‘Bernoulli’s principle’ or ‘Bernoulli effect’ seems a very common term in our science books. It holds an important place in the fundamental foundation of Fluid Dynamics. The effect states that if there is an increase in the speed of the fluid, there will be a simultaneous decrease in the static pressure or a decrease in the potential energy of the fluid.
BERNOULLI’S PRINCIPLE – HISTORY
The Bernoulli effect is named after scientist Daniel Bernoulli who published this principle in his book named ‘Hydrodynamica’ that came up in the year 1738. Although Bernoulli deduced that when pressure decreases the speed of the flow of any fluid increases, but it was Leonhard Euler who derived the Bernoulli’s equation in its actual form in the year 1752. The principle is only applicable for only those flows when the effects of the various irreversible processes are negligible and the other non-adiabatic processes, like the radiation of the heat, are small and can be easily neglected.
Bernoulli’s principle can be applied to various types of fluid flow, which results in various forms of Bernoulli’s equations. Because of this very reason, there are different forms of Bernoulli’s equation for different types of flows. The simplest form of the Bernoulli’s equation is valid for the flows that are incompressible.
Bernoulli’s principle can also be derived from the principle of the conservation of energy. This law states that, in any steady flow, the addition of all the forms of energy in a fluid is said to be the same at all points on the streamline. This works when the sum of kinetic energy, potential energy, and internal energy remains constant that is they may not vary from time to time. Thus, we can say that an increase in the speed of the fluid shows that there is an increase in its kinetic energy and simultaneously there occurs a decrease in its potential energy as well as the internal energy. If the fluid is flowing out of any reservoir, the sum of all forms of energy is just the same on all the streamlines, this is because in a reservoir the energy per unit volume is the same everywhere.
NEWTON’S 2nd LAW OF MOTION
Bernoulli’s effect is basically the flow of a fluid which can also be derived directly from Isaac Newton’s Second Law of Motion. The second law states that if a small volume of fluid is flowing horizontally from any region of high pressure towards the region of lower pressure, then there is more pressure on the behind side than on the front side. The fluid particles are subject only to the pressure and also their own weight.
If a fluid is flowing horizontally and along a section of a streamline, where the speed is increasing. It can only be possible because the fluid on that section has moved from a region of higher pressure towards the region of low pressure. There can also be a condition where the speed is decreasing if its speed decreases, then the reason can be that the fluid has moved from a region of lower pressure to a region of higher pressure. Within a fluid that is flowing horizontally, the highest speed is seen where the pressure is the lowest, and the lowest speed can be seen where the pressure is the highest.
THE FUNDAMENTAL USAGES
In our modern everyday life, there are many observations that can be successfully seen happening by the application of Bernoulli’s effect. Bernoulli’s principle can be used to calculate the lift force. For example, if the air that is flowing past the top surface of any aircraft wing is moving faster than the air flowing under the bottom surface, then the Bernoulli’s effect states that the pressure on the surfaces of the wing will be lower above than on the bottom side. This pressure difference will, therefore, result in an upward-lifting force.
The Bernoulli’s effect does not explain why the air flows faster from the top of the wing and why it is slower past the underside. The flow speed of any fluid can be measured by using a simple device such as a Venturi meter or an orifice plate, which can be easily placed into a pipe to reduce the diameter of that flow. In the case of an incompressible fluid, the reduction in diameter will eventually cause an increase in the fluid flow speed. The Bernoulli’s effect then shows that there must be a decrease in the pressure in the region where the diameter was reduced. Then there arises a new phenomenon which is known as the ‘Venturi effect’.
PRACTICAL IMPLICATIONS – BERNOULLI’S PRINCIPLE
Another use of this effect is that the maximum possible drainage rate for a tank with a slight hole or even tap at the base can be calculated directly using the Bernoulli’s equation, and this rate is found to be proportional to the square root of the height of the fluid inside the tank. The Bernoulli grip relies on the Bernoulli effect to create a non-contact adhesive kind of force between the surface and the gripper. The Bernoulli’s effect is also applicable in the swinging of a cricket ball.
During a cricket match, the bowlers continuously polish one side of the ball. After some time, we can see that one side is quite rough and the other side is still smooth. Hence, when the ball is bowled and passes through the air, the speed on one side of the ball is faster as compared on the other side, due to this difference in the smoothness of surfaces of the ball, there arises a pressure difference between both the sides and this leads to the ball rotating or swinging while it is traveling through the air. This even gives an advantage to the bowlers.