Water flows through the tube shown in figure (13-E10). 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.

Question

Water flows through the tube shown in figure (13-E10). 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.

Philoid · Accepted Answer

Let the wider tube be called A and the narrow tube be called B.

Given, area of cross-section of tube A,

area of cross-section of tube B,

Rate of flow through the tubes,

Let the velocity of flow at A and B be and respectively.

From the equation of continuity, we know

Similarly,

The pressure difference between the points is equal to the difference in the mercury columns. Let the pressure at A be and that at B be . Also, Let the difference in height of the mercury columns be

From the Bernoulli’s equation

Water flows through the tube shown in figure (13-E10). 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 (13-E10). 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.