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. D

    Bernoulli Equation and Newton Law

    Hello friends, I have a problem in Bernoulli equation and Newton Law. I'm going to calculate how much power is needed to lift up an object with weight W. I'm planning to put the object in a 10 inches diameter. How can I calculate the power needed by the motor to lift up the object? Does...
  2. C

    Bernoulli effect for spinning disks

    For a stationary disk, the air pressure on the platter is atmospheric pressure. For a disk spinning at 10,000 RPM, say 140 miles per hour for a 5.25 inch disk, I assume the Bernoulli effect would reduce the pressure, but because of the Ekman flow, the pressure would be more than the pressure...
  3. T

    Bernoulli Principle Problem

    Homework Statement Find the lift in Newtons due to the Bernoulli Principle on a wing of a plane of area 84.5 m^2 if the air passes over the top and the bottom surfaces at speeds of 347m/s and 289 m/s Homework Equations P1+(1/2)densityV^2 =P2+(1/2)densityV^2 The Attempt at a...
  4. O

    Questions on Bernoulli Equation: Pressure, Energy & More

    Hi, I have some questions about this equation. P + (1/2)mv^2 + mgh = constant. So obviously (1/2)mv^2 is the kinetic energy, and pgh is the potential energy. 1.) Is this equation basically a statement of conservation of energy? 2.) If yes, then how exactly is pressure, 'energy'? I...
  5. L

    Fluid Mechanics- Bernoulli Equation

    The Bernoulli Equation for non-uniform flows have a constant at the kinetic energy term which describes the velocity profile at that place. The problem is this, If a have water flowing through a pipe with a parabolic velocity profile and then the water exit the pipe at free jet and there is now...
  6. T

    Solve Bernoulli Equation x'=b(t)x+c(t)x^n when n<0

    How do I solve a Bernoulli equation of the form x' = b(t)x + c(t)x^n when n < 0?
  7. S

    Help with first order, Bernoulli ODE

    Help with first order, "Bernoulli" ODE We just covered: -First order linear ordinary differential equations -Bernoulli Equations -Simple substitutions. This problem was assigned. Its supposedly a Bernoulli equation with respect to y, but I can't figure it out...
  8. T

    River channel problem using Bernoulli and Continuity

    [SOLVED] River channel problem using Bernoulli and Continuity Homework Statement A river (100 m wide) flows through its rectangular channel at a depth of 2.560 m at a velocity of 2.050 m/s. What is the velocity of the discharge if the channel is narrowed to 90 m? Homework Equations...
  9. T

    Bernoulli and Continuity Question

    Bernoulli and Continuity Question! A river (100 m wide) flows through its rectangular channel at a depth of 2.560 m at a velocity of 2.050 m/s. What is the velocity of the discharge if the channel is narrowed to 90 m? Continuity equation: Q1 = 100m x 2.560 m x 2.050 m/s...
  10. M

    Solving Bernoulli Problems Homework: Pressure Differential Question

    Homework Statement A long horizontal hose of diameter 3.8 cm is connected to a faucet. At the other end, there is a nozzle of diameter 1.8 cm. Water squirts from the nozzle at velocity 38 m/sec. Assume that the water has no viscosity or other form of energy dissipation. a) What is the...
  11. Y

    Bernoulli Recursions: Formula & Solutions

    I don't know if this is appropriate or not, here or anywhere. However, I propose this thread be used to post recursive formula for the Bernoulli numbers. It saves a great deal of frustration. The first is simply, \sum_{k = 0}^{n-1} \binom{n}{k} B_{k} = 0
  12. B

    How to find Velocity V2 with bernoulli Equation?

    Water is fed via a 200m long, 125mm diameter pipe to a field. The take is 12m elevation. the friction factor is 0.008 and k factors add up to 3.3. Pressure is all atmospheric and V1 is 0. Homework Equations Bernoulli Equation with the addition of friction, elevation and k factors...
  13. R

    Solving Bernoulli Problem: Find Water Tank Height

    Hey guys, I've got a pressure problem that I've been stuck on for a while now and was just wondering if somebody could give me some guidance in solving it. The problem is as follows: "A water tank open to the atmosphere at the top has two small holes punched in its side, one above the other...
  14. M

    Bernoulli Continuity Water Jet Problem

    Homework Statement A disk with mass M=5.0 lbm is constrained horizontally but is allowed to freely move vertically. The disk is struck from below by a vertical jet of water the water jet has a velocity V=35ft/s and a diameter d=1 inch at the exit of the nozzle. (a) Derive the general expression...
  15. T

    Bernoulli, Poisson &amp; Normal Probability

    [SOLVED] Bernoulli, Poisson &amp; Normal Probability Homework Statement Every chocolate bar contains 100 squares, with 10% of the individual squares presenting a health hazard to people consuming them. (a) Using the Binomial, Poisson and Normal distributions, write down formulas for...
  16. A

    Bernoulli Application: Explaining How a Dime Blows Across a Table

    Homework Statement With a little effort we can blow across a dime on a table and make it land in a cup, but how can it be explained? I know that is because the bernoulli princle (qv^2)/2 +qgh + p = const Homework Equations but what happens with pressure during this action?
  17. C

    Understanding Bernoulli's Theory: Explained for Fluid Mechanics

    Hello, I am studying fluid mechanics and we have worked on Bernoullis theory a lot over the past couple of years. I am really struggling to grasp the concept of the theory and what it is about. Bernoulli states that in a system the pressure will always be constant (hence Pt = Ps + Pv + Ph) at...
  18. A

    How to calculate confidence limits in bernoulli trials with only one outcome.

    I have this problem that I have been trying to figure out all week and can't seem to get. I have a process that produces one of two outcomes "OK" (in some unknown porportion: p) or "NOT OK" (in porportion q = 1-p). Let's say I ran the process [x] times (like 20) in a row and it reported...
  19. G

    Bernoulli & static pressure

    A hydroelectric power station is supplied with water from a reservoir. A pipeline connects the reservoir to the turbine hall. The flow of water through the pipeline is controlled by a valve which is located 500 metres below the surface of the water in the reservoir. The lower end of the...
  20. S

    System curve and Bernoulli equation problem

    Homework Statement I have a pump pumping 50 gallons per minute of water from a tank at atmospheric pressure to another tank at atmospheric pressure. The main discharge pipe (internal diameter is 4.03 inches) is divided onto 5 smaller pipes (internal diameter is 1.05 inches). The pressure on...
  21. S

    How Do You Calculate the First Three Bernoulli Numbers?

    Homework Statement Let x/((e^x)-1)= 1 + B1x+B2((x^2)/2!) + B3((x^3)/3!)+… where Bn are called the Bernoulli numbers. Determine B1 , B2 and B3. Homework Equations I think this one: (1+x)^n = 1 + nx + ((n)(n-1)/2!)(x^2)+... The Attempt at a Solution i wrote it in this form...
  22. S

    Differential Equations - Bernoulli Problem

    Homework Statement Solve the equation y' = \frac{2xy}{x^2-y^2} Homework Equations The Bernoulli multiplier thing which I don't feel like typing out. The Attempt at a Solution I'm attempting to separate the equation so I can have y and dy on one side and x and dx on the other, but the...
  23. C

    How can I solve this Bernoulli Equation with a given initial condition?

    Homework Statement x^2y' + 2xy = 5y^3 Homework Equations Bernoulli Equation The Attempt at a Solution so... v=y^-2, y=v^(-1/2) y' = -1/2v'v^(-3/2) moving everything over... y'/y^3 + 2/(xy^2) = 5/x^2 and plugging everything in... -1/2v' + 2v/x = 5/x^2 v' - 4v/x = -10/x^2 v' -...
  24. S

    Can't Make Sense of Bernoulli Equation

    it...just...does...not...make...the...slightest...sense...to...me...:confused: Here it goes... y' + \frac{y}{x} = 3x^2y^2 This is a Bernoulli equation with P = \frac{1}{2}, Q = 3x^2, and n = 2. We first divide through by y^2, obtaining... \frac{1}{y^2} \frac{dy}{dx} + \frac{y^-^1}{x} =...
  25. quasar987

    Is P(\Omega) Equal to 1 in Bernoulli Trials?

    Consider a sequence of Bernoulli trials where we play until the rth success is attained. Denote \Omega the fundamental set. We define a function P on \Omega by saying say that an elementary event that is a k-tuple has a probability of occurence of q^{k-r}p^r because the trials are...
  26. C

    Bernoulli Differential Equations

    Solve the equation \frac{dy}{dx}-y = -xe^{-2x}y^{3} . So a Bernoulli differential equation is in the form \frac{dy}{dx} + P(x)y = Q(x)y^{n} . Isn't the above equation in this form already?I set u = y^{-2} and \frac{du}{dx} = -2y^{-3 . So -2y^{-3} + 2y^{-2} = 2xe^{-2x} . From here what do...
  27. Pengwuino

    Did I prove this Bernoulli equation correctly?

    Given a differential equation with the form: \frac{{dy}}{{dx}} + P(x)y = Q(x)y^n and using the substitution v = y^{1 - n} I attempted to prove that it transforms into \frac{{dv}}{{dx}} + (1 - n)P(x)v = (1 - n)Q(x) Here’s the proof, did I do it correctly? I got the write answer so I assume...
  28. W

    Having trouble using bernoulli eq.

    So, I'm tweaking my understanding of applying Bernoulli's equation, and I'm having a problem understanding the change in pressure and velocity when a fluid flows down a tube of constant diameter. The way i see it; either the pressure changes with height and the velocity stays the same, or the...
  29. K

    Standard deviation and Bernoulli distribution

    Let us assume that X has Bernoulli distribution, with P(X = 1) = p and P(X = 0) = q = 1 - p. Of course, E(X) = p and Var(X) = pq. Now, since pq < 1, standard deviation is bigger than variance. I have got the following question: Does this fact make standard deviations and theorems based on...
  30. M

    Bernoulli differential equation, i got the form down, where did i f it up? :-x

    Hello everyone! ITS ME! I'm having a good time with some Bernoulli differential equations, and yet it didn't work. Here is the directions: A Bernoulli differential equation is one of the form: http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/c4/3f85cf0e6820be855c6d2a21d051b71.png...
  31. B

    Bernoulli inequality proof

    Hi I'm doing a small induction proof for bernoullis inequailty: Proof: Given the inequality A(n) = (1+x) ^n \geq 1+nx r \geq -1, n \in \mathbb{N} Initial step: A(n=1) is true cause (1+x) \geq 1 + x is true. Induction step: A(n) is true is since n = 1 and r \geq -1 so 0 \geq 0...
  32. E

    Bernoulli formula for integrals

    let be the Bernoulli formula for calculating an integral in the form: \int{f(x)dx}=C+\sum_{n=1}^{\infty}(-1)^{n}x^{n}\frac{d^{n}f}{dx^{n}}\frac{1}{\Gamma(n)} my question is..could we calculate the integral from this series?..thanks.
  33. A

    Solve Bernoulli Equation: A Guide to Understanding

    can someone explain how to solve the bernoulli equation? I'm having a hard time understanding...
  34. A

    Solving Bernoulli Equation - Can't Get Correct Answer

    I cannot get the correct answer to this for some reason: t^2y'+2ty-y^3=0 I use the substitution v=y^{1-n}=y^{-2}\implies y=v^{-\frac{1}{2}} and come up with y'=-\frac{1}{2}v^{-\frac{3}{2}} and y^3=v^{-\frac{3}{2}}. -\frac{1}{2}t^2v^{-\frac{3}{2}}+2tv^{-\frac{1}{2}}-v^{-\frac{3}{2}}=0...
  35. G

    Bernoulli's Principle Explained: Ball vs Plane Wing

    Can someone explain to me Bernoulli's principle as simply as possible? Would this principle would be the same when applied to a ball as opposed to a plane's wing? Thanks a lot! :biggrin:
  36. B

    Optimizing Boat Hull Shape for Maximum Speed: A Calculus of Variations Approach

    Was wondering if it was possible to derive the best possible shape of a boat hull to achieve maximum speed? As it is the equation on how to calculate the speed of a sphere moving in water... or else I am just totally wrong and you can bluntly ignore this post :tongue:
  37. Clausius2

    Need a confirmation. Bernoulli.

    I'm not sure completely of this. Can you confirm if, assuming IDEAL (Bernoulli) flow there is a loss of stagnation(total) pressure in the geometry attached. I think there is a loss of stagnation pressure indeed. The flow enters with a stagnation pressure Po1, pass through an orifice at 2...
  38. S

    Potential Energy and Bernoulli

    P_1 + \frac{1}{2} \rho (v_1)^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho (v_2)^2 + \rho g h_2 In this equation (and regular energy equations for that matter) is g= 9.8 or -9.8 m/s^2 ? To make sense mathematically I believe it has to be 9.8 or else pressure and velocity would increase as a...
  39. T

    How Does Bernoulli's Equation Apply in a Bourbon Distillery's Plumbing System?

    In a bourbon distillery plant, the refined product, approximated as 40% by weight ethanol, 60% by weight water, is pumped through a plumbing system. At the OUTLET, where the inner diameter of the pipe is 5.08cm, the product fills an aluminum open cylinder (Diameter .442m, height 1.26m) in 98.9...
  40. L

    How can Bernoulli's equation be applied to calculate gas flow rate in a tube?

    My statistical dynamics and other useful areas of physics was sorely lacking in my undergrad education. Take this for instance, at work I need to calculate the gas flow rate from a tube into a very large chamber. I know the diameter of the tube and pressures of the gas. Bernoulli's equation...
  41. S

    A-Level Investigation into Bernoulli Principle

    Hi! I'm a UK based student undertaking A-Level Physics. I am now in my second year completing my majour investigation. We are allowed to study and investigate any physics phenomina(sp) of our choice, I have decided upon a ball in a jet looking into the effects of Bernoulli. One of the...
  42. S

    Bernoulli Principle: Intuitive Explanation?

    I have read and understood the explanation of the Bernoulli principle based on conservation of energy, but what I would like is a more intuitive way of picturing just how the reduced pressure develops in, say, a venturi tube. I want to be able to mentally track an element of the fluid and...
  43. J

    Is Bernoulli's Principle of Water Flow Really Flawless in Hydraulic Engineering?

    For fourty years the Bernoulli terms of H+Z+v^2/2g = K offered me a seemingly perfect tool for hydraulic engineering. Suddenly the wheels have fallen off this wagon because v^2 in a STRAIGHT line has a potential equivalence of H... v^2 in a CIRCULAR path has 2H equivalence ? A Newtonian...
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