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Water ideally flows through a pipe of radius 6 centimeters at a rate of 5 meters per second. The pipe then narrows to a radius of 2 centimeters. What is the new velocity of the water?

Water ideally flows through a pipe of radius 6 centimeters at a rate of 5 meters per second. The pipe then narrows to a radius of 2 centimeters. What is the new velocity of the water? Correct Answer 55 m/s

First convert everything to basic metric units. (6cm)((1m)/(100cm)) = .06m (2cm)((1m)/(100cm)) = .02m Now find the cross-sectional area in both sections of the pipe. A = π(r)2 π(.06)2 ≈ 0.011m2 π(.02)2 ≈ 0.001m2 Next, use the equation of continuity with the areas you have obtained and the given velocity. A1v1 = A2v2 (0.011m2)(5m/s) = (.001m2)v2 0.055m3/s = (.001m2)v2 55m/s = v2.

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