Related rates calculus problem about a water tank

In summary, the conversation discusses finding the amount of water that comes out of each of the 100 holes in a rectangular water tank. The flow rate of each hole is the same, but there is an error in the measurement of the water height, which cannot exceed ±1 cm. The conversation also mentions using differential to solve the problem and asks for help or hints on how to do so.
  • #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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  • #2
jaychay said:
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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What is a related rates calculus problem about a water tank?

A related rates calculus problem about a water tank involves using calculus to find the rate at which a certain variable (such as the water level or volume) is changing in relation to another variable (such as time or the flow rate of water into the tank).

What are the key steps in solving a related rates calculus problem about a water tank?

The key steps in solving a related rates calculus problem about a water tank are identifying the relevant variables, setting up a mathematical equation that relates these variables, taking the derivative of the equation with respect to time, plugging in the known values and solving for the desired rate.

What are some common real-life applications of related rates calculus problems about water tanks?

Related rates calculus problems about water tanks can be applied to real-life situations such as calculating the rate at which water is draining from a swimming pool, the rate at which a water tank is filling or emptying, or the rate at which the water level in a reservoir is changing.

What are some tips for successfully solving related rates calculus problems about water tanks?

Some tips for successfully solving related rates calculus problems about water tanks include carefully labeling and identifying all variables, drawing a diagram to visualize the problem, and checking your solution for reasonableness.

What are some common mistakes to avoid when solving related rates calculus problems about water tanks?

Some common mistakes to avoid when solving related rates calculus problems about water tanks include using incorrect units, not taking the derivative correctly, and forgetting to include all relevant variables in the equation.

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