Bernoulli's Principle

Every volume element $V$ in a liquid with the density $\varrho$ moves with the speed $v$ and has therefore the kinetic energy $$E_\mathrm{kin} = \frac{1}{2}V\varrho v^2$$ The potential energy is given as $$E_\mathrm{pot} = V\varrho gh$$ In addition to that, the energy from the static pressure can be written as $$E_\mathrm{stat} = pV$$ Due to the conservation of energy, the sum of all these three forms has to be a constant. Dividing the resulting equation by $V$ leads to $$\boxed{\underbrace{\frac{1}{2} \varrho v^2}_{p_d} + \underbrace{\varrho g h}_{p_h} + p_s = \mathrm{const}}$$ This equation is called Bernoulli's equation and the underlying principle therefore Bernoulli's principle. All three sum terms are pressures and names as follows:

• $p_d$: dynamic pressure
• $p_h$: hydrostatic pressure
• $p_s$: static pressure