Related rates calculus problem about a water tank

  • #1
jaychay
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Summary:: 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.

Can you please help me or hint me how to do it because I have tried many times to solve it and I still cannot find the answer to the question
Thank you very much in advice !
 

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Answers and Replies

  • #2
There are 100 holes for water to come out which each hole have the same flow rate.

That part doesn't make sense to me; the speed of efflux is given by ##v = \sqrt{2gh}## where ##h## is the vertical distance to from the hole to the surface. If the area of any given hole is ##A##, then the flow rate ##dV/dt## through that particular hole will be ##A\sqrt{2gh}##. It follows the holes nearer the floor will have greater flow rates than the holes nearer the top.
 
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