What is Bernoulli: Definition and 343 Discussions

Jacob Bernoulli (also known as James or Jacques; 6 January 1655 [O.S. 27 December 1654] – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy. He is known for his numerous contributions to calculus, and along with his brother Johann, was one of the founders of the calculus of variations. He also discovered the fundamental mathematical constant e. However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work Ars Conjectandi.

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  1. Grey Area

    Bernoulli effect in multiple channels

    Hi al;l, it's Mr. ALKIADT again (A Little Knowledge Is A Dangerous Thing)...in this case, my knowledge of Bernoulli effect. I know that when a fluid passes through a restriction, the flow rate speeds up to maintain the flow rate of the wider cross sectional area behind it...so if you've got one...
  2. JTC

    Bernoulli to explain Magnus Effect

    Hi I have been reading some internet articles that state the Bernoulli equation does NOT explain the Magnus Effect. The articles state that the effect is due to circulation (Bernoulli requires inviscid flows) Could someone explain the cause of the Magnus effect without reference Bernoulli's...
  3. A

    I How Does a Pressurized Tank Empty Over Time Through a Hole?

    I having difficulty wrapping my head around a concept that I wish to solve. I have a 10L tank of compressed air at 100psi. When an outlet hole of cross-sectional area of 0.115 in^2 is opened, I wish to develop a curve of pressure vs. time from t=0 until pressure drops to atmospheric. Many things...
  4. A

    Different answers from equation of continuity and Bernoulli

    Hi there, So I was doing the dishes this morning using a sink wand hat can toggle between different flow speeds. The way that I've always thought of this working is using the equation of continuity: Volume flow rate: = Area*velocity Pressing a button on the wand decreases the cross-sectional...
  5. sturle

    How does a vacuum ejector using air work?

    Hello I`m working on a vacuum project, and I am trying to understand how the vacuum ejector I am using works. I understant the basic principle of how it works, but can anybody here try to explain the concept in detail, taking into consideration that I am using air? Most of the stuff i find...
  6. J

    Filling and emptying a barrel -- Bernoulli

    << Mentor Note -- thread moved from the schoolwork forums to ME for better views >> 1. Homework Statement Not really homework as this is for work. We are washing a cylindrical container (15.5 cm) with only one (1.8" dia) hole at the bottom the rest is sealed. Our machine sticks a .5" pipe with...
  7. Zahid Iftikhar

    Problem related to the Bernoulli Equation

    Homework Statement What gauge pressure is requried for water in a water supply line to reach a vertical height of 15m? Homework Equations Bernoulli Equation The Attempt at a Solution I have tried this numerical by taking velocity at ground level to be equal to velocity at top i.e. 15m height...
  8. melo

    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...
  9. Pushoam

    Derivation of Bernoulli Binomial distribution

    Homework Statement Derive the bernoulli binomial distribution.Homework EquationsThe Attempt at a Solution Each bernoulii trial could have only two possible outcomes . Let’s name one outcome as success and another outcome as failure. Let’s denote the probability of getting success and failure in...
  10. M

    Fluids Bernoulli and a pressure field

    I have a text that writes a pressure balance for a cylindrical shape of fluid, where the linearized Bernoulli gives the pressure field ##p = p_0+\rho\partial_t \phi : \vec{v} = -\nabla \phi## where ##\vec{v}## is the velocity vector. ##p_0## is the static pressure required to maintain the...
  11. R

    Follow-up Question to: The Concept of Pressure in Bernoulli’

    I have been looking all over the net for answers for the unintuitive relationship between pressure and velocity in Bernoulli's equation and this thread (https://www.physicsforums.com/threads/the-concept-of-pressure-in-bernoullis-principle.585231/) answered most of my questions. I have one last...
  12. R

    Sign on velocity term in Bernoulli Equation

    Homework Statement This was a problem on my fluids final and I'm trying to figure out if my rationale was correct here. The problem was an open air tank filled with water and at the bottom was a pipe pointing straight down. You had to find the exit velocity at the bottom of the pipe and account...
  13. D

    A An intuitive meaning of Bernoulli numbers

    Recently, I was intrigued by the summations of finite powers and therefore by the formula which generalizes the summations. "Faulhaber's formula". However, I didn't find an intuitive simple meaning of "bernoulli numbers", only meaning by their applications, which, of course, I can't understand...
  14. U

    Bernoulli equation derivation with added mechanical work

    I´m able to derive Bernoulli equation from the force bilance of the flowing element (particle): dm\cdot \left (\frac{D \vec{v}}{D \tau } \right )_{flowing particle}=\vec{dF}_{g}+\vec{dF}_{p} where dFg is the gravitational force acting on the particle, dFp is the pressure force acting on the...
  15. C

    What is a good film that has examples of the Bernoulli Principle

    We have to find a movie that has 3 good examples and 3 bad examples of this principle. We were thinking about doing Finding Nemo however we can't think of 3 bad ones and we are worried that our physics teacher might reject it since it is not a "serious" movie. Any ideas?
  16. Z

    Using Snell's Law for Brachistochrone Project

    Hi all, I'm after a little guidance for I do not know what is going wrong. I understand that for Johann Bernoulli's proof of the brachistochrone problem he used refraction of light and Fermat's principle of least time. I have decided to do a project on the subject, in which I am dividing up a...
  17. G

    Calculating Flow from Tank to Vessel w/ Power

    I am trying to calculate the flow in a system from an underground tank up through a pump into a vessel. But cannot find or derive a formula that yields a good result, I don't think I can use the same head calculations as Velocity will have changed. 1. Homework Statement ρ = 1000 kg m–3 μ =...
  18. G

    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 =...
  19. S

    Bernoulli Equation and its application to turbines and pumps

    Hi, I have never found a satisfactory explanation for why the Bernoulli equation is not valid when the streamline passes through a turbine, pump or another work transferring device. I have read many books that simply state this limitation without providing a convincing reason. Bernoulli...
  20. goatz4real

    Find velocity of air using Bernoulli principle

    Homework Statement A horizontal stream of air is blown just above the open end of the hares apparatus with an initial speed "V". The density of air is 1.2 kgm-3.Then the water column rises to 6 cm in the respective limb.Density of water is 103 kgm-3 Using Bernoulli`s principle find "V"...
  21. 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...
  22. Z

    Statistics Bernoulli single-server queuing process

    Homework Statement [/B]Suppose your office telephone has two lines, allowing you to talk with someone and have at most one other person on hold. You receive 10 calls per hour and a conversation takes 2 minutes, on average. Use a Bernoulli single-server queuing process with limited capacity and...
  23. hdp12

    Fluid Mechanics: Bernoulli & Energy Equations Problem- Help?

    Hello there. I took a test yesterday in my thermal fluids 1 class and I was hoping somebody could confirm or critique my answer. (Don't worry, I asked the professor first if I could take the picture) The problem is: Water is pumped from a lake to a pool through a 0.05 m diameter pipe. System...
  24. F

    Centrifugal Pump: Water Pressure at 50m & 4 Bar Gauge

    I have a centrifugal pump 50 m above a vessel, I’m pumping water in at 4 bar gauge into this vessel. I then close a valve to cease pumping ensuring no air enters the system.My question is, if I now open that same valve to atmospheric air this time, will the water exit from the pipe through the...
  25. T

    Is the Bernoulli Equation enough to determine pump selection?

    Here is an illustration of something that came into my head: http://imgur.com/a/V9V8S (also attached to question) If we do a energy balance (in terms of head) between point 1 and point 2 (ignoring friction for now, it's not really important): $$\frac{P_1}{\rho g} + \frac{v^2_1}{2g} + z_1 +...
  26. Euler2718

    (Ordinary) Differential Equation Trouble

    Homework Statement Find the solution of the differential equation by using appropriate method: t^{2}y^{\prime} + 2ty - y^{3} = 0 Homework Equations I'm thinking substitution method of a Bernoulli equation: v = y^{1-n} The Attempt at a Solution [/B] t^{2}y^{\prime} + 2ty - y^{3} = 0...
  27. M

    The Bernoulli principle from the perspective of statistical mechanics

    Hi community, I have a question about the Bernoulli principle. From statistical mechanics the pressure in the ideal gas is independent of velocity. But in the case of the flow of an ideal gas in a channel, the pressure depends on the velocity. Where can I clarify this misunderstanding...
  28. 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...
  29. X

    Bernoulli Equation and Velocities

    Homework Statement A cubic wine box of dimensional length ##h## has a small tap at an angle at the bottom. When the box is full and is lying on a horizontal plane with the tap open, the wine comes out with a speed ##v_0##. i) What is the speed of the wine if the box is half empty? (Neglect...
  30. Zahid Iftikhar

    How to solve using Bernoulli equation

    Homework Statement What gauge pressure is required by city mains for a stream from a fire hose connected to the mains to reach a vertical height of 15m? Homework Equations Bernoulli Equation: The Attempt at a Solution
  31. Zahid Iftikhar

    Bernoulli Equation and Leakage in a Pipe

    Hi boneh3ad Your discussion on Bernoulli Equation was very impressive and helped me a lot to understand this rather complicated equation. I have a question which puzzles me a lot when I want to solve it using Bernoulli equation. Here is the statement. " If there is some fluid flowing thru a...
  32. Z

    Bernoulli vs Newton - air flow characteristics

    One thing that has always puzzled me is the fact that in a venturi, air accelerates as it approaches the narrow part of the structure. there are those that argue with the fact that pressure has to raise first , because as we all know, acceleration has to be caused by an increased force (...
  33. FQVBSina

    Pressure and flow speed relationship in wind tunnel

    I need 250 m/s of airflow speed in a wind tunnel. I can assume for this purpose, the test section of the wind tunnel has uniform flow. However, the wind tunnel can only generate a flow rate of 100 m/s but the pressure can be increased. I am drawing a blank on how could a generic boundary layer...
  34. M

    Bernoulli Equation and Navier-Stokes

    Hi PF! I was reading about Bernoulli's equation for steady, inviscid, incompressible flow. Now it's my understanding this equation is derived from the Navier-Stokes (momentum balance); then these two equations are identical regarding information offered. However, while thinking about...
  35. A

    Pressure at the closed end of a pipe with a leak?

    Suppose I have an air pipe that is used for "grasping" other objects using negative pressure. When an object is grasped, assume it is a perfect seal and that end of the pipe is closed. On the other end of the pipe is the pressure source creating the vacuum. Somewhere in the middle is a short...
  36. G

    When will the house be flooded?

    Homework Statement [/B] A simplified schematic of the rain drainage system for a barn is shown in the figure. Rain falling on the slanted roof runs off into gutters around the roof edge; it then drains through several downspouts (only one is shown) into a main drainage pipe M below the...
  37. L

    Probability and Bernoulli trials

    Homework Statement A box contains m white and n black balls. Suppose k balls are drawn. Find the probability of drawing at least one white ball. Homework Equations Probability of one success = P({1 successful trial}) = n * p * qn-1 p = probability where q = 1-p Fundamental theorem of...
  38. W

    Bernoulli equation exercise from Fanning and Moody

    Homework Statement I would really appreciate it if you could give me a hand with this exercise, not sure on what I've done. Data: Moody: L=55*10-3m D=10-1m k=0.0002m Homework Equations ##Re=\frac{D*u*ρ} {μ}## ##Re=\frac{4*m} {pi*D*μ}## Relative roughness ##ξ=\frac k D## where k=rougness...
  39. J

    Diameter of hole vs time to submerge

    Hey everyone, I'm new to physics forums and I would really like some help with my physics report. For my high school physics topic I have chosen an experiment where holes with differing diameters are drilled into the centre of the bottom of PVC pipe caps and the time taken for the each cap to...
  40. W

    Bernoulli equation with losses dilemma

    Homework Statement Hello,Could you please lend me a hand with this problem?I would really appreciate it. Question:[/B] Their Answer: KL=2*0.75(2 elbows) D=5*10^-2 m ;f=0.001(fanning friction factor) Assumptions I made: Point 1 which is at the top of the liquid in the tank: h1=23 m...
  41. Grandma Susan

    Ping-pong balls, Bernoulli, and water

    So I saw the post with the Bernoulli math, but playing with my grandsons in the leisure pool we have observed a ping pong ball released from about 12 inches below clear the surface of the water by an unmeasured inch and a half. And when the twelve year old swims to the bottom of the four foot...
  42. S

    Pump used to halve the time taken by fluid to flow out

    Homework Statement The tank in picture has section ##S_1## and it's linked with a tube of section ##S_2=\frac{1}{\sqrt{17}} S_1##. The tank is filled at an height ##h## and this level is kept constant by a sink ##R##, in such way that the exiting volumetric flow rate is ##Q=0.3 m^3/s## and...
  43. S

    Use of Bernoulli equation for pumps

    I have a doubt on the use of Bernoulli equation for pumps. Consider the situation in the picture. I marked different points: ##1## on the surface of first tank, ##2## in the exit from first tank, ##3## just before the pump, ##4## just after the pump and ##5## entering the second tank. Now...
  44. S

    Bernoulli equation related to minimum pressure inside train

    Homework Statement The train is traveling in a gallery at ##v=70 km/h##. Outside air is not moving and pressure is ##p_0=101325 Pa## and temperature ##T=283 K ##. The area of the face of the train is ##A=9 m^2##. Determine the minimum area of the section of the gallery such that the pressure...
  45. J

    Pressure required for air flow through nozzle

    I need to know the maximum compression speed that can be applied to a rectangular bladder which has a open air port that will avoid rupturing the bladder. The bladder is 40" wide, 100" long, and 10" tall. The compression equipment is a large metal panel that is larger than the surface area of...
  46. A

    Pressure in tank pipe -- Bernoulli Equations

    Homework Statement [/B] A pressurized cylindrical tank, 5m in diameter, contains water which emerges from the pipe at point C with a velocity of 25 m/s. Point A is 10m above point B and point C is 3m above point B. The area of the pipe at point B is 0.07 m2 and the pipe narrows to an area of...
  47. lucytranxx

    MHB Bernoulli Trials and Probability

    Let X be a random variable defined as the sum of 5 independent Bernoulli trials in which the probability of each Bernoulli taking the value 1 is given by r. Suppose that prior to the 5 Bernoulli trials, r is chosen to take one of three possible values with the following probabilities: R=r...
  48. J

    Is there a difference between redirection and converging flow in fluid dynamics?

    Fluid or sleeve bearings use an off center shaft location to generate a hydrodynamic wedge in direction of rotation. This converging fluid causes higher pressure and can support a load applied normal to shaft axis during rotation. This action appears to be similar to the hydrodynamic support of...
  49. S

    Solve Bernoulli Problem: Velocity of Water Outlet

    Homework Statement " A water filled verticle pipe of cross section area 25 cm^2 is open at the top. If an outlet of cross section area 15 cm^2 is made on it's side at a depth of 10 m from the level of the water at the top, then the velocity of the water exiting from the outlet is? Homework...
  50. L

    Is There an Error in My Bernoulli and Waterflow Homework Solution?

    Homework Statement http://imgur.com/rhaQabj radius of watertank = 5.5cm Homework Equations https://en.wikipedia.org/wiki/Bernoulli's_principle https://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation The Attempt at a Solution I've tried to put up to equations on the form...
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