The Principle of Continuity in Fluid Dynamics
What happens to the speed of water when a pipe narrows?
A pipe contains water flowing with a speed of 1.6 m/s. When the pipe narrows to one-half its original diameter, what is the speed of the water?
A) 1.6 m/s
B) 3.2 m/s
C) 6.4 m/s
D) 9.6 m/s
E) 12.8 m/s
Final answer:
When a pipe narrows to half its original diameter, the water speed quadruples due to the principle of continuity in fluid dynamics. Therefore, if the initial speed was 1.6 m/s, the new speed when the pipe narrows would be 6.4 m/s. Therefore, the correct option is C) 6.4 m/s
Explanation:
The question is about the concept of continuity within fluid dynamics, a part of Physics. The principle of continuity states that the mass flow rate in a pipe must remain constant: the product of area and velocity at any two points along the pipe must be equal. In an ideal situation, when the diameter of a pipe decreases by half, its area decreases by a factor of four (since area is proportional to the square of the diameter).
In this case, the speed should quadruple to maintain constant flow rate. Thus, to find the new speed, you multiply the original speed by four. Therefore, if the initial speed was 1.6 m/s, the speed when the pipe narrows to half its original diameter would be 1.6 m/s x 4 = 6.4 m/s. Hence, the correct answer is C) 6.4 m/s.