Related rates calculus problem about water tank

Related rates calculus problem about water tank

Postby jaychay » Wed Sep 02, 2020 1:43 am

Consider the rectangular water tank, at the base the length is the same for 200 cm. There are 100 holes for water to come out which each hole have the same flow rate. Find the amount of water that come out in each hole by using differential when we know that there is an error in the measurement of the height of the water in the tank is not exceed ± 1 cm.

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Re: Related rates calculus problem about water tank

Postby HallsofIvy » Sat Sep 05, 2020 4:16 pm

The picture contradicts the statement of the problem! "Each hole have the same flow rate." is only possible if every hole is at the same level. The speed with water comes out of a hole depends on the water pressure at that point, which depends on the height of water above the hole and the diameter of the hole. My first thought was that the upper holes could have the same flow of water from them if the upper holes had larger diameter than the lower holes but the picture does not show that.

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