# What is Bernoulli principle: Definition and 27 Discussions

In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler who derived Bernoulli's equation in its usual form in 1752. The principle is only applicable for isentropic flows: when the effects of irreversible processes (like turbulence) and non-adiabatic processes (e.g. heat radiation) are small and can be neglected.
Bernoulli's principle can be applied to various types of fluid flow, resulting in various forms of Bernoulli's equation. The simple form of Bernoulli's equation is valid for incompressible flows (e.g. most liquid flows and gases moving at low Mach number). More advanced forms may be applied to compressible flows at higher Mach numbers (see the derivations of the Bernoulli equation).
Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy, potential energy and internal energy remains constant. Thus an increase in the speed of the fluid – implying an increase in its kinetic energy (dynamic pressure) – occurs with a simultaneous decrease in (the sum of) its potential energy (including the static pressure) and internal energy. If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ρ g h) is the same everywhere.Bernoulli's principle can also be derived directly from Isaac Newton's Second Law of Motion. If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline.Fluid particles are subject only to pressure and their own weight. If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can only be because the fluid on that section has moved from a region of higher pressure to a region of lower pressure; and if its speed decreases, it can only be because it has moved from a region of lower pressure to a region of higher pressure. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest.

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1. ### Can you please explain Bernoulli's equation?

Can you please explain why is there work done by F2(on photo of textbook explanation of Bernoully equation (photo below)). I can understand that W2 is caused by F2 which is gravitational force(screenshot photo from YT). But for the explanation in textbook pipe is straight, no height...
2. ### I Help Regarding Application of Bernoulli in a Boundary Layer

Hey all, I recently took an aerodynamics exam that included the question "Please Explain how the Bernoulli Equation can be Applied Inside a Boundary Layer". Now, it is my belief that the Bernoulli equation, defined by my textbook as P+0.5ρV2=ℂ, requires inviscid flow to be properly applied...
3. ### Bernoulli Principle For Pitot Tubes

Here is the setup: Apply Bernoulli Principle to the top (free surface) of the two pitot tubes (1 for static and 2 for dynamic with the points colored in red): $$\frac{p_1}{\rho_w g}=h+\frac{p_2}{\rho_w g}$$ The difference in air pressure would give the following:$$p_1=p_2+h\rho_{air} g$$...
4. ### I Laminar-turbulent transition and Reynolds number

Hi all! This is my first post here, so hopefully I am not in violation of any rules or etiquette. I'm looking to derive an equation for Reynolds number as function of pressure for a pinhole leak in a pressurized gas line. The line is regular air and is pressurized to 1 atmosphere and is leaking...
5. ### Bernoulli Principle from a molecular scale

Good evening everyone. Can you tell me if it is possible to mathematically derive the Bernoulli principle from a microscopic analysis? In particular, in the hypothesis of an incompressible stationary flow, at a constant altitude, it states that: P + 0.5ρV^2 = cost Well, in textbooks this...
6. ### Bernoulli Principle vs. Coanda Effect

In the past couple of days I've been watching video demonstrations on YouTube that use the Bernoulli Principle to explain what is happening (e.g. the hairdryer and ball experiment) Then, I saw this one video using the Coanda Effect as the explanation (they were also using the hairdryer and ball...
7. ### Physics concepts behind pneumatic tube systems?

I have a project for my physics class that revolves around the idea of building a working pneumatic tube system. I understand how I would build it and such but my teacher wants me to explain the theory behind it. Does anyone have any ideas about the physics behind this or the principles, rules...
8. ### Model pressure loss vs time for air in a cylinder w/ hole

Related to an engineering project I will be working on. The situation is that essentially I will have a closed cylinder (5.5 in x 26 in) with a small 15mm hole on the side (not on a circular face), which allows the air inside to be at equilibrium pressure/temperature with the outside. Then a...
9. ### A1v1=a2v2? pressure and velocity are inversely proportional?

If Bernoulli's equation P + 1/2ρv2 + ρgh = constant, implying that pressure decreases as velocity increases, and the Venturi effect states that a1v1 = a2v, what resolves this apparent contradiction? The velocity slows as the cross sectional area increases, but a narrower pipe would have greater...
10. ### What is a good film that has examples of the Bernoulli Principle

We have to find a movie that has 3 good examples and 3 bad examples of this principle. We were thinking about doing Finding Nemo however we can't think of 3 bad ones and we are worried that our physics teacher might reject it since it is not a "serious" movie. Any ideas?
11. ### Find velocity of air using Bernoulli principle

Homework Statement A horizontal stream of air is blown just above the open end of the hares apparatus with an initial speed "V". The density of air is 1.2 kgm-3.Then the water column rises to 6 cm in the respective limb.Density of water is 103 kgm-3 Using Bernoulli`s principle find "V"...
12. ### The Bernoulli principle from the perspective of statistical mechanics

Hi community, I have a question about the Bernoulli principle. From statistical mechanics the pressure in the ideal gas is independent of velocity. But in the case of the flow of an ideal gas in a channel, the pressure depends on the velocity. Where can I clarify this misunderstanding...
13. ### Bernoulli principle and fluid particle

Hello, Bernoulli principle describes the flow of a fluid for steady, incompressible flow along a streamline. But it is said for a particle of a fluid along a streamline. My question is a particle of fluid refers to a molecule or a group of molecules? Thank you
14. ### Bernoulli Principle and fluid velocity

I have been trying to fully understand this concept of Bernoulli's Principle , the Venturi effect and fluid velocity and energy. I need to grasp this to develop an idea that I have been working on. 1. As water is forced down a narrowing pipe, as the pipe gets more narrow, it means it losses...
15. ### Bernoulli principle and venturi effect.

I have a specific problem involving two reservoirs filled with water with a height difference Y and total head H, and was wondering if a venturi like device could be used to calculate the resulting pressure head x and if it will exceed the bottom of reservoir 1. Also the drain length is d...
16. ### Bernoulli principle - negative pressure

I will write a program about principle bernoulli, but i have a problem. My input data: Pressure(p1) = 1000 Cross-section(A1) = 1 Velocity(V1) = 1 Cross-section(A2) = 0.5 Velocity(v2)= (V1A1)/A2 to simplify: h1=h2 i'm counting the pressure p2 : p2 = p1 + 0.5*v1*v1 - 0.5*v2*v2...
17. ### Bernoulli Principle: Homework Solution

Homework Statement Water Flows upward throw the pipe shown in the diagram at 96 L/Min. If the pressure at the lower end is 80kPa, find the velocity of the water is at both ends and the pressure at the upper end. Assume that the density of water remains constant throughout the tube and that...
18. ### Solving Bernoulli Principle Homework: Water Flows in Pipe

Homework Statement Water Flows upward throw the pipe shown in the diagram at 96 L/Min. If the pressure at the lower end is 80kPa, find the velocity of the water is at both ends and the pressure at the upper end. Assume that the density of water remains constant throughout the tube and that...
19. ### Bernoulli principle or due to Viscosity?

Why the speed of water in the middle of the smooth flowing stream is high than its speed on the sides? Is it due to Adhesion or cohesion forces or viscosity or Bernoulli principle holds here? Kindly tell me exact reason .
20. ### Bernoulli Principle of fluid question about velocity

Homework Statement A dairy farmer notices that a circular water trough near the barn has become rusty and now has a hole near the base. The hole is 0.11 m below the level of the water that is in the tank. If the top of the trough is open to the atmosphere, what is the speed of the water as it...
21. ### Bernoulli Principle with Bullets

Hi I was reading about long range sniper bullets been affected by gyroscopic affect with the spin of the bullet. I was wondering if Bernoulli's principle could be applied to this, as the pressure at one side of the bullet is greater than the other (depending on the rotation). Is this true and...
22. ### Quick question about Bernoulli principle and resistance?

Ok I studied bernoulli and I can see how fluid would travel faster in narrowed regions but in most examples I see when something is narrowed the flow is reduced. Is this because of resistance? Also when there is resistance speed in the narrowed section is reduced right? I like to know what do...
23. ### I think I understood Bernoulli principle but I need to clarify one thing quickly

Ok after hours of contemplating I think I finally understood the concept(hopefully ). However I still need 1 quick clarification. When water flows suddenly from a larger to a small dimater Bernoulli says 1. Pressure decreases 2. Velocity of fluid increases I'll put numbers just for...
24. ### Is Bernoulli principle the cause of suction truck?

Is Bernoulli principle the cause of suction truck?? Hello! I’d like to know this question: When a truck walks to a high speed we see how the road tree leaves are dragged behind it. I would like to know the real cause of this problem. I think the air viscosity makes the truck drag a thin...
25. ### Bernoulli Principle Problem

Homework Statement Find the lift in Newtons due to the Bernoulli Principle on a wing of a plane of area 84.5 m^2 if the air passes over the top and the bottom surfaces at speeds of 347m/s and 289 m/s Homework Equations P1+(1/2)densityV^2 =P2+(1/2)densityV^2 The Attempt at a...
26. ### A-Level Investigation into Bernoulli Principle

Hi! I'm a UK based student undertaking A-Level Physics. I am now in my second year completing my majour investigation. We are allowed to study and investigate any physics phenomina(sp) of our choice, I have decided upon a ball in a jet looking into the effects of Bernoulli. One of the...
27. ### Bernoulli Principle: Intuitive Explanation?

I have read and understood the explanation of the Bernoulli principle based on conservation of energy, but what I would like is a more intuitive way of picturing just how the reduced pressure develops in, say, a venturi tube. I want to be able to mentally track an element of the fluid and...