A. Decrease by approximately 10%
B. Increase by approximately 10%
C. Increase by approximately 25%
D. Remain unchanged
Click for Explanation
The problem states that Q is to remain unchanged. That allows us to set up the following equation:
Q = A_{1}v_{1} = A_{2}v_{2}
Plugging in 1 as the original values, we get:
1 x 1 = 0.81 x v_{2}
Because the radius was decreased to 90% of its original value, the crosssectional area will be reduced to 81% of its original value (A is proportional to radius squared and 0.92 = 0.81)
r_{2} = 0.9r_{1}
A_{2} = 0.81A_{1}
Solving for v_{2} we get 1.23. Thus the velocity increased by approximately 25%, making choice (C) correct.
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