# What is Bernoulli's principle: Definition and 81 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. ### Formula derivation connecting vertical water flowrate & horizontal distance moved by a suspended sphere

TL;DR Summary: I am Highschool student writing a 4000 word research paper on Bernoulli's principle and the coanda effect. I need help with derivation of a formula that connects flow rate of water and distance moved by the sphere in my experiment. I am a high school student writing a 4000 word...
2. ### I Fluid dynamics: drag coefficient and pressure at the stagnation point.

Hi, In my textbook the author say that the drag coefficient is the drag force divided by the pressure at the stagnation point time the area perpendicular to the stream. ##c_d = \frac{2F_d}{\rho v^2 A}## To get the pressure at the stagnation point I'm using Bernoulli for an incompressible fluid...
3. ### B Fluid Flow Deflection Bending Ahead of Airfoil?

Hi, I am a high school teacher in need of some help explaining fluid flow. I don't have much experience with fluids at a college level. We were reviewing lift (Bernoulli's velocity/pressure relation, deflection of air downwards, etc) and I showed them: this online simulation. One student asked...
4. ### I Proving Torricelli's Law Using Bernoulli's Principle

There is a standard proof of this kind in which two points are taken - one at the top of the water and one just outside the spout or opening. I guess my question kind of assumes that you've seen something like this. A key step of the proof is to say that the difference of pressures, perhaps...
5. ### Mass loss in Bernoulli's Principle?

Hi, I could really use help. I am trying to understand what would happen to the velocity of a freestream air if it loses mass while traveling down a tube. For example, suppose that you have 1 cubic meter of air traveling at 10 m/s down a duct with a 1m^2 cross section. And then suppose that you...
6. ### Pressure Differential in Fluid Dynamics: Why More on the '+s' Side?

Here i added a page from my fluid dynamics book where it shows particle model for deriving the equation. My question is why pressure is more at stream side aka 'positive "s" direction'.I would expected more pressure on the other side because for example when you trying to push a rigid object or...
7. ### Need some help with Bernoulli's principle and how it applies to a drone

Hi there, I am building a drone for a school project and I am looking at physics behind how it flies. I stumbled upon Bernoulli's principle and the Coanda effect but I am struggling to find out how it can apply to the rotors of a drone. I understand the primary aspect of as the fluid's speed...
8. ### Need help with horizontal syringe Bernoulli's Principle problem.

Did I do this problem correctly? I felt like I did this wrong because the answer is suppose to be around 50 m/s.
9. ### Bernoulli's Principle -- correct derivation

In this scenario I'm assuming that there is a shared velocity of water within the pipes, as well as a shared pressure and that water is non-compressible. If I understand correctly when someone says that pressure at a point is P at some point, it is the same as saying that if I put a small cube...
10. ### Bernoulli's Principle and Fans [split]

That's confusing. If the velocity at the exit is increased, that simply means kinetic energy is increased. But as the pressure is decreased and suppose the process is adiabatic (in case of compressible fluid), that means the temperature too is decreased. That simply means the enthalpy of the...
11. ### What is the relation between Bernoulli's principle & Pascal?

Bernoulli's principle states that under dynamic conditions total energy inside the fluid container remains constant. and if area is decreases then pressure decrease . and Pascal states that pressure = force/area . here if area decreases then pressure increase . I'm getting confusing...
12. ### How do we use Bernoulli's Principle in this situation?

Homework Statement A large water tank, open at the top, has a small hole in the bottom. When the water level is ## 30## ##m## above the bottom of the tank, the speed of the water leaking from the hole: A. is ##2.5## ##m/s## B. is ##24## ##m/s## C. is ##44## ##m/s## D. cannot be calculated...
13. ### Understanding Bernoulli's Principle

My understanding of Bernoulli's Principle is something like this: Pressure is inversely proportional to velocity. Fluid flowing through smaller cross-sectional area has increase velocity & decrease in pressure. Also P = F/A... so would force also decrease for fluid going through small area...
14. ### Pascal's Principle vs. Bernoulli's Principle

Hi, There is a basic problem I am having with fluid dynamics that has been really confusing me. I have been told that as a result of conservation of energy and Pascal's principle, for an incompressible fluid Pin=Pout, or pressure is constant. However, pressure is not necessarily constant in...
15. ### Is there a way to find the velocity of air in a flute?

Homework Statement I am working on a math investigation which involves the physics of the flute and I can't move on unless I find an equation for the change in required velocity of the air stream to produce different frequencies. I have a feeling I might have to abandon this idea and do...
16. M

### How Does Bernoulli's Principle Apply to Varying Pipe Diameters and Water Flow?

Homework Statement A horizontal length of pipe starts out with an inner diameter (not radius!) of 2.60 cm, but then has a tapered middle part which narrows to a diameter of 1.60 cm. When water flows through the pipe at a certain rate, the gauge pressure is 34 kPa in the first (wider) section...
17. ### Trouble with Bernoulli's principle

I have some trouble with the derivation of Bernoulli's principle. The Wikipedia gives two derivations, for an incompressible fluid, and I have trouble with both of them: https://en.wikipedia.org/wiki/Bernoulli%27s_principle#Derivations_of_the_Bernoulli_equation In the first derivation, using...
18. C

### How Can Bernoulli's Principle be Related to Fire Hoses

Hello everybody: I am trying to test, using Bernoulli's Principle, when firehoses are most effective. I know this is extremely broad, but does anyone have any ideas for independent variables? I am thinking about the the width of the end piece of the nozzle... Any help/guidance would be...
19. ### An odd question regarding Bernoulli's Principle

I don't know if anyone remembers me. I'm not a physicist but I tend to do pretty well at understanding some of the basic principles of classical physics, and that's recently created food for thought on my part.There's a message board I've found that is devoted primarily to debunking popular...
20. ### Bernoulli's Principle equation help

Hi everyone and thank you in advance. My first problem is: if v1=constan in a section S1, it should not be ∑ F = 0 ? Or maybe Σ M = 0 ? Because all forces that i recognize are gravity and pressure, but i never found the equation mg - PS = 0 or something similar. I was thinking about something...
21. ### Bernoulli's principle and work energy theorem

for a stream line flow of ideal liquid (non-viscous) imcompressible the sum of pressure energy per unit volume kinetic energy per unit volume , potential energy per unit volume remains constant mathematically P+1/2roV2+ROGH=constant consider a fluid flowing in a pipe of various crossections we...
22. ### Bernoulli's Principle and Energetics of Flowing blood

My understanding and application: Flowing blood with mass m, and velocity v has KE proportional to mean velocity squared as blood flows inside the vasculature, pressure is also exerted laterally against the walls of the vessels So, it is then reasonable to use Bernoulli's for the blood and...
23. ### Aircraft lift - is it all Bernoulli's principle?

I find it hard to believe that the only factor important in computing aircraft lift is Bernoulli's principle. Doesn't good old Newton's Second Law play an effect? In other words simply deflecting the airflow downwards. Does anyone know the relative importance of these factors? (EG for a...
24. ### Bernoulli's Principle Problem/Energy Conservation

Homework Statement Hi! The problem states: Water through a certain sprinkler system flows trhough a level hose connected to a nozzle which is directed directly upwards. The water leaves the nozzle and shoots to a height, h, before falling back down again into a pool. The hose is connected to...
25. ### Bernoulli's principle, flow rate, velocity and pressure

Hello, I need some help understanding Bernoulli's principle, flow rate, velocity and pressure. I understand that when the diameter of a pipe decreases, the velocity will increase and the pressure will decrease. But I am having a hard time applying this to a practical application. For...
26. ### Conceptual question: Bernoulli's Principle Syringes

Homework Statement I'm interested in an explanation of the forces/principles involved in the following scenario: There are two syringes, level with one another, containing the same volume of water. The difference between the syringes is the gauge of the needle; one is of greater diameter...
27. ### Stuck understanding Bernoulli's Principle, would love some help

Hi all - I was having a debate with some students in my flipped class today and I can't wrap my head around Bernoulli's Principle as it relates to the sea. Can anyone explain how Bernoulli's principle works with a sail boat? I don't know how the force vectors resolve to push a sail boat...
28. ### Bernoulli's principle in stagnant situations

please note in the process proving bernoulli we use the CONTINUITY equation.Consider a situation wherein a pitot tube is used to measure pressure/velocity in a steady flow(picture attached for reference).Here we use bernoulli for pressure measurement.we apply the bernoulli theorem for a...
29. ### Bernoulli's Principle alternative view

Hi guys, Could anyone explain Bernoulli's Principle to me so that it makes sense from an alternative point of view? http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html I can make sense of the maths but I'm trying to understand what actually happens so I can visualise it. At first...
30. ### Bernoulli's Principle (Possibly involving Venturi's Effect)

Homework Statement Two very large open tanks A and F (the figure (Figure 1) ) contain the same liquid. A horizontal pipe BCD, having a constriction at C and open to the air at D, leads out of the bottom of tank A, and a vertical pipe E opens into the constriction at C and dips into the liquid...
31. ### Bernoulli's Principle with a Venturi Tube, find flow rate

So that's the question and I'm stuck on Part b. I don't even know how to approach it. I know A1= 3A2 but I don't know A1 and I need V2 and I don't know V1 or A2. I'm just confused as to how to do this. Please help!
32. ### How does the reference height affect Bernoulli's principle calculations?

Homework Statement Please click on the following link for the solution. http://s1292.photobucket.com/albums/b580/cathy12121/?action=view&current=Bernoullisequation_zps0d4485d7.jpg Homework Equations P1 + .5(rho)v12 + (rho)gy1 = P2 + .5(rho)v22 + (rho)gy2 The Attempt at a...
33. ### I don't understand Bernoulli's principle applications

I'm extremely raged right now, I see people applying Bernoulli's equation at fans, atmonizers etc. Let's look at the classic example where you blow through a straw and make liquid be drawn up from a can (through a second straw)...
34. ### Bernoulli's Principle density and velocity

Homework Statement The density of the liquid flowing through a horizontal pipe is 1600 kg/m3. The speed of the fluid at point A is 4 m/s while at point B it is 8.0 m/s. What is the difference in pressure, PB - PA, between points B and A? a. -1.9 x 10^3Pa b. -3.8 x 10^4Pa c...
35. ### Condensation of gas using bernoulli's principle

hi experts This ought to be obvious but it sounds wrong. If I have a pipe carrying butane at a constant flow rate at room temperature fed from a liquid gas bottle without a restrictor so that the gas is almost condensing, then have a constriction in the pipe to accelerate the gas, will...
36. ### Building a science exhibit demonstrating Bernoulli's Principle

Hi guys, I'm building a science exhibit demonstrating Bernoulli's Principle for a competition. It's similar to the setup found here () at 2:51 to 2:57. So, I tried a ping pong ball and a hair blower. Doesn't work. Firstly, the hair blower is pretty weak, so when the setup is in upright...
37. ### Atomizer Design Challenge? (Bernoulli's Principle)

I understand why liquid is sucked into a tube of flowing air with a constricted end due to Bernoulli's principle, what puzzles me is why the air doesn't just take the path of least resistance instead of inducing liquid suction (see attached image). For example, if a 1/4 inch line at 30 psi has...
38. ### Bernoulli's Principle and water tank

Homework Statement A sealed tank is completely full of water. The water in the tank is stationary. The gauge pressure at the top of the tank is 150 kPa. A mechanical failure of the tank creates a hole of area 1.00 cm2 at the top of the tank. Water flows out of the hole, rising in a vertical...
39. ### Bernoulli's Principle applied to Blood Pressures at different heights.

We will construct a simple model of the circulatory system to investigate the rate at which cuts bleed. In this model we will assume that blood is a Newtonian fluid at all length scales so that the equations of fluid flow which we have been studying will apply. We will also assume that the...
40. ### Bernoulli's Principle: Venturi Pipe

1. Where did i go wrong, please explain. Homework Statement The Horizontal Venturi pipe has a cross sectional area of 50cm^2 at the wider portions(A_1) and 25cm^2 at the constriction(A_2). Air density of 1.29 kg/(m^3) is flowing in the pipe. Theres a attachment of a picture to reference...
41. ### Another question on Bernoulli's principle

Homework Statement I have read this thread https://www.physicsforums.com/showthread.php?p=3185555&posted=1" I am still a bit confused. So I am putting this quantitatively with a slightly different scenario. Assuming water coming out of water pipe with Area A1 with a water flow rate of J...
42. ### Exploring the Applications of Bernoulli's Principle in Fluid Dynamics

1. what is the Bernoulli's Principle ?
43. ### Bernoulli's Principle and pressure

Hi guys, I have what I hope is an easy question. When you put your thumb over the end of a water hose, why does the water coming out feel like it has a HIGH pressure (meaning, it will hurt somebody being sprayed by it) EVEN THOUGH Bernoulli's Principle says that the pressure should...
44. ### The Topic That Wouldn't Die: Bernoulli's Principle and airfoils

Recently, I was discussing airfoils with a friend. I thought I was being clever and said "No, Bernoulli's Law isn't what's keeping it in the air - that's a fallacy. If it were Bernoulli's Law keeping it in the air, then airplanes would not be able to fly upside down. What keeps a plane in the...
45. ### Is Bernoulli's Principle Related to Potential Energy and Lifting Water?

The Bernoulli's principle ? I'm having difficulty understanding the principle. Particularly the concept of lowering potential energy. What i am also interested in is the effects of this principle. Would a segment of hose with water running through it be easier to lift than the same segment...
46. ### Exhaust pressure on over-run (bernoulli's principle?)

Hi all, I have a car with a straight through exhaust, consisting of a 4 into 1 manifold, a single pipe, then a single silencer. Between the manifold and silencer is a join. When i am driving on over run (closed throttle, decellerating) i know this joint sucks air in, as the exhaust makes a...
47. ### Applicability of Bernoulli's principle to ideal gases

Bernoulli's equation as I understand it is an expression (or possibly a consequence) of conservation of energy in an incompressible fluid flow. My question is: how can the "standard" Bernoulli's equation ever apply to an ideal gas? Wikipedia gives a different version of Bernoulli's...
48. ### Bernoulli's principle with venturi effect

So, I need some info on how to get the data that I'm missing on my project. My english is not great and is very hard for me to try figure this out by myself so if you guys could help me out I will appreciate. I need to know how much vacuum in HG I will get at the B on my picture, and if will...
49. ### Bernoulli's principle and the 3rd law of motion

I know that a faster moving fluid creates a lower pressure which can give lift to an airplane. Although I do not know what the opposite reaction is during lift.You have the upward force on the wing, but where is the downward force that should be opposite being exerted. Does the downward force...
50. ### What is the Derivation of delta(Pa)/delta(Pb) in Terms of Da and Db?

Homework Statement Using these equations: 1) Vb/Va = (Da/Db)^2 and 2) Va^2 = (2(Pa-Pb)) / [density*((Da/Db)^4)-1] Derive a mathematical expression for delta(Pa)/delta(Pb) in terms of Da and Db Homework Equations 1) Vb/Va = (Da/Db)^2 2) Va^2 = (2(Pa-Pb)) /...