Bernoulli’s theorem is a statement in fluid mechanics that relates the pressure and velocity of a flowing fluid. It is called after Daniel Bernoulli, who broadcasted it in his book Hydrodynamica in 1738. The theorem states that for an inviscid flow (a flow where the viscosity of the fluid can be ignored), the sum of the pressure and kinetic energy per unit volume is constant. In other words, as the velocity of a fluid increases, its pressure decreases. This theorem has many applications in physics and engineering, and we will discuss some of them in this blog post.

What is Bernoulli’s theorem?

In liquid dynamics, Bernoulli’s theorem states that an upsurge in the pace of a fluid occurs simultaneously with a decrease in pressure or a reduction in the potential energy of the fluid. The theorem is prescribed after Daniel Bernoulli who printed it in his book Hydrodynamica in 1738.

Application of Bernoulli’s theorem:

Bernoulli theorem has a lot of use in fluid mechanics. It can be used to derive the Bernoulli equation which is a very important equation in fluid mechanics. Here are some examples of applications of Bernoulli’s theorem:

-working of aeroplane:

An aeroplane works on the principle of Bernoulli’s theorem. When an aeroplane flies, the wings create a low-pressure area above them. This low-pressure area sucks the air from below the wings and creates lift.

-working of a venturi:

A venturi is a device that is used to measure the flow rate of a fluid. It works on the principle of Bernoulli’s theorem. The fluid is accelerated as it passes through a narrow constriction in the venturi. This causes a decrease in pressure which can be measured.

working of a pitot tube:

A pitot tube is used to measure the rate of a fluid. It works on the principle of Bernoulli’s theorem. The fluid is accelerated as it passes through a narrow constriction in the pitot tube. This causes a decrease in pressure which can be measured.

Action of atomiser:

An atomiser is a device that is used to spray a liquid in the form of fine droplets. It works on the principle of Bernoulli’s theorem. The liquid is accelerated as it passes through a narrow constriction in the atomiser. This causes a decrease in pressure which vaporises the liquid and breaks it up into fine droplets.

So these are some examples of applications of Bernoulli’s theorem.

Derivation of Bernoulli’s theorem:

Bernoulli’s equation can be derived from the conservation of energy equation. If we consider a control volume that is moving with the fluid, Bernoulli’s equation states that the sum of all forms of energy within the control volume must remain constant.

Here is the bernoulli equation:

p+1/2V2+gh=constant

where:

P is the pressure

is the density

V is the velocity

H is the elevation

G is the gravitational accelarartion

So this was all about the derivation of Bernoulli’s theorem.

Limitations of Bernoulli fluid mechanics Bernoulli equation:

Bernoulli’s equation has certain limitations:

-It is a statement of energy conservation and as such, it cannot be applied to open systems.

-It is only strictly valid for inviscid, incompressible flow. However, it can be applied to viscous flow if the fluid speed is small enough and the fluid density is constant.

-It is only valid for steady flow. However, it can be applied to unsteady flow if the fluid speed is small enough and the fluid density is constant.

-It cannot be applied to flow with a significant change in elevation (i.e. large height difference between the two points where the pressure is measured).

-It cannot be applied to flow with significant curvature (i.e. the fluid path between the two points where the pressure is measured is not straight).

-It cannot be applied to flow with significant friction (i.e. the fluid is moving through a pipe or other constriction).

-It cannot be applied to flow with significant heat transfer (i.e. the fluid temperature is changing).

-It cannot be applied to flow with significant electrical effects (i.e. the fluid is conducting electricity).

-It cannot be applied to flow with significant magnetic effects (i.e. the fluid is moving through a magnet).

-It cannot be applied to nuclear reactions (i.e. the fluid is radioactive).

-It cannot be applied to gravitational effects (i.e. the fluid is under the influence of gravity).

-It cannot be applied to flow in a vacuum (i.e. there is no fluid).

Conclusion

So there you have it! Three examples of Bernoulli’s Theorem in action. Of course, this is just a tiny sampling of all the places you’ll find Bernoulli’s Theorem at work. This principle is truly ubiquitous in fluid mechanics! The application of the Bernoulli theorem is not just limited to ideal fluids but also non-ideal fluids. Bernoulli’s theorem can be applied to derive the Bernoulli equation which is widely used in fluid mechanics. We hope you enjoyed this quick tour of Bernoulli’s Theorem. Hopefully, this article has given you a better understanding of how and where Bernoulli’s Theorem crops up in the world around us. Thanks for reading!