We were discussing the basic concept
of streamline
and equipotential line, dimensional
homogeneity, Buckingham
pi theorem, difference
between model and prototype, basic
principle of similitude i.e. types of similarity, various
forces acting on moving fluid and model laws or similarity laws and in
the subject of fluid mechanics, in our recent posts.
Now we will go ahead to find out the Bernoulli’s equation from Euler’s equation of motion of a fluid, in the subject of fluid mechanics, with the help of this post.
Now we will go ahead to find out the Bernoulli’s equation from Euler’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 Euler’s
equation of motion. We will find out now the Bernoulli’s equation from Euler’s
equation of motion of a fluid.
Bernoulli’s equation from Euler’s
equation of motion could be derived by integrating the Euler’s equation of motion.
According to Bernoulli’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
Bernoulli’s equation from Euler’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 Euler’s equation of motion.
We will integrate the Euler’s equation of motion in order to secure the Bernoulli’s
equation.
Above equation is termed as Bernoulli’s
equation.
We will now find out the Bernoulli’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
Image Courtesy: Google
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