# Write an expression indicating the Bernoulli equation, define all the symbols used and state all the conservation of energy involved?

Aug 10, 2015

Bernoulli equaton describes the relationship between Pressure and Velocity in a fluid:

#### Explanation:

You can write it as:
$\textcolor{red}{\frac{1}{2} \rho {v}^{2} + \rho g z + P = c o n s t .}$
where:
$\rho =$density;
$v =$velocity;
$P =$pressure.

Every term has a meaning in terms of energetic properties of the fluid (always considering a volume of your fluid); so:

$P$ represents the energy due to pressure (remember the work done by a force on a gas/liquid studied in thermodynamics and given as function of pressure and volume as $P \Delta V$)

$\frac{1}{2} \rho {v}^{2}$ represents the contribution from Kinetic Energy $K$ (including the volume dependence in our usual expression $K = \frac{1}{2} m {v}^{2}$);

$\rho g z$ represents the contribution from Gravitational Potential Energy $U$ (including the volume dependence in our usual expression $U = m g h$);

Bernoulli tells us that an element of fluid "trades" speed for height or pressure during its movement along the tube but its energy remains fixed (conserved) so that if you increase one term the others change accordingly to compensate and maintain the sum constant!!!

hope it helps!