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    Derive eulers equation

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    1- Derive. From first principles eulers equation from the rate of change of momentum
    2- Show by integration how Eulers equation derives Bernoullis equation
    3- Explain the use of Eulers equation as applied to compressible fluids.

    Many thanks for any help

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    Problem:

    1- Derive. From first principles Euler's equation from the rate of change of momentum
    2- Show by integration how Euler's equation derives Bernoulli's equation
    3- Explain the use of Euler's equation as applied to compressible fluids.

    Solution:

    1. The Euler's equation can be derived by applying the Newton's 2-nd law on a volume of an inviscid fluid (force = rate of change of momentum):

    ( 1)
    where sum of all forces acting on the considered volume of fluid
    m = mass of the considered volume of fluid:
    ( 2)
    acceleration, ( 3)

    The nature of the forces can be:
    - pressure
    - external field (like gravity, electromagnetic etc.)

    The integral of pressure on the surface [] bounding the volume is given by:
    ...

    Solution Summary

    The expert derives eulers equations.

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