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Old Apr 27th 2019, 11:38 PM   #1
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Euler's equation and integration help!

Hey guys,

So I'm going to give you two links to imgur, one is the question and the other the answer.

I know how he gets the answer, i can get the answer myself but i have a question..

Do we ALWAYS integrate Euler's equation to use it? OR is this a special case where it gets integrated? If so, what happens when it doesn't get integrated, is a gradient needed?

Thanks

https://imgur.com/a/CHaQCia

https://imgur.com/a/C7YgXrn (Click to zoom)
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Old Apr 28th 2019, 06:08 AM   #2
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If you're starting with a differential equation then yes, you integrate to get to a final answer. In this particular case however an easier approach is to simply recognize that the pressure is equal to the sum of pressures caused by (a) the 10 cm of head of water and (b) the acceleration of the mass of 10 cm of water:

$P_1 = \rho h g + \rho h a = \rho h (a + g) $
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