Fluid Flow: Bernoulli's theorem

Bernoulli's theorem is based on the principle of conservation of energy. In a flow of ideal fluid, we consider three types of energies on a macroscopic level, Potential Energy due to height from a reference point, Kinetic Energy due to velocity of fluid, Pressure Energy due to forces applied on the fluid. In Bernoulli's theorem three heads Potential head (z), kinetic head [(v^2)/2g] and pressure head (p/gρ). The total energy at every point in the flow is constant. the easy way to remember this equation is with the help of dimensions like [P/gρ =  (v^2)/2g = z ] have the same dimensions of length.

For a horizontal pipe flow, potential head is constant. the change in velocity head is converted into pressure head, which is the principle behind the flow meters.

As the area decreases pressure decreases according to Bernoulli's theorem but according to hydro-static law pressure is inversely proportional to area. In Bernoulli's theorem the pressure is hydrodynamic that means fluid is in motion. in this case, if area decreases velocity increases which results in decrease in pressure.