Bernoulli’s Equation

Bernoulli’s principle is named after the Dutch Swiss mathematician Daniel Bernoulli; during 1738 he published his principle in his book hydrodynamica.  Bernoulli’s equations states that when a fluid or liquid flows through the restricted area, velocity will be increased with the decrease in pressure. Bernoulli’s equation can be applied to various type of fluid flow; in fact there are different forms of Bernoulli equation for different types of flow.  For incompressible flows (liquid flows) and compressible flows (gases) moving at Mach number the simple form of Bernoulli principle is valid.

From the principle of conservation of energy, Bernoulli’s equation can be derived. This states that, the sum of all forms of mechanical energy in the fluid along streamline is the same at all points on that streamline in a steady flow and this requires that the sum of kinetic energy and potential energy remains constant. In some case, if the fluid is flowing out of reservoir, then the sum of all forms of energy is the same on all streamlines, because the energy per unit mass is same everywhere in a reservoir.

Fluid particles are subjected only to pressure and their own weight. In the streamline section the fluid flows horizontally, the velocity of the fluid increases with decrease in pressure, because  the fluid is flowing from the higher pressure region to lower pressure region; if the velocity decreases, it is only because the fluid flows from the region of lower pressure to the upper pressure. As a result, within the fluid flowing horizontally, the highest speed of the fluid occurs in the area, where the pressure is lowest and lowest speed occurs only in the area where the pressure is highest, vice versa.

Bernoulli’s equation in Real World

To calculate the lift of an airfoil Bernoulli’s principle can be used, if the behavior of the fluid flow in the vicinity of the foil is known.  How the aircraft derives lift? It derives lift by means of air, the air which passes over the upper chamber of wing has to travel faster to reach the trailing edge of the wing compared with the lower chamber of the wing, so the pressure drops heavily in the upper chamber and velocity increases. So the lower pressure in the upper chamber and higher pressure in lower chamber produces lift, i.e. this pressure difference produces lift.  Whenever the distribution of the speed past the top and bottom surfaces of a wing is known, the lift forces can be calculated using Bernoulli’s equations – established by Bernoulli over a century, before the man made wings used for the flight.

Questions:

• Explain Bernoulli’s equation?
• How Bernoulli’s equation is used in flight?