# Derive eulers equation

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.