Water is flowing in a pipe of diameter 4 cm with a velocity 3 m/s. The water then enters into a pipe of diameter 2 cm. The velocity of water in the other pipe is:

Question

Water is flowing in a pipe of diameter 4 cm with a velocity 3 m/s. The water then enters into a pipe of diameter 2 cm. The velocity of water in the other pipe is: (A) 3 m/s (B) 6 m/s (C) 12 m/s (D) 8 m/s

Tardigrade Admin · Accepted Answer

According to principle of continuity, when an incompressible and non-viscous liquid flows in a streamlined motion through a tube of non-uniform cross-section, then the product of the area of cross-section and the velocity of flow is same at every point in the tube.
Thus,

A v =

constant or

A_{1} v_{1} = A_{2} v_{2}

or

π r_{1}^{2} v_{1} = π r_{2}^{2} v_{2}

Given,

r_{1} = \frac{4}{2} c m = 0.02 m,

r_{2} = \frac{2}{3} c m = 0.01 m,

v_{1} = 3 m / s

∴

π (0.02)^{2} \times 3 = π (0.01)^{2} v_{2}

or

v_{2} = (\frac{0.02}{0.01})^{2} \times 3

= 12 m / s

Q. Water is flowing in a pipe of diameter 4cm with a velocity 3m/s. The water then enters into a pipe of diameter 2cm. The velocity of water in the other pipe is:

3 m/s

6 m/s

12 m/s

8 m/s

Q. Water is flowing in a pipe of diameter $4 c m$ with a velocity $3 m / s$ . The water then enters into a pipe of diameter $2 c m$ . The velocity of water in the other pipe is: