Water flows through the tube shown in figure. The areas of cross–section of the wide and the narrow portions of the tube are $5 c m^{2}$ and $2 c m^{2}$ respectively. The rate of flow of water through the tube is $500 c m^{3} / s$ . Find the difference of mercury levels in the U–tube.

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2.1 cm

1.7 cm

1.11 cm

1.97 cm

answer is B.

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Detailed Solution

In this case, the rate of flow is given by

$Q = A_{1} A_{2} \sqrt{\frac{2 ρ_{m} g h}{ρ (A_{1}^{2} - A_{2}^{2})}} 500 = 5 \times 2 \sqrt{\frac{2 \times 13.6 \times 981 \times h}{1 (5^{2} - 2^{2})}}$

After simplifying,we get $h = 1.97 c m$ .

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