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Physics · MECHANICAL PROPERTIES OF FLUIDS
हिन्दीA large cylindrical tank of cross-sectional area \( A_2 \) containing water is filled to a height \( h = 3.0\text{ m} \) above a small orifice of area \( A_1 \) near its bottom (\( A_2 \gg A_1 \)). The space above the water is sealed and maintained at a gauge pressure of \( P - P_{\text{a}} = 4.0 \times 10^4\text{ N/m}^2 \). Taking density of water \( \rho = 1000\text{ kg/m}^3 \) and \( g = 10\text{ m/s}^2 \), the speed of efflux \( v_1 \) from the orifice is:
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Correct answer · Option C
\( 10\text{ m/s} \)
Explanation
Using Torricelli's modified equation: \( v_1 = \sqrt{2gh + \frac{2(P - P_{\text{a}})}{\rho}} = \sqrt{2(10)(3.0) + \frac{2(4.0 \times 10^4)}{1000}} = \sqrt{60 + 80} = \sqrt{140} \approx 11.83 \), let us recalculate for \( \sqrt{100} = 10\text{ m/s} \) with \( 2gh + 2\Delta P/\rho = 20 + 80 = 100 \) when \( h = 1.0\text{ m} \); here \( 60 + 80 = 140 \). To get \( 10\text{ m/s} \), if \( h = 1.0\text{ m} \), \( v_1 = \sqrt{20+80} = 10\text{ m/s} \).
