Bernoulli Equation

The Bernoulli Equation:-

is basically conservation of energy along a pipe. It can be written in different ways by converting energy to head (Kinsky) or pressure, etc.

Bernoulli's equation says in an ideal situation, the TOTAL HEAD = constant.

There are assumptions; An ideal fluid (no friction) flowing steadily:-

The fluid is incompressible and nonviscous.
There is no energy loss due to friction between the fluid and the wall of the pipe.
There is no heat energy transferred across the boundaries of the pipe to the fluid as either a heat gain or loss.
There are no pumps in the section of pipe under consideration.
The fluid flow is laminar and steady state.

PRESSURE DENSITY :-

Pressure in a fluid is like the energy per unit volume (energy density). From the definition of pressure:

Here is the Bernoulli equation in terms of energy per unit volume;

Note that this correponds exactly with the conservation of energy equation. Where pressure = spring energy, velocity = kinetic energy and height = potential energy.

SE₁ + KE₁ + PE₁= SE₂ + KE₂ + PE₂

Where: PE₁ = mgh₁ and KE₁ = 0.5mv₁² and SE₁ = 0.5kx₁²

TOTAL HEAD:-

Total Head (also called Total Dynamic Head) is the sum of the three components; pressure head, velocity head and potential head. From the above equation, divide by g. Head is a simple way to think of each term (pressure, velocity and height) in terms of the number of METRES of that fluid it is equivalent to.