# What is Bernoulli's: Definition and 322 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 About Bernoulli's equation for fluid flow

Hello, I am currently studiying Bernoulli's equation and I have trubble understanding something , say we have a horizontal hose (no change in altitude of pressure ) Bernoulli's equation state that an ideal fluid can flow thought the hose with the same velocity , does an ideal fluid need a...
3. ### I Bernoulli's equation and the work energy theorem

Hello physics researchers, teachers and enthusiasts. I notice one little thing is confusing me in the derivation of Bernoulli's equation in the article, they write:$$dW = dK + dU$$where dW is the work done to the fluid, dK is the change in kinetic energy of the fluid, and dU is the change in...
4. ### [Aerodynamics] Bernoulli's equation and Pressure Coefficient

We know that the definition of the pressure coefficient is $$C_p=\frac{p-p_\infty}{q_\infty}$$, where ##p## is the pressure at a point, ##p_\infty## is the ambient pressure (free-stream), and ##q_\infty## is the free-stream dynamic pressure. We also know that the Bernoulli's equation is...
5. ### 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...
6. ### I Fluids: Bernoulli's Equation Derivation Question

I figure that either the Force F2 is applied in the opposite direction because of some kind of resistance, but I'm not sure. Thanks!
7. ### 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...
8. ### Can I apply Bernoulli's equation to this situation?

Can Bernoulli's equation be applied between points 1 and 2, ignoring the another tank ?
9. ### Bernoulli's equation from an elemental fixed streamtube control volume

Elemental fixed streamtube control volume from Professor White’s textbook “Fuid Mechanics”: I was unable to develop the intermediate steps for the following approximations: (continuity equation according to the book ) Where and (Momentum equation according to the book) In...
10. ### Bernoulli's Equation With Losses

Hello community I have been trying to get my head around Bernoulli's equation when factoring in energy loss due to friction. I am trying to understand the concepts and i was hoping someone could remove some doubt from my mind by confirming the following:- 1) Would the following statement be...
11. ### 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...
12. ### Bernoulli's Equation and water rockets

So I'm playing around with some water rockets and I'm trying to figure out how fast the exhaust velocity of the water is. I've had an experimental approach using high fps camera to record and analyse (using tracker) the exhaust velocity. I'm using a 0,5 l soda bottle with 0,085 L ; 0,135 ; L...
13. ### A question regarding Bernoulli's equation

P1 + ρgh1 + 0.5ρv21 = P2 + ρgh2 + 0.5ρv22 In the derivation of this equation from the theorem of Work-Kinetic Energy, pressures ( P1 and P2) represent are derived from F = PA, forces affected by other portions of fluid upon the fluid in the middle (which is our concern) at 2 different points. So...
14. ### Is Bernoulli's Equation related to the Conservation of Mechanical Energy?

So the Bernoulli's Equation.. My question : Are the terms on the left hand side equal to the total mechanical energy? So can I rewrite this equation as ?
15. ### Pumps and Bernoulli's equation

Hello, My understanding is that pumps (whatever type) add energy to the fluid and cause the fluid to move. The fluid can be either brought to a higher elevation or not. I am unclear on how pumps "provide a larger pressure". Do they? If so, in what sense? Are pumps simply speeding up, i.e...
16. ### What is pressure energy in Bernoulli's theorem?

In Bernoulli's theorem I understood the gravitational potential and kinetic energy but I can't understand what is pressure energy.
17. ### 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.
18. ### 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...
19. ### Deriving Bernoulli's Equation Using Euler's Law of Motion

Hi all, I have attached an image of a page out of the book I am using for context. The blue arrow in Figure 12-3 describes the motion of the particle. I figured the net force would need to be in the same direction, but apparently the net force opposes the motion. So, in Figure 12-3 the pressure...
20. ### Bernoulli's Equation Pressure at Blockage

Would it be because I'm comparing two different streams as opposed to two portions of the same stream?
21. ### Bernoulli's equation applicability question....

Hello, I just want to make sure I am on the right track: the three terms in Bernoulli's equation add to the same exact constant for any two points along the same streamline if the fluid is: stationary incompressible inviscid However, if the fluid is also irrotational, the the three terms add...
22. ### Help with Bernoulli's equation for a central heating system

so far I have found the velocity 1 and 2 by dividing the volume flow rate over the area which I got from pi x dia squared/4 my v1 = 1.01859m/s and v2= 2.82942m/s i have then figured out a pressure for the 15mm pipe which i got an answer of 2.71 bar however i am stuck on the rest of the question...
23. ### Can Bernoulli's Inequality Be Proven for All Real Numbers?

Homework Statement Prove bernullis inequality: If h>-1 then (1+h)^n ≥ 1+ nhHomework EquationsThe Attempt at a Solution How can I prove something that is false for h =1 n<1 ?
24. ### Demystifying the Often Misunderstood Bernoulli's Equation - Comments

Greg Bernhardt submitted a new blog post Demystifying the Often Misunderstood Bernoulli's Equation Continue reading the Original Blog Post.
25. ### 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...
26. ### Fluid mechanics: Bernoulli's equation and conservation of mass

Homework Statement A mechanical servo-mechanism comprising of a movable piston-cylinder within a vertical cylinder operates based on a venturi contraction in a horizontal 350mm diameter pipe that delivers a fluid of relative density 0.95. The upper end of the 100mm diameter vertical cylinder is...
27. ### 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...
28. ### What is pressure accourding to Bernoulli's theorem?

Hello everyone, In Bernoulli's theorem, I understand Potential energy (because of height) and Kinetic energy (because of velocity), but I don't understand pressure [energy]; Is it something like the vibration of molecules and bumping them into each other (in simple words). Any help or simulation...
29. ### When to apply Pascal's Law vs Bernoulli's equation

Hello, I was solving a problem regarding pressure at different elevations. The question regarded water flowing through a pipe which travels up 5 meters. I used Pascal's Law (p = p(initial) + rho*g*h : rho is density of fluid, g is gravity and h is the height) and came up with an answer...
30. ### MATLAB Sovling Bernoulli's differential equation in matlab?

I have a first order bernoullis differential equation. I need to solve this in matlab. Can anyone help me?
31. ### 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...
32. ### 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...
33. ### Bernoulli's equation, different streamlines, and wings

Hello Everyone, Bernoulli's equations expresses the conservation of mechanical energy for a particular fluid parcel moving inside a time-independent flow. The parcel is restricted to move and remain along a particular streamlines. The sum of the trinomial is equal to a constant on every...
34. ### Does Bernoulli's equation apply to a fountain?

Can I use Bernoulli's equation to calculate certain measures of a fountain, or does it only apply to fluids in pipes? Also if so, how could I calculate the pressure inside a tube used in a fountain?
35. ### Bernoulli's Equation, Find gauge pressure at 2nd point

Homework Statement At a certain point in a pipeline, the velocity is 1 m/s and the gauge pressure is 3 x 105 N/m2. Find the gauge pressure at a second point in the line 20 m lower than the first if the cross-section at the second point is one half that at the first. The liquid in the pipe is...
36. ### 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...
37. 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...
38. S

### Confusion about Bernoulli's Equation & Airplane Wing

Hi, I'm a little confused about the theory behind this problem related to fluids/Bernoulli's equation: "An airplane wing is designed so that the speed of the air across the top of the wing is 251 m/s when the speed of the air below the wing is 225 m/s. The density of the air is 1.29 kg/m3...
39. ### 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...
40. 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...
41. ### Bernoulli's equation, Venturi effect, hydraulic head, nozzle

Hi, I have this problem: I have a vertical tube 1 meter D, in the bottom end there is a nozzle with 0,5 m D. The tube is full of water. the tube length is 10 meters and the nozzle length is 2 meters. I need to calculate the power of this by this equation: W = Q * g * h * p where W is watt, Q...
42. ### Trouble understanding energy aspect of Bernoulli's Equation

So the Bernoulli's EQ comes from conservation of energy. From the figure, I see that if Force 1 is greater than Force 2, the water will move to the right. The distance Force 1 travels gives work of F1d1, and the distance Force 2 is pushed back gives work F2d2, and net work on the system is F1d1...
43. ### Using Bernoulli's Equation to find Power Requirement

Homework Statement Calculate head required for the pump and then its power requirement assuming 70% efficiency. The lower storage vessel is vented to atmosphere (assume 1 bar pressure) . I have the following given information: Pipe Area = 0.00636m^3. Flow(Q)= 0.01m^3/s Average Velocity =...
44. M

### How to show Bernoulli's equation applies on same streamline?

When deriving Bernoulli's equation from Navier Stokes, how do we know it is only valid along a streamline? At the very end of my derivation, assuming Newtonian, incompressible, inviscid, irrotational flow I have ##\nabla(\partial_t \phi + |\vec{u}|^2/2+p/\rho + g z) = \vec{0} \implies \partial_t...
45. ### 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...
46. ### Why is Bernoulli's Equation Isentropic

I have trouble understanding why we classify an inviscid adiabatic incompressible flow along a streamline as isentropic I understand this from a Thermodynamic definition/explanation $$dS = dQ/T$$ Adiabatic Invsicid $$dQ =0= dS$$ So no heat added or lost no change in entropy I'm fine with that...
47. ### Bernoulli's Princple vs Flow Equation (deltaP=QR)

First off, I'm a pathology resident, so it's been a long time since I've done real physics. But I really like physics and I try, whenever possible, to at least develop a basic understanding of the physics underlying physiology. With that as prelude, this question was inspired by blood flow but I...
48. ### Split Pipe Flow: Multiple Inlets and Outlets (Bernoulli's)

http://tinypic.com/view.php?pic=mhvarc&s=9#.WD__u_mLTIU Hey guys, So, I've got this problem, attached. I've used Bernoulli's to produce P1 + (1/2)p(u1)^2 +P2 + (1/2)p(u2)^2 = P3+ (1/2)p(u3)^2 +P4 + (1/2)p(u4)^2 +P5 + (1/2)p(u5)^2, Plugging in the values you get 82500 + P2 + 500(u2)^2 = P3 +...
49. ### Bernoulli's law in a network of a tube and a reservoir

Homework Statement I am looking at the following system: It shows a pore/tube (B) which is attached to a reservoir A. The fluid in reservoir A has a non-zero velocity in the horizontal direction, but I assume that the tube B is so long that the velocity there is unaffected and still zero...
50. ### Bernoulli's Eq: P1=P2 & Torricelli's Eq

When using Bernoulli's equation to describe fluid that is coming out from a spigot, why is it that P1 = P2 are the same? This cancellation will eventually lead to the Torricelli's equation.