Water flows through the tube shown in figure.The areas of cross-section of the wide and 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.

1.67 c m

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1.77 c m

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1.87 c m

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1.97 c m

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Solution

The correct option is D $1.97 c m$
It is known that
$A_{1} v_{1} = A_{2} v_{2} = rate of flow of water$

$5 v_{1} = 2 v_{2} = 500 {c m}^{3} / s$

$∴ v_{1} = 100 c m / s = 1.0 m / s$

$v_{2} = 250 c m / s = 2.5 m / s$

$\frac{1}{2} ρ_{w} (v_{2}^{2} - v_{1}^{2}) = ρ_{H g} {g h}_{H g}$

$∴ h_{H g} = \frac{ρ_{w} (v_{2}^{2} - v_{1}^{2})}{2 ρ_{H g} g}$

$= \frac{10^{3} (6.25 - 1)}{2 \times 13.6 \times 10^{3} \times 9.8}$

$= 0.0196 m$

$\approx 1.97 c m$
Hence option D is correct

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Similar questions

Q. 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 cm² and 2 cm² respectively. The rate of flow of water through the tube is 500 cm³ s⁻¹. Find the difference of mercury levels in the U-tube.

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 $c m^{3}$ $s^{- 1}$ . Find the difference of mercury levels in the U-tube.

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 cm² and 2 cm² respectively. The rate of flow of water through the tube is 500 cm³ s^-1. Find the difference of mercury levels in the U-tube. Assume this tube lying horizontally on a table.

Q. Water flows through the tube shown Area of cross-section of wide and narrow part are

5 {c m}^{2}

2 {c m}^{2}

. The rate of flow is 500

{c m}^{3} / s e c

Find difference mercury level of U-tube:

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Water flows through the tube shown in figure.The areas of cross-section of the wide and narrow portions of the tube are 5cm2 and 2cm2 respectively. The rate of flow of water through the tube is 500cm3/s. Find the difference of mercury levels in the U-tube.

The correct option is D 1.97cmIt is known that A1v1=A2v2= rate of flow of water 5v1=2v2=500 cm3/s∴v1=100 cm/s=1.0 m/sv2=250 cm/s=2.5 m/s12ρw(v22−v21)=ρHgghHg∴hHg=ρw(v22−v21)2ρHgg=103(6.25−1)2×13.6×103×9.8=0.0196 m≈1.97 cmHence option D is correct

Water flows through the tube shown in figure.The areas of cross-section of the wide and 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.