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March 29, 2024, 08:22:27 pm

Author Topic: Volume of water  (Read 745 times)  Share 

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Volume of water
« on: August 24, 2008, 07:21:21 pm »
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A water trough has a constant cross-section described by , where . The trough is 2m long. The units on the axes are in metres.

Let h  m be the depth of water in the trough when measured at the deepest part of the trough.
Show that the volume of water, , in the  trough, in terms of h, is given by



I keep getting a different answer though:

Let y = h represent the height of water.





What's up with that?

 ??? ???

Thanks

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Re: Volume of water
« Reply #1 on: August 24, 2008, 07:25:49 pm »
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Also in a calculator exam is this all the working I need to show?

Mao

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Re: Volume of water
« Reply #2 on: August 27, 2008, 10:04:05 am »
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it might help to rearrange:

(let us only consider the positive side, since the graph is symmetrical about x=0)

area on one side: Area=width*height. In this case, width is x, and height is dy

Area on two sides:








your error is in the integral itself, by assuming the intervals to be at . If the height is less, the intervals would shrink.

and if I were you i'd evaluate the integral and write that down, in case of any arithmetic errors [or wrong input] into the calculator.
« Last Edit: August 27, 2008, 10:07:42 am by Mao »
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Re: Volume of water
« Reply #3 on: August 31, 2008, 12:45:08 pm »
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Thanks mao, looks like I missed  a lot of steps.

sorry for taking so long to reply, I've been sick for the past few days :P