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.
Homework Statement
A wide tank contains a non-viscous liquid. The surface of the liquid is at a height 0.5 m above a hole situated at the bottom of the tank. Assuming streamline flow, calculate the velocity of the liquid emerging from the hole.
Homework Equations
P + 1/2 Dv^2 + Dgh =...
In my Fluid Mechanics textbook they use the Euler equation to derive Bernoulli's principle for incompressible fluids with gravity. In my earlier introduction to mechanics textbook they used energy conservation. Is there a reason for using the Euler equation or is it just to show more ways to...
Situation: a car moving quickly down the road with a window open.
Car reference frame: the air outside is moving, thus has lower pressure, thus the air inside the car will be sucked out the window.
World reference frame: the air in the car is moving, thus has lower pressure, thus the...
It has always been explained to me that balls curve because a thin layer of fluid adheres to its surface as a boundary layer. This boundary layer retards the flow on one side of the ball and speeds it on the other. And then Bernoulli's principle is applied to make the pressure difference happen...
Homework Statement
This isn't a homework question, but more like a theory question that my teacher and I are having trouble figuring out. We're trying to figure out why this ball, more or less, stays still in a high speed stream of air:
http://laserpablo.com/videos/videofiles/Bernoulli.htm...
water flows through a horizontal pipe at a velocity of 50 ft per sec. Owing to the pipe gradually expanding to a larger size, the velocity decreases to 35 ft per sec. what is the difference between the pressures at two points, one in each size of pipe?
Homework Statement
air is flowing horizontally at a speed of 100 mph through a duct 4 square feet in cross section. the duct gradually narrows down to a throat section. if a U-tube shows a difference in pressure between the throat and main sections of 7 inch of water, what is the cross...
Homework Statement
You need to siphon water from a clogged sink. The sink has an area of 0.496 m2 and is filled to a height of 4.0 cm. Your siphon tube rises 50 cm above the bottom of the sink and then descends h = 93 cm to a pail as shown above. The siphon tube has a diameter of 1.57 cm.
a...
Does Bernoulli's Principle affect a non-flowing fluid in a moving container?
As in, if I am in an air-sealed airplane at rest, and then the plane accelerates on the ground (but does not fly), does the gas pressure inside the plane change because the fluid (air inside the cabin) has a velocity...
Homework Statement
A can has two vertically aligned holes in it. The height of the fluid is h, and the heights of the two holes are h1 and h2.
a) Show that the two streams of water will hit the ground at the same spot when h = h1 +h2.
b) If you had such a can, how would you keep h constant...
Homework Statement
Examine the schematic of the tower. Water flows in at the top to balance the water flowing out through the holes, so the height of the water in the tower stays fixed.
Take state 1 at the top of the water in the tower and state 2 in the water just as it flows out of the...
I have in my notes that as speed of a fluid increases, density decreases.
This doesn't make sense to me. When a fluid passes through a narrower area, doesn't that mean that its density is increasing because it is now packed more tightly together? If this is the case, shouldn't the rule be that...
Do anyone know about any website were the Bernoulli equation is developed from the Newton Second law and without the assumption of steady state and incompressible fluid?
With differential calculus, please.
My textbook just give out the equations for unsteady state and incompressible, but I...
"Wing Commander Physics" and Bernoulli's Principle?
Hey guys, I was wondering if you could lend me a hand on how to deal with a particular situation I have. I have an assignment regarding bad physics in movies, and the movie I chose is really an easy one to bash: "Wing Commander" (1999). If...
According to bernoullli, assuming ideal flow, if you increase the area of a tube... vessel in this case, pressure increases as well
however, high blood pressure is caused by constriction of arteries... so is blood flow just not ideal then?
Homework Statement
The water supply of a building is fed through a main entrance pipe 6.0 cm in diameter. A 2.0 cm diameter faucet tap positioned 2.0 m above the main pipe fills a 25 liter container in 30 s.
(a) What is the speed at which the water leaves the faucet.
(b) What is the gauge...
There's a simple explanation that wasn't covered in the last thread about this.
Start off with an ideal incompressable fluid with no viscosity in a pipe. The flow rate in the pipe is fixed. The amount of mass per unit time moving past any cross section in the pipe is constant, otherwise mass...
Liquid flows through a 4cm diameter at 1m/s. There is 2cm diameter restriction i n the line. Find fluid velocity in restriction.
p_1+ \rho\cdot g \cdot y_1 + \frac{1}{2}\rho \cdot(v_1)^2 = p_2+ \rho \cdot g\cdot y_2 + \frac{1}{2}\cdot \rho\cdot(v_2)^2
I know I have to use Bernoulli's...
Hello,
I am a student taking Conceptual Physics in College. We have just completed going over Bernoulli's Principle of lift. Please bear with me on this as it will most likely seem elementary to most of you. Below are several claims that I've heard and that my logical reasoning tells me to be...
This isn’t really homework, but it might as well be with all the calculations involved.
I am trying to figure out the difference in pressures inside a pipe carrying a fluid when the pipe goes from a ¼” diameter to 1/8” diameter when the constant flow rate is 9 Liter per minute. I got an...
I have this problem:
Water flowing in a horizontal pipe is at a pressure of 1.5 105 Pa at a point where its cross-sectional area is 1.50 m2. When the pipe narrows to 0.400 m2, the pressure drops to 1.16 105 Pa.
(a) Find the water's speed in the wider pipe
(b) Find the water's speed in the...
This isn't really a homework problem, but my physics teacher was going over a test review and he made up some numbers on the spot for a problem involving Bernoulli's equation and a building. The specifics were,
A water pipeline with the water under a pressure of 5 atm is being pumped into a...
I have two problems that I can not figure out. Thanks for your help.
Problem #1: A horizontal pipe 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter. If the pressure of the water in the larger pipe is 8.00 x 10^4 Pa and the pressure in the smaller pipe is 6.00 x 10^4...
According to the popular interpretation of 'Bernoulli's Principle', moving air should always be associated with a lower static gas pressure than resting air, but clearly this can not be correct:
If one considers a pipe with air resting in it, then the static pressure on the inside of the wall...
Hey,
I have this experiment i have to do and i have to undnerstand Bernoulli's Principle and it is just not getting to me. I don't understand how the pressure will decrease as the speed increases, or how the pressure will increase if the speed decreases.
Like in the textbook, it says...
A pump and its horizontal intake pipe are located 12 m beneath the surface of a reservoir. The speed of te water in the intake pipe causes the pressure there to decrease, in accord with Bernoulli's principle. Assuming nonviscous flow, what is the maximum speed with which water can flow through...
I need some help with some review questions for the test. I am trying to check the answers I get with the ones the teacher provided, bit I'm getting stuck. Knowing which equations to use etc... would be really helpful.
What is the maximum weight an aircraft with a wing area of x m^2 can...
Hi! This is the first question on my homework, so it's suppost to be the easiest, but I'm not sure how to tackle it. It's a Bernoulli's principle problem. Here it is:
A horizontal pipe 11.6 cm in diameter has a smooth reduction to a pipe 4.72 cm in diameter. If the pressure of the water...
Hello everyone, I am having some difficulty with the following problem about bernoullis principle:
THe problem says that the level of liquid h = y_2 - y_1 drops at a rate
\frac{dh}{dt} = -\sqrt\frac{2gh{A_1}^2}{{A_2}^2-{A_1}^2}
where A_1 and A_2 are the areas of the opening (water...