Q. 32

# Water flows through a horizontal tube as shown in figure (13-E9). If the difference of heights of water column in the vertical tubes is 2 cm, and the areas of cross section at A and B are 4 cm^{2} and 2 cm^{2} respectively, find the rate of flow of water across any section.

Answer :

Given, area of cross-section of tube A,

area of cross-section of tube B,

Difference in height in the two columns,

Let the speed of water at A be and speed of water at B be .

From the equation of continuity

—————(1)

The pressure difference between A and B is —————(2)

We consider the flow at two points in A and B such that they lie on the same horizontal plane. Applying Bernoulli’s equation,

Using (2)

Therefore, the rate of flow is

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