We were discussing the basic concept ofÂ streamline and equipotential line,Â dimensional homogeneity,Â Buckingham pi theorem,Â difference between model and prototype,Â basic principle of similitude i.e. types of similarity, various forces acting on moving fluidÂ and model laws or similarity laws and in the subject of fluid mechanics, in our recent posts.Â

Now we will go ahead to find out the Bernoulliâ€™s equation from Eulerâ€™s equation of motion of a fluid, in the subject of fluid mechanics, with the help of this post.

Before going ahead, we will first see the recent post which will explain the fundamentals and derivation of Eulerâ€™s equation of motion. We will find out now the Bernoulliâ€™s equation from Eulerâ€™s equation of motion of a fluid.

#### Eulerâ€™s Equation of motion

Bernoulliâ€™s equation from Eulerâ€™s equation of motion could be derived by integrating the Eulerâ€™s equation of motion.

### According to Bernoulliâ€™s theorem.....

In an incompressible, ideal fluid when the flow is steady and continuous, the sum of pressure energy, kinetic energy and potential energy will be constant along a stream line.

### Assumptions

Assumptions made for deriving the Bernoulliâ€™s equation from Eulerâ€™s equation of motion is as mentioned here.

1. Fluid is ideal, i.e. inviscid and incompressible.
2. Fluid flow is steady, one-dimensional and uniform
3. Fluid flow is irrational
4. Forces which are considered are only pressure force and gravity force. Rest forces acting on fluid are neglected.

Let us recall the Eulerâ€™s equation of motion. We will integrate the Eulerâ€™s equation of motion in order to secure the Bernoulliâ€™s equation.

Above equation is termed as Bernoulliâ€™s equation.

We will now find out the Bernoulliâ€™s equation for real fluid in the subject of fluid mechanics in our next post.

Do you have any suggestions? Please write in comment box.

### Reference:

Fluid mechanics, By R. K. Bansal

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