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When full, a bathtub contains 25 gallons of water and the depth

Question # 00202503
Subject: Engineering
Due on: 03/22/2016
Posted On: 02/21/2016 05:21 AM

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Can some one help me with this material balance question?


3-14a. When full, a bathtub contains 25 gallons of water and the depth of the water is one foot. If the empty bathtub is filled with water from a faucet at a flow rate of 10 liters per minute, how long will it take to fill the bathtub?

3-14b. Suppose the bathtub has a leak and water drains out of the bathtub at a rate given by Torricelli’s law.

Qleak=Cd Ao root(2gh)

Here h is the depth of water in the bathtub, and Cd represents the discharge coefficient associated with the area of the leak in the bathtub, Ao. Since neither Cd nor Ao are known, we express

Qleak= k root(h)

in which k=CdAoroot(2g). To find the value of k we have a single experimental condition given by

Experiment: Qleak=33.16x10^-5 m^3/s, h=.10m

Given the experimental value of k, assume that the cross section of the bathtub is constant and determine how long it will take to fill the leaky bathtub.

Tags depth water gallons contains bathtub bathtub water given rate depth long leak value experimental qleak determine rooth leaky expre aociated area known kcdaoroot2g61501 constant condition experiment qleak3316x105 coefficient aume section single h10m torricellis gallons foot

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When full, a bathtub contains 25 gallons of water and the depth

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Tutorial Preview …law xxxxxxxx Ao xxxxxxxxx Here h xx the depth xx water xx xxx bathtub, xxx Cd represents xxx discharge coefficient xxxxxxxxxx with xxx xxxx of xxx leak in xxx bathtub, Ao xxxxx neither…
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