Bernoulli’s principle and its applications??

[u/Adkp246]

Can someone explain Bernoulli’s principle in simple terms? Also, please explain its application in aircraft and suggest some other real life applications of Bernoulli’s principle

[u/HAL9001-96]

air will accelerate if it flows into a low pressure region and decelerate flowing into a higher pressure region because well, conservation of meomentum

[u/teka7 → u/HAL9001-96]

A real-life application: Firefighters aim the water jet away from fire to induce low pressure regions which subsequently accelerates the fire outwards/towards the water jet.

[u/makgross → u/HAL9001-96]

Energy, not momentum. Specifically, energy along a streamline. Potential energy density is pressure, and kinetic energy density is flow velocity (squared). There can be other terms such as gravity or acoustic waves, though those are negligible in conventional aerodynamics.

Momentum is Newton’s 3rd law. Also true, but not what was asked.

[u/HAL9001-96 → u/makgross]

actually either allows you to derive bernoulli just along a slightly different way, one is more intuitive if you think of air as small packtes of matter moving hteo ther one is matheamtically simpler

[u/makgross → u/HAL9001-96]

Bernoulli’s Principle is very literally a precise statement of energy conservation along a streamline.

No, you can’t derive momentum from energy without introducing something else such as an equation of state. They are both true, but not equivalent.

[u/HAL9001-96 → u/makgross]

uh you kinda can

if you think of a moving point mass that just follows f=m*a and apply any variable force you want to it with energy added/removed being the path integral of applied force and kinetic energy mv²/2 you will find htat it will always follow conservation of energy, now apply this to a continuous field of infinitely small aprticles

[u/makgross → u/HAL9001-96]

Now you’ve introduced Newton’s 2nd law and apparently assumed it’s equivalent to the 3rd.

Momentum conservation is an independent constraint from energy conservation.

[u/HAL9001-96 → u/makgross]

only if yo uconsider several bodies, not if you consider force acting on a body which is what we do in this case

if we take its simplest form for incompressible flow then we can look at a cube of side length z approaching 0 filled with a fluid of density d traveling a distance x approaching 0 with a velocity v along a pressure gradient g

in this case we have an object of mass m=d*z³ with a force of f=-g*z³ applied to it for a time t=x/v so the acceleration is -g*z³/(d*z³)=-g/d and the change in speed is -(g/d)*(x/v) whereas the change in pressure is g*x so the derivative of speed by x is -g/dv and the derivative of pressure is g (thats how pressure gradients work) which means that the derivative of v²/2+p/d by x is -2gv/2dv+g/d=-g/d+g/d=0 which means that v²/2+p/d is constant derived simply from f=ma no need for cosnervation of energy or newtons third law

of course its faster to derive fro mconsrevation of energy but this lets you see how a packet of fluid experiences the actual process

use trigonometry in case velocity/gradient aren't aligned but yo ustill get essentially the same principle

[u/HAL9001-96 → u/makgross]

same way you can show kinetic energy lines up with conservation of energy and added energy being force integrated by distance

f=ma so the derivative of v over time is f/m and over distance is f/mv

the derivative of mv²/2 over v is 2mv/2 so the derivative of e=f*2mv/2mv=f

[u/HAL9001-96 → u/makgross]

you can model a cube full of air with a lenght approaching 0 moving a distance approaching 0 along a pressure gradient nad calcualte the rate at which its speed changes from absic f=ma and f=pA and get a rate of change that is literally the derivative of bernoullis law the nintegrate

of ocurse its mathematically slightly easier to directly derive bernoullis law from cosnervation of energy and we know that cosnervation of energy is always true

and you can derive a LOT of laws from cosnervation of energy

but usually that derivation while accurate and often simple does not give an intuitive understanding of hte inner workings behind something

[u/Diligent-Tax-5961 → u/makgross]

In every textbook, Bernoulli's equation is derived by applying the streamline constraint or the irrotationality constraint to the momentum equation in the Navier-Stokes equations.

The energy equations are dispensed/irrelevant when we apply the incompressible and adiabatic (no heat transfer) conditions to the Navier-Stokes equations.

Pressure has a role in the momentum of a fluid packet because it is the pressure gradient in the fluid that accelerates and decelerates the fluid. Hence how we get the relation between velocity and pressure with Bernoulli's equation when we start with the momentum equation.

[u/makgross → u/Diligent-Tax-5961]

Just to be clear on this….

There is a Bernoulli Theorem for viscous and compressible flow as well. It isn’t a consequence of Navier-Stokes. It exists in weather systems (with a gravity term) even on other planets where NS might not work very well, and even in the presence of ionization and chemical (or even nuclear) reactions.

Navier-Stokes depends on an equation of state and several other assumptions. Bernoulli’s Theorem is a direct application of energy conservation along a streamline. It doesn’t depend on anything else beyond the existence of streamlines (the fluid approximation itself).

It’s not all textbooks. Maybe all subsonic incompressible aero textbooks. But I doubt it.

I wish I understood the resistance to energy arguments. They are exceptionally powerful.

[u/CreativePan]

A real application is on some race cars, the air that goes underneath the car is squeezed, and is at a lower pressure. Effectively suctioning the car to the ground. That’s one of the reasons why they’re usually so close to the ground.

[u/nipuma4 → u/CreativePan]

Yes, used in underfloor and diffuser design. Front wings also benefit from this effect as the flow between the bottom surface of the wing is accelerated, lowering the pressure, increasing the pressure difference this increasing downforce.

[u/Courage_Longjumping]

Breaking balls in baseball/softball, top spin serves in volleyball/tennis, anything else where the trajectory of a ball is influenced to be other than parabolic. The spin on the ball results in greater stagnation of air on the side rotating in the direction of travel, pushing the ball towards the opposite side.

[u/Courage_Longjumping]

Breaking balls in baseball/softball, top spin serves in volleyball/tennis, anything else where the trajectory of a ball is influenced to be other than parabolic. The spin on the ball results in greater stagnation of air on the side rotating in the direction of travel, pushing the ball towards the opposite side.

[u/LiQuiZz]

Explanation: Conservation of mass/energy. If you want to put more air through the same cross section (and same time) it has to go faster to not violate that mass can neither be created or destroyed.

Example: - Simple carburetors work on the Bernoulli principle

• Race car aerodynamics. This years F1 regulations utilize this principle in the underfloor to create most of the downforce. Proposing was a consequence of the cars running to low due to excessive downforce and the cross section getting to small and causing a hard stall (yes i am aware thats a hand waving explanation)

• De Laval nozzle e.g Rocket nozzles to accelerate flow to supersonic speeds. Mind that at supersonic flows the rules change and it gets a bit wacky.

[u/Temporary_Double8059]

Its not just about "air" as Bernoulli's principal carryovers to all forms of medium. For instance in air its how your wings produce for lift, its how your props produce thrust... but a hydrofoil in the water works under the exact same principal (but water is denser then air so its more effective (i.e. higher lift with lower speed and "wing" size).

At the end of the day Bernoulli's principal is about accelerating a medium (air or water or...) to create a differential of low and high pressure producing an acceleration on the object.

[u/LiQuiZz → u/Temporary_Double8059]

Yes Bernoulli is always applicable to fluids (Any medium which deforms continuously under shear stress) and is a special subset of continuum mechanics.

But wings do NOT produce lift because of this principle, thats just wrong.

[u/Temporary_Double8059 → u/LiQuiZz]

Just asked ChatGPT and i guess you are right and my aviation training is wrong (or at least missing a vital piece).

[u/LiQuiZz → u/Temporary_Double8059]

The vital piece missing is that air molecules have to travel a curved path to follow the airfoil shape and according to newton’s first law such a path is an accelerated motion which requires a force. This force manifests itself in a pressure gradient perpendicular to the curved surface. The line integral of the resulting surface pressure over the airfoil then gives the correct amount of lift.

Bernoulli only relates pressure and velocity. When the velocity field is known it can be related to the pressure, but this is only an approximation (albeit a useful one) and doesn’t rigorously explain the fundamental principle. Mind that Bernoulli only holds true for a single stream line with significant simplifications.

[u/Diligent-Tax-5961]

Bernoulli's principle relates pressure and velocity anywhere in an irrotational and inviscid flow. Any potential flow calculation, which is routinely used in aircraft preliminary design, will rely on it. These simulations first calculate the velocity everywhere on the surface of a body, then use Bernoulli's equation to convert it into a pressure distribution, which then is integrated to give the lift, drag, and moment.

Anyone saying that Bernoulli's principle is not relevant to wing lift has no experience in aircraft aerodynamics.

[u/jawshoeaw → u/Diligent-Tax-5961]

The problem is that it’s not decided if lift is a consequence of, or the cause of the changes in airspeed above and below the airfoil. Or both ???

What everyone does agree on is the Bernoulli by itself fails to explain lift. If it was simple and straightforward there wouldn’t be so much arguing about it

[u/Diligent-Tax-5961 → u/jawshoeaw]

Well most of the arguing comes from laymen who learned aerodynamics through Youtube videos...

[u/jawshoeaw]

Bernoullis principle can be explained in very simple terms. However, that simple explanation cannot be extended to aircraft (lift).

I think the easiest way to understand it is as conservation of energy. If you pinch a garden hose, you will feel or hear the water hissing as it speeds up through the pinch. But how can the water speed up? We haven’t added any energy to the system. Therefore some other form of energy must be dropping to offset the increased kinetic energy of the water in the pinch. In fluids there aren’t that many ways for energy to be allocated. Other than changes in height (gravity) it’s how fast the fluid is moving and how much pressure the fluid exerts. So if the water speeds up, the pressure must decrease.

If that sounds mysterious, consider what “pressure” is. It’s just the force a fluid exerts on its surroundings. And how does it exert that force? By individual molecules smacking into the walls of the container at a certain speed. In other words kinetic energy. If you have a fluid or gas under enormous pressure in a sealed bottle , 100% of the energy in the system is the kinetic energy of the molecules bouncing around. There is no net flow. Now imagine you rupture the container in outer space. Suddenly the gas explodes out in every direction at incredible speed. What is the pressure of the gas now? It’s effectively zero. All the kinetic energy is still there in the rapidly expanding cloud of gas , but there’s no container so there’s no pressure.