Physics Help Forum Euler's equation and integration help!

 Thermodynamics and Fluid Mechanics Thermodynamics and Fluid Mechanics Physics Help Forum

 Apr 27th 2019, 11:38 PM #1 Junior Member   Join Date: Apr 2019 Posts: 1 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)
 Apr 28th 2019, 06:08 AM #2 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,338 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: $P_1 = \rho h g + \rho h a = \rho h (a + g)$ topsquark likes this.

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