What is Bernouli: Definition and 19 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. A

    Bernoulli equation and parallel pipe branch

    Hello! I have a question regarding the application of the bernoulli equation and calculation of the flow through a parallel pipe branch. It's more the basic understanding how the flow will establish. You can find a sketch attached to follow my explanation. Let's assume I have a pipe with...
  2. M

    B Does the Bernouli Effect Work On Cars?

    Hi Geniuses... I joined this group because I have a question I can't answer myself. This is about cars. We're all familiar with classic cars having a grill up front and a space right after it, and then usually a radiator to cool the water/coolant in the engine. The discussion we're having in a...
  3. N

    How Do You Calculate the Flow Rate of Oxygen in a Pressurized System?

    I am trying to calculate the flow rate of O2 from a known volume 25 in^3. The cylinder will fill up to a maximum pressure of 140 psi in 11.26 seconds. Any help to determine the flow rate will be appreciated. Do I use Bernoulli equation to find the flow rate?
  4. person123

    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:$$p_1=p_2+h\rho_{air} g$$...
  5. A

    Can I apply Bernoulli's equation to this situation?

    Can Bernoulli's equation be applied between points 1 and 2, ignoring the another tank ?
  6. M

    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...
  7. Emanuel Silva

    Pressure generated by a column of air

    Applying Bernoulli, Does the term ρ*g*h matters ? I am trying to select a fan
  8. Behrouz

    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...
  9. C

    Calculating Pressure from Air Displacement in Gasoline Tank

    I am struggling with what seemed to be a simple problem and any help would be greatly appreciated. I have to determine the amount of pressure created when air is displaced buy gasoline flowing into a tank. The gas enters the tank at 10gpm. The entrance has a diameter of 1.5" and the vent has a...
  10. R

    Calculating pressure within a system at a specific location?

    Homework Statement Solution: Homework Equations dp/dz = -ρh Pressure varies linearly with the depth. The Attempt at a Solution Firstly, I have calculated the pressure at point B. PB = PA - (0.3m)*(1000kg/m^3)*(9.81m/s^2) PB = 88057 Pa Calculating the pressure at point C. However, my...
  11. Z

    Statistics Bernoulli single-server queuing process with ATMS

    Homework Statement Customers arrive at an ATM at a rate of 12 per hour and spend 2 minutes using it, on average. Model this system using a Bernoulli single-server queuing process with 1-minute frames. a. Compute the transition probability matrix for the system. b. If the ATM is idle now, find...
  12. jerry wickey

    How can Bernoulli's principle help explain pressure changes in fluid dynamics?

    Can someone smarter than I, please express p1 and p2 in terms of f, or v and r? The pump pushes out water at f rate which creates velocity v in the bigger pipe. When the water comes to the restriction velocity increases while flow rate is conserved. Bernouli tells us that the change in...
  13. S

    How does the siphon method work and why does the pipe width matter?

    1. I found this diagram on book but there weren't any description.can someone tell me, what its trying to tell specially by those two red lines meeting the ground at the same place...? 2.this is a diagram for siphon method of removing water. I have read somewhere that the siphon stops if the...
  14. S

    Getting Qideal from Bernouli and continuity

    So, I found a paper relating to a lab report that I've been working on that says that I can get Qideal=(pi*d^2)/4) √((2ΔP/(ρ(1-D/D')^4 )) From Bernouli which my book has as: P1/ρ1+1/2v1^2+gh1=P2/ρ2+(1/2)v2^2+gh2 and Continuity which my book has as: ρ1A1V1 = ρ2A2V2 I'm able to get kind of in...
  15. D

    How can you find height in bernouli equation?

    I am having a hard time figuring out the step in the equation. For an example, I was given a problem that water flows from the bottom at a velocity of 5.0m/s up to a bucket at (unknown) height. The hose radius is the same so it is not given. Known: V_1=5.0m/s Density p= 1000kg/m^3 Gravity=...
  16. B

    Bernouli equation with pump work input

    Homework Statement Hey. I've posted a few questions around here lately, and really appreciate any help! thanks Right, attached is an image showing a simple pump system. pump inlet gauge pressure = Pi = -34.2 kPa nozzle diameter = 5cm rho = 1000kg/m3 Calculate the flow rate 2. The...
  17. N

    Solving Bernouli Equation with x $\frac{dy}{dx}+y=\frac{1}{y^2}$

    Recently I've been going back in my differential equation book to review some differential equation solving skills, in particular bernouli, ricatti's, and clairaut's equations; simple things enough. However when doing the exercises I have kept running into a "problem" with one question. x...
  18. K

    What is the Gauge Pressure Just Downstream of a Fan in a Duct System?

    Homework Statement A duct system that exhausts air of density 1.2kg/m3 from a building out into the atmosphere is shown in fig. A2 (attachment). The air flow is driven by a fan across which is a monometer that reads 2 cm of water. The cross sectional areas of the upstream and downstream...
  19. M

    Coanda or Bernouli, which describes lift?

    When firing my pulse jet I tried various approaches at increasing its' performance without significantly increasing its' weight. When (while holding a piece of larger diameter pipe with channel locks) introducing a larger diameter than the jet diameter pipe into and partially allowing the...