Question

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.
Figure

Answer 1

Explanation:

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.

FigureWater 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.

FigureWater 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.

FigureWater 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.

FigureWater 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.

FigureWater 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.

FigureWater 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.

FigureWater 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.

FigureWater 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.

Figure

Answer 2

The difference of mercury levels in the U-tube is $1.97 \mathrm{cm}$

Explanation:

The Discharge $\mathrm{Q}=500 \mathrm{cm}^{3} / \mathrm{s}$  

Speed in broad segment $\mathrm{V}_{\mathrm{a}}=\frac{500}{5}=100 \mathrm{cm} / \mathrm{s}=1 \mathrm{m} / \mathrm{s}$

Speed at narrow section $\mathrm{V}_{\beta}=\frac{500}{2}=250 \mathrm{cm} / \mathrm{s}=2.5 \mathrm{m} / \mathrm{s}$

Let the difference in mercury levels = h

The gap in pressure at both points  = $\rho^{\prime} g h$

If the pressure in the broad section is = Pa and the narrow section is = $\mathrm{P} \beta$,

Then continue with the Bernoulli theorem

$P_{\mathrm{a}}+\frac{1}{2} \rho V_{\mathrm{a}}^{2}=P_{\beta}+1 / 2 \rho V_{\beta}^{2}$

$\frac{1}{2} \rho\left(V_{\beta}^{2}-V_{\mathrm{a}}^{2}\right)=P_{\mathrm{a}}-P_{\beta}$

$\frac{1}{2} \times 1000 \times\left(2.5^{2}-1^{2}\right)=\rho^{\prime} g h=13600 \times 9.8 \times h$

$h=10 \times \frac{6.25-1}{2 \times 136 \times 9.8} \mathrm{m}$

$h=52.5 \times \frac{100}{2665.6} \mathrm{cm}$

$h=\frac{5250}{2665.6}=1.97 \mathrm{cm}$