# Applications of Bernoulli’s Theorem

### Applications of Bernoulli’s Theorem

According to Bernoulli’s theorem, whenever there is an increase in the speed of the liquid, there is a simultaneous decrease in the potential energy of the fluid and also we can say that there is a decrease in the pressure of the fluid. Basically, it is principle of conservation of energy in the case of ideal fluids. If the fluid flows horizontally such that there is no change in the gravitational potential energy of the fluid then increase in velocity of the fluid results in a decrease in pressure of the fluid and vice versa.

Bernoulli’s Principle Equation: This theorem is a consequence of the principle of conservation of energy, applied to ideal liquid in motion. As per the theorem statement that is for the streamline flow of an ideal liquid, the total energy per unit mass remains constant at every cross section throughout the flow.

$$\frac{p}{\rho }+gh+\frac{1}{2}{{v}^{2}}$$ = Constant.

Applications of Bernoulli’s Theorem:

1. Air Flight: The way Bernoulli’s theorem applies here is in the architecture of the plane’s wings. The top of the airplane wing is a little curved and the bottom is completely flat. But air travels across both parts of the wings simultaneously in the sky. Being of different designs, the air on the bottom part of the wings move slower increasing the pressure on the bottom of the wing and with more speed on the top the pressure of air on top wing decreases. This results in a lift that helps plane in flying.

2. BA SEBALL: The entire pitch of the baseball is working on the principle of Bernoulli’s Theorem. The stitches of the ball can be seen forming a curve which makes it necessary for the pitcher to grip the ball’s seams. This helps the pitcher in spinning the ball. So when there is less speed on the top part of the ball than its bottom part, then the bottom part of the ball accelerates in down direction at a speed more than the top part that allows the ball accelerates in down direction at a speed more than the top part that allows the ball to curve downward and thus the batter is not able to calculate the position of the ball correctly.

3. SAILING: It is another application in which Bernoulli’s theorem is used. When the boat is not travelling with the help of the wind, in that case, it is moving in a direction perpendicular to the wind. This implies that the boat is not being moved because of the dragging of the wind but it is moving due to the concept of the lift as in the case of airplanes. All types of sailboats have two parts. One is a sail which is always pointing towards the north direction and second is a keel that always points in the opposite direction of the sail. When the air possesses more speed on the sail, the pressure is less on the sail and the converse happens with a keel that is less pressure and more speed. This causes the lift and thus propels the sail to proceed in the water.

Examples:

1. A very common example of the principle of Bernoulli’s theorem is in the case of perfume bottles. When the bulb over the fluid is squeezed, it creates a low-pressure area because of the increasing speed of the air. This results in drawing the fluid up.
2. In the case of hurricanes as well it is advised to open as many windows as possible so as to equalize the pressure in and out of the house. This is because the speed of the hurricane is very high outside the window which reduces the pressure of air outside than inside. The difference in force pushes windows outward and this might actually even result in exploding of windows.