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. E

    Bernoulli trial summation by hand

    Homework Statement Show that the expected number of successes in n Bernoulli trials w probability p of success is <x> = np Homework Equations The Attempt at a Solution So I get the right answer which is this: E\left( x\right) =\sum _{x=0}^{n}x\left( \begin{matrix} n\\...
  2. B

    Can Bernoulli's Law Increase the Depth Range of Submarines?

    Hi people, It may be a strange question, or impossible, but maybe you could help me out. It's about submarines, high pressure and Bernoulli's law. What if we build some kind of jet engine-like thing on the front of the submarine, not to 'pull' it forward, but to speed up the water...
  3. T

    Central Limit Theorem applied to a Bernoulli distribution

    As I understand it, one result of the central limit theorem is that the sampling distribution of means drawn from any population will be approximately normal. Assume the population consist of Bernoulli trials with a given probability p and we want to estimate p. Then our population consist of...
  4. S

    MHB Bernoulli to Linear First Order

    I know how to do a Linear First Order and I know how to do a Bernoulli (kind of). The kind of part may be why I'm having a problem. dy/dx+xy=xy^2 So I know in order for that to be a normal linear differential, that square on the last y has to go away somehow... I'm not sure how to do this...
  5. D

    Understanding Lift Force and the Bernoulli Equation in Small Aircraft

    Homework Statement See attachment Homework Equations Maybe lift force = ClρAv2 A=area Cl= lift coefficient= 0.3 ρ= air density V=air speed but don't know which one it represents... Under or below wing or average? And the bernoulli equation seems to be needed as well... The Attempt at a...
  6. Z

    Integration of partials, specifically Euler to Bernoulli Equation

    Hi! I am having trouble following the derivation from Euler's Equation to Bernoulli's Equation. The trouble lies in the math, not the physics part. Especially the step when partial derivatives are being integrated. I have attached the relevant part as a screenshot. How does the...
  7. L

    Relationship Between Trig Funtions and Bernoulli Numbers

    Homework Statement Prove the formula xcscx=2B(ix)-B(2ix)Homework Equations B(x)=x/((ex)-1) sinx= (eix-e-ix)/2i The Attempt at a Solution I know that it makes sense to use the formula for B(x) with x=ix and x=2ix, and rewrite xcsc(x) as x/sin(x), plugging the above relevant equation in for...
  8. MarkFL

    MHB Khaled's question at Yahoo Answers regarding a Bernoulli equation

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  9. B

    MHB Solving Integrals with Exponential Functions

    Solve the ff: $\displaystyle\frac{dy}{dx}-y=xy^5$ $\displaystyle\frac{dy}{dx}-\frac{y}{x}=-\frac{5}{2}x^2y^3$ can you help start solving these problems? thanks!
  10. MarkFL

    MHB Ewaz's question at Yahoo Answers regarding a Bernoulli Equation

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  11. S

    Bernoulli principle and venturi effect.

    I have a specific problem involving two reservoirs filled with water with a height difference Y and total head H, and was wondering if a venturi like device could be used to calculate the resulting pressure head x and if it will exceed the bottom of reservoir 1. Also the drain length is d...
  12. L

    Bernoulli, hypertension, migraine

    I found the following thread on PF: https://www.physicsforums.com/showthread.php?t=207950 that relates hypertension to Bernoulli's fluid pressure equations, and it got me to thinking: I am aware that sometimes migraine headache leads to temporarily elevated blood pressure. I have read...
  13. B

    Bernoulli / pressure equation

    Homework Statement A large water tank has an inlet pipe and an outlet pipe. The inlet pipe has a diameter of 1.89 cm and is 1.29 m above the bottom of the tank. The outlet pipe has a diameter of 5.47 cm and is 4.25 m above the bottom of the tank. A volume of 0.697 m3 of water enters the tank...
  14. M

    MHB Solving the Bernoulli Equation: Find Initial Value u(1)

    Hello! I have the following Bernoulli equation: 2xyy'+(1+x)y^2=e^{x} , x>0 lim_{x -> 0^{+}} y(x) <\infty The transformation is u=y^{2} . So, u'+(\frac{1}{x}+1)u=\frac{e^{2x}}{x}.How can I find the initial value u(1) so that lim_{x -> 0^{+}} u(x) <\infty ??
  15. B

    Bernoulli and Continuity Equations

    Hi, Consider a vertical relatively long cylinder of constant radius open at both ends. We fill this cylinder with water and prevent water from falling down by a certain sheet as seen in the figure. Now suppose we remove the sheet suddenly. Let v1 be the speed of the upper surface of...
  16. N

    Can the Bernoulli equation be used for turbulent flow?

    Hey! So if the vorticity of a fluid = 0, it is in steady state laminar flow and friction is negligible (and viscosity too?), you can use the bernoulli equation between any two arbitrary points in the fluid, regardless if they are connected by a streamline. If the vorticity is non-zero, can...
  17. D

    Aerodynamics: Drag & Bernoulli in Turbulent Flows

    I have a question but it's not so much a specific HW problem as it is with trying to conceptualize the physics behind it. So when dealing with aerodynamics, let's take for example a wing / airfoil. I understand due to a difference in pressure lift is generated. Higher pressure wants to...
  18. K

    Bernoulli, Gauge pressure in hose?

    Homework Statement A village maintains a large tank with an open top, containing water for emergencies. The water can drain from the tank through a hose of diameter 6.60cm. the hose ends with a nozzle of diameter 2.20 cm. A rubber stopper is inserted into the nozzle. the water level in the...
  19. MarkFL

    MHB Tonnie's question at Yahoo Answers regarding a Bernoulli equation

    Here is the question: Here is a link to the question: Determine the solution to the following differential equation.? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  20. P

    Limiting dist for sum of dependent and non-identical Bernoulli vars

    A Binomial distribution has a standard normal limiting distribution, i.e. (X-E[X])/se(X) -> N(0,1), where X is the sum of independent and identically distributed Bernoulli variables. Does this hold even when i) the Bernoulli variables are independent but non-identically distributed? That...
  21. L

    Stagnation Point - Bernoulli Equation

    Homework Statement Can anyone tell me why, in the figure attached, the pressure in the manometer at 1 is a stagnation pressure? I understand that you get stagnation pressure at a stagnation point but point one is below the stagnation point, not on the stagnation point. Therefore how can it be...
  22. B

    Solving a Bernoulli differential equation

    Hello! I'm stuck at the moment with this differential equation. I've been trying to use the method for solving these equations, but my answer is not correct according to my book. Could anyone please explain what I'm doing wrong? Thanks!
  23. L

    Testing Hypotheses with Bernoulli Distribution

    This is the question: Suppose that X1...Xn form a random sample from the Bernoulli Distribution with unknown parameter P. Let Po and P1 be specified values such that 0<P1<Po<1, and suppose that is desired to test the following simple hypotheses: Ho: P=Po, H1: P=P1. A. Show that a test...
  24. M

    Question regarding Bernoulli Differential Equation

    In a video I was watching regarding how to solve these, the lecturer said that the form of a Bernoulli Differential Equation is y'+P(x)y=q(x)y^n where n>1 This means that if n = 1, it wouldn't be a Bernoulli differential equation and would be a first order linear differential equation, but if...
  25. K

    Bernoulli Equation Simple derivation help

    Homework Statement Please help me as I am quite confused in Bernoulli's theorem derivation...In my textbook,it is considered that Fluid Moves from a Greater height h1 to lower height h2,The pressure on upper end is positive,while at the lower end,it is negative,i.e against the motion of...
  26. E

    Thermodynamics - Bernoulli Equation question

    Thermodynamics -- Bernoulli Equation question "The Bernoulli Equation is restricted to frictionless incompressible fluids, the S.F.E.E is not".? Explain the fact ?
  27. L

    Bernoulli Equation - fluid mechanics question

    Hi, I am a first year studying mechanical engineering and I am having trouble understanding bernoulli equation. This is the first question in the tutorial and I can't seem to get the right answer. Water flows through the pipe contraction shown in the figure below. For the given 0.2 m...
  28. M

    Bernoulli principle - negative pressure

    I will write a program about principle bernoulli, but i have a problem. My input data: Pressure(p1) = 1000 Cross-section(A1) = 1 Velocity(V1) = 1 Cross-section(A2) = 0.5 Velocity(v2)= (V1A1)/A2 to simplify: h1=h2 i'm counting the pressure p2 : p2 = p1 + 0.5*v1*v1 - 0.5*v2*v2...
  29. soothsayer

    Bernoulli Equation for Rotational Flow

    Hi PF! I've been working on a research problem involving fluid dynamics, and I'm currently looking at a "bathtub flow". This is where water is draining through a hole, and we have a vortex. In a paper I have found dealing with this flow, the velocity potential was written as: \psi = Alnr + B\phi...
  30. 1

    Is My Solution to the Bernoulli Equation Correct?

    Homework Statement t^2y' + 2ty - y^3 = 0 Homework Equations The Attempt at a Solution y'+(2/t)y = (1/t^2)y^3 Let v = y^-2; then dv/dy = -2y^-3(dy/dt) and (dy/dt)=(-1/2)y^3(dv/dy) Making that sub we have: (-1/2)y^3(dv/dy)+(2/t)y = (1/t^2)y^3 (dv/dy)+(-4/t)y^-2 =...
  31. D

    Global solution to inhomogeneous Bernoulli ODE

    Hi everyone, I have an inhomogeneous Bernoulli type ODE given by u'(t) = \kappa u(t) + \ell(t) u^{\gamma}(t) + v(t),\ \ \ u(T)=b>0,...(1) where t\in[0,T],\ \ \gamma\in (0,1) . My concern is that how to prove the existence and uniqueness of the solution u(t) for all t\in [0,T]...
  32. J

    An answer I get with the Bernoulli Method doesn't check

    When I plug what I get for y back into the original Eq. to check it, it doesn't pass. I did something wrong somewhere but it all seems right to me. Where did I go wrong?
  33. H

    Will this aerofoil generate lift, Bernoulli

    I essentially want to understand weather or not an aerofoil with a zero attack angle will generate lift, i.e. using only Bernoulli. I have attached an image to illustrate my question, will the orange block lift if airflow is passed horizontally over the top of it? Many thanks
  34. G

    Physical Applications of the Bernoulli Diff Eq

    I am curious what the nonlinear bernoulli equation is used to model. Is there a certain topic or context where it shows up often? Can any suggest some references for more info? I am reviewing some ODE stuff for an upcoming exam and would really like an intuitive feel for the equation and its...
  35. B

    Timoshenko - Euler Bernoulli In Plane Curved Beams

    Folks, Searches of Timoshenko and Euler Bernoulli Beam Theory show differential equations for straight beams. Is there any material out there illustrating differential equations for "curved in plane beams"..? Thanks
  36. S

    Bernoulli Principle: Homework Solution

    Homework Statement Water Flows upward throw the pipe shown in the diagram at 96 L/Min. If the pressure at the lower end is 80kPa, find the velocity of the water is at both ends and the pressure at the upper end. Assume that the density of water remains constant throughout the tube and that...
  37. S

    Solving Bernoulli Principle Homework: Water Flows in Pipe

    Homework Statement Water Flows upward throw the pipe shown in the diagram at 96 L/Min. If the pressure at the lower end is 80kPa, find the velocity of the water is at both ends and the pressure at the upper end. Assume that the density of water remains constant throughout the tube and that...
  38. B

    Kinematics of Euler Bernoulli and Timoshenko Beam Elements

    Folks, Trying to get some appreciation for what is going on in the attached schematic of 1)Euler bernoulli and 2) Timoshenko beam elements. For the first one, ie the top picture, how was ##u- z \frac{dw}{dx}## arrived at? thanks
  39. A

    Bernoulli Problem (Somewhat Complicated?)

    Homework Statement So I'm dealing with a flow as seen in this image. There are 2 tanks, filled with 2 gases of different known densities, gas A and gas B. Gas A flows from a tank with a static pressure sensor at point 1 through a line with diameter D1. Gas B flows from a tank with a...
  40. B

    Solve bernoulli differential equation with extra constant

    Homework Statement Find a solution for: u'(t)=c*u(t)^2-c*(a+b)*u(t)+c*a*b The Attempt at a Solution I've found the solution for the homogeneous equation: u_0(t)=(\frac{1}{a+b}+d*e^{c(a+b)t)})^{-1} Where c is a random constant. Now I've tried the solution u(t)=x(t)*u_0(t), when I fill...
  41. B

    Euler Bernoulli Beam 4th order ODE -Balance of Units

    Folks, I am trying to understand the balance of units for this eqn ## \displaystyle \frac{d^2}{dx^2}(E(x)I(x) \frac{d^2 w(x)}{dx^2})+c_f(x)w(x)=q(x)## where ##E## is the modulus of Elasticity, ##I## is the second moment of area, ##c_f## is the elastic foundation modulus, ##w## is...
  42. T

    Misunderstanding of Pressure in the Bernoulli Equation

    First, this is is not a homework problem, per se, but it is a conceptual difficulty I am having with my physics 1 course, in which we are studying fluid mechanics (moderators please move this post if there is a more appropriate subforum). Homework Statement I was going over the derivation...
  43. L

    Bernoulli single-server queueing process

    Homework Statement Performance of a car wash center is modeled by the single-server Bernoulli queueing process with 2-minute frames. Cars arrive every 10 minutes, on the average. The average service time is 6 minutes. Capacity is unlimited. If there are no cars at the center at 10 am, compute...
  44. K

    Bernoulli & Navier-Stokes: Relation Explained

    hi all, I'm little confuse about the relation of these two equation. is it right to say that Bernoulli's equation is just a case(incompressible,inviscid,steady) of navier stoke equation?
  45. D

    Bernoulli Equation and flow loss

    Homework Statement Liquid, specific density 0.8, flows with velocity 4 m/s in a pipe that has a downward slope of 1:50. At a certain point in the pipe, a pressure gauge shows a pressure of 80 kPa. Determine the pressure at a point 200 m downstream of the gauge if: flow losses are ignored...
  46. MotoMike

    Lift more complex than Bernoulli?

    Hello Over the past year I've taken up the hobby of RC model airplane flying. During that time I've had many discussions with fellow modelers about lift. I've additionally read a bit about it as well. Most explanations I see like to explain it on Bernoulli's principle. That the wing...
  47. S

    Covariance - Bernoulli Distribution

    1. Consider the random variables X,Y where X~B(1,p) and f(y|x=0) = 1/2 0<y<2 f(y|x=1) = 1 0<y<1 Find cov(x,y) Homework Equations Cov(x,y) = E(XY) - E(X)E(Y) = E[(x-E(x))(y-E(y))] E(XY)=E[XE(Y|X)] The Attempt at a Solution E(X) = p (known since it's Bernoulli, can also...
  48. A

    Bernoulli Distribution/ Random Variables

    Homework Statement Take Ω = [0, 1] and P the uniform probability. (a) Give an example of two random variables X and Y defined on Ω that both have the same Bernoulli distribution with parameter θ = 1/3. (b) Give an example of such random variables that are independent, and not independent...
  49. L

    Quiet Bernoulli Levitation (Aerodynamic Levitation)

    Bernoulli levitation, or aerodynamic levitation, is a great physics demonstration. You've probably seen it before. The classic demonstration is: take a hair dryer, point it straight up, and put a ping-pong ball in the stream of air. The ping-pong ball floats in mid-air. But, most hair dryers...
  50. M

    Bernoulli equation and velocity problem

    In the Bernoulli equation, i know that velocity is in m/s and mass in N which gives energy in joules. Likewise potential energy id also in joules being mgh. In pressure energy what are the variants? i.e what is formula for calcualting the pressure energy term in the equation? If we compute...
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