Card 26 / 41: Consider a tank 1 m in diameter and 10 m high. The tank is being filled with a liquid at a rate of 10 gallons/min. The liquid drains from the tank at a rate Q = f h, where h is the height of liquid in the tank, and f is 1 gal/(min m). Which of the following best represents how long it takes to fill the tank to a height of 5 m?
A) 1.44 hours
B) 172 minutes
C) 144 minutes
D) 1.72 hours

Answer:
A) 1.44 hours

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Explanation:

Write an ordinary differential equation for the height of fluid in the tank as dh/dt x Area= (10 gal/min - f h). Be careful to convert units appropriately. In order to integrate, use a substitution U = 10 - fh. Upon integration, one gets an exponential approach to filling the tank.

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https://www.jobilize.com/fluid-mechanics-mcq-quiz-by-stephanie-redfern-tuan-dinh

Fluid Mechanics ME201

Author:

Stephanie Redfern

The Saylor Foundation

USA

Access: Public Instant Grading

Attribution: Stephanie Redfern and Tuan Dinh. Fluid Mechanics. The Saylor Academy 2014, http://www.saylor.org/courses/me201/

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