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Common Applications of Bernoulli's Principle

Learn about some of the common examples and applications of Bernoulli’s principle in this guide.

Common Applications of Bernoulli's Principle

Author Cadence CFD

Key Takeaways

Bernoulli’s principle is a universal relation describing flow behavior for ideal fluids.

Some common applications of Bernoulli’s principle are its use to explain flow behavior in simple systems.

More complex flow behavior can be explained with modified versions of Bernoulli’s principle.

Some relations from fluid dynamics are universal, and one of these is Bernoulli’s principle. This simple relationship defines a range of flow behavior for ideal fluids, but many real systems can be approximated in such a way that Bernoulli’s principle is relevant. To see where applications of Bernoulli’s principle can be treated with the standard form, we’ll look at a few common fluid flow situations that illustrate the applicability of this universal relation.

Are There Applications of Bernoulli’s Principle?

Systems engineers do not necessarily use Bernoulli’s principle as the basis for designing systems that rely on fluid flow. Bernoulli’s principle is an explanatory tool that describes why fluid behavior occurs in certain ways—it is not really a design tool. That being said, there are some applications or examples of fluid flow that can be best explained and understood using Bernoulli’s principle. As we’ll see in the next section, Bernoulli’s principle is something of a universal relation involving certain types of flows.

What Is Bernoulli’s Principle?

Bernoulli’s principle is essentially a statement regarding the conservation of energy in a flowing fluid, and it defines the conservation of mechanical energy for all streamlines that make up the flow. There is a simple form of Bernoulli’s equation that can be derived from Euler’s equations describing certain types of flows:

Steady flow: Bernoulli’s principle only applies to steady flows, as unsteady flows would require the addition or dissipation of energy in the fluid by an external force.

Incompressible: The fluid density appears in Bernoulli’s principle, but the fluid density is assumed constant for all streamlines. Note that this does not mean the fluid energy will be the same everywhere; this will depend on the velocity field.

Irrotational: The flow is defined as being irrotational everywhere. This is equivalent to stating that there are no convective forces acting on the flowing fluid, i.e., the flow is in the laminar regime.

Inviscid: The fluid is assumed to be inviscid or approximately inviscid along all streamlines. In other words, there is no frictional force that would cause mechanical energy to be lost to heat.

Conservative forces: The counterpart to the previous point is that all forces acting on the fluid are conservative. This is not possible in reality, although in low Reynolds number flows we can approximate that only conservative forces are dominant.

The simplest form of Bernoulli’s principle for these types of flows defines a constitutive relation for any streamline in pressure-driven fluid flow:

Simplest form of Bernoulli’s principle for incompressible, irrotational, inviscid flows.

With this in mind, we can look at a few common fluid flow situations that can be explained using Bernoulli’s principle.

Lift in Aerodynamics

In aerodynamics, fluid flow across an airfoil will generate lift due to a vertical pressure gradient along the cross section of the wing. The pressure gradient in the vertical direction can be predicted using Bernoulli’s equation from the flow streamlines. Streamlines are commonly visualized along an airfoil, which allows the pressure gradient and lift to be predicted.

From the example streamline map shown below, we can see clearly that airflow is faster along the top surface of the airfoil, thus pressure will be higher on the bottom surface, creating lift. We can also see where flow separation and vortical flow occur along the back side of the wing, which would be expected at high Reynolds numbers.

Example streamline map along an airfoil (Image source).

Flow Through Nozzles and Channels

Low Reynolds number flows being directed through nozzles or channels can be described using Bernoulli’s principle. In particular, the change in flow rate as the system dimensions change can be predicted using Bernoulli’s equation. This effectively explains the Venturi effect, where a pressure-driven flow rate will change in accordance with conservation of energy.

Fluid Flow Measurements

A related application of Bernoulli’s principle is fluid flow rate measurements. The flow rate of a fluid can be measured by taking advantage of the Venturi effect. As fluid flows into an orifice plate with a small aperture of known diameter, the reduction in diameter will cause an increase in the fluid flow speed. Based on this measurement inside the channel, the flow rate outside the orifice plate can be calculated using Bernoulli’s principle.

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Application of Bernoulli's theorem

Application of Bernoulli's theorem (i) Lift of an aircraft wing (ii) Blowing of roofs (iii) Bunsen burner (iv) Motion of two parallel boats

Chapter: 11th 12th std standard Class Physics sciense Higher secondary school College Notes

Chapter: 11th 12th std standard Class Physics sciense Higher secondary school College Notes Application of Bernoulli's theorem

Application of Bernoulli's theorem (i) Lift of an aircraft wing (ii) Blowing of roofs (iii) Bunsen burner (iv) Motion of two parallel boats

A section of an aircraft wing and the flow lines are shown in Fig. The orientation of the wing relative to the flow direction causes the flow lines to crowd together above the wing. This corresponds to increased velocity in this region and  hence the pressure is reduced. But below the wing, the pressure is nearly equal to the atmospheric pressure. As a result of this, the upward force on the underside of the wing is greater than the downward force on the topside. Thus there is a net upward force or lift.

During a storm, the roofs of huts or tinned roofs are blown off without any damage to other parts of the hut. The blowing wind creates a low pressure P1 on top of the roof. The pressure P2 under the roof is however greater than P1. Due to this pressure difference, the roof is lifted  and blown off with the wind.

In a Bunsen burner, the gas comes out of the nozzle with high velocity. Due to this the pressure in the stem of the burner decreases. So, air from the atmosphere rushes into the burner.

When two boats separated by a small distance row parallel to each other along the same direction, the velocity of water between the boats becomes very large compared to that on the outer sides. Because of this, the pressure in between the two boats gets reduced. The high pressure on the outer side pushes the boats inwards. As a result of this, the boats come closer and may even collide.

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11th 12th std standard Class Physics sciense Higher secondary school College Notes : Application of Bernoulli's theorem |

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Mention any two examples (or) applications that Obey Bernoullis theorem and justify them.

Applications of Bernoulli's theorem: 1) Dynamic lift on the wings of an aeroplane is due to Bernoulli's theorem. 2) Swinging of a spring cricket ball is a consequence of Bernoulli's theorem. 3) During cyclones, the roof of thatched houses will fly away. This is a consequence of Bernoulli's theorem.

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Mention any two examples (or) applications that Obey Bernoullis theorem and justify them.

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Updated On: 27-06-2022

Text Solution Solution

Applications of Bernoulli's theorem:

1) Dynamic lift on the wings of an aeroplane is due to Bernoulli's theorem.

2) Swinging of a spring cricket ball is a consequence of Bernoulli's theorem.

3) During cyclones, the roof of thatched houses will fly away. This is a consequence of Bernoulli's theorem.

Answer

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