Two water pipes of diameters 2 cm and 4 cm are connected with the main supply. The velocity of flow of water supply line in the pipe of 2 cm diameter is:
Correct answer: A. The velocity is 4 times that in the other pipe
- A. The velocity is 4 times that in the other pipe
- B. The velocity is 1/4 times that in the other pipe
- C. The velocity is 2 times that in the other pipe
- D. The velocity is 1/2 times that in the other pipe
Explanation
The correct answer is that the velocity in the 2 cm diameter pipe is 4 times that in the 4 cm diameter pipe. According to the principle of continuity, the flow rate (area × velocity) must be constant in a closed system. Since the area of a circle is proportional to the square of its diameter, the velocity in the narrower pipe is higher because it compensates for the smaller cross-sectional area. Specifically, the velocity is inversely proportional to the square of the diameter ratio. Therefore, (4/2)^2 = 4, meaning the velocity in the 2 cm pipe is 4 times that in the 4 cm pipe. The other options are incorrect as they misunderstand the relationship between diameter and velocity as dictated by the continuity equation.
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