{\pi}\right) \times 0.2}


Answers (1)

best_answer

\mathrm{\begin{aligned} & a=g \frac{0.1}{\frac{\pi}{2} \times 0.1+0.2}=g \frac{2}{\pi+4} \\ & g_{\text {eff }}=g-a=g\left[1-\frac{2}{\pi+4}\right]=g \frac{\pi+2}{\pi+4} \\ & P=P a \rho g_{\text {eff }} 0.2 \end{aligned}}

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