Question

The water faucet on a stoppered kitchen sink was accidentally left slightly open. The faucet volumetric flow rate is 0.12 gal/min. If the sink is a rectangular basin 45 cm by 56 cm and 22 cm deep, how long will it take the sink to overflow? How long will it take to flood the 350-ft2 apartment to a depth of 1 in. if there is no leakage through the floor or baseboards? Formally apply the principles of conservation of

Answer 1

Answer:

2 hours, 4 minutes and 51 seconds

32 hours 45 minutes and 3 seconds

Explanation:

Volume of sink

$v=lwh\\\Rightarrow v=45\times 56\times 22\\\Rightarrow v=55440\ cm^3$

Converting gallon to cm³

$1\ gal=3785.41\ cm^3$

$\\\Rightarrow 0.12\ gal=0.12\times 3785.41\ cm^3=454.2492\ cm^3$

$\dot v$ = Volumetric flow rate = 454.2492 cm³/min

Time taken

$t=\frac{v}{\dot v}\\\Rightarrow t=\frac{55440}{454.2492}\\\Rightarrow t=122.04754\ minutes$

Time it takes to overflow the sink is 122.04754 minutes or 2 hours, 4 minutes and 51 seconds

Volume of apartment

$v=350\times \frac{1}{12}\\\Rightarrow v=\frac{175}{6}\ ft^3$

Converting gallon to ft³

$1\ gal=\frac{1}{7.48052}\ ft^3$

$\\\Rightarrow 0.12\ gal=0.12\times \frac{1}{7.48052}\ ft^3=0.01604\ ft^3$

Time taken

$t=\frac{v}{\dot v}\\\Rightarrow t=\frac{\frac{175}{6}}{0.01604}\\\Rightarrow t=1818.37\ minutes$

Time taken to flood the room would be 122.04754+1818.37 = 1940.41754 minutes or 32 hours 45 minutes and 3 seconds