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

2 hours, 4 minutes and 51 seconds

32 hours 45 minutes and 3 seconds

Step-by-step explanation:

Volume of sink

`v=lwh\\\Rightarrow v=45* 56* 22\\\Rightarrow v=55440\ cm^3`

Converting gallon to cm³

`1\ gal=3785.41\ cm^3`

`\\\Rightarrow 0.12\ gal=0.12* 3785.41\ cm^3=454.2492\ cm^3`

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

Time taken

`t=(v)/(\dot v)\\\Rightarrow t=(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* (1)/(12)\\\Rightarrow v=(175)/(6)\ ft^3`

Converting gallon to ft³

`1\ gal=(1)/(7.48052)\ ft^3`

`\\\Rightarrow 0.12\ gal=0.12* (1)/(7.48052)\ ft^3=0.01604\ ft^3`

Time taken

`t=(v)/(\dot v)\\\Rightarrow t=((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