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. JulienB

    Bernoulli equation (watering can)

    Homework Statement Hi everybody! Here is a classical Bernoulli problem, which I'd like you to review to check if I (finally!) make a proper use of Bernoulli's equation! A gardener waters a bush with the help of a watering can (see attached pic). The water level in the can lays at height H =...
  2. G

    Bernoulli vs Energy Conservation?

    In the example, is it possible to have same velocities at the two ends of the tube? How would you construct energy conversation equation?
  3. JulienB

    Solve Bernoulli Problem: Mass of Water in Tube

    Homework Statement Hi everybody! I'm back with another Bernoulli problem :) A reservoir with constant pressure P = 105 Pa releases through a tube water (density ρ = 1 g/cm3) with the velocity v = 4 m⋅s-1. That tube is then connected to another perpendicular tube (area A = 0.1 m2, height h =...
  4. L

    Does an eductor work on the Bernoulli equation?

    What i know is that the Bernoulli equation is applied only along a streamline. Is it correct to say that eductors work on the Bernoulli equation?
  5. JulienB

    Understanding the Bernoulli Equation: Solving a Fluid Dynamics Problem

    Hi everybody! I'm training for an upcoming exam, and I'd like to know if I correctly use the Bernoulli equation. Homework Statement The problem is kind of difficult to describe without a drawing, please check out the attached jpg to see the situation and the known data. The questions are: a)...
  6. O

    How is Bernoulli's equation related to saxon bowls?

    Homework Statement This is a lab that we have to design and carry out that goes above and beyond our course. I am investigating how the diameter of a hole in a bowl affects its sink time when put in a larger bowl of water (saxon bowl, or sinking bowl as they are known.) I will have to plot them...
  7. C

    Proof of Baker-Campbell-Hausdorff involving Bernoulli numbers

    Homework Statement The BCH formula states that the product of two exponentials of non commuting operators can be combined into a single exponential involving commutators of these operators. One may write that ##\ln(e^A e^B) = \sum_{n \geq 1} c_n(A,B)## where $$c_{n+1} = \frac{1}{n+1} \left(...
  8. Alettix

    Choosing Reference Points in Bernoulli's Equation for Fluid Flow

    Hello! I have encountered some trouble with choosing the right reference points when using Bernoulli's equation and I would be glad if you could help me sort it out with this made up example. :) 1. Homework Statement There is a large, open, cylindrical water tank with a cross section area of...
  9. L

    Bernoulli Equation - sign of gravitational acceleration

    Homework Statement Water flows from the faucet on the first floor of the building shown in the figure with a maximum velocity of 20 ft/s. For steady inviscid flow, determine the maximum water velocity from the basement faucet and from the faucet on the second floor. Assume each floor is 12 ft...
  10. vincekillics

    Fluid Dynamics: Calculating Speed and Force in Syringe Experiments"

    Homework Statement It is time for aged physics lecturers to have their flu shots but even that can be interesting. Assume the density of the vaccine in the syringe is the same as the density of water. The diameter of the syringe is 6mm, the length of the needle is 3cm and by reading the packet...
  11. Z

    Calculate Flow Rate of a Syringe: Poiseuille's & Bernoulli's Laws

    I am trying to come up with a mathematical model so that, when the displacement of the plunger of a syringe is know, I can calculate the amount of a specific liquid in the barrel. Or the relationship between the speed of the plunger and flow rate at the tip of the needle (Again assuming that the...
  12. D

    Bernoulli River: Calculating Water Speed

    Homework Statement : River Pascal with a volume flow rate of 4.8×105L/s joins with River Archimedes, which carries 1.04×106L/s , to form the Bernoulli River. The Bernoulli River is 190 m wide and 20 m deep.[/B]Homework Equations : What is the speed of the water in the Bernoulli River? Express...
  13. needing

    Bernoulli effect at spray nozzle

    Hi. First post so I hope I have the correct thread location. I am reverse engineering a 40+ year old vertical slide carburettor design i.e. the venturi is horizontal. The current spray nozzle protudes vertically into the airflow but is straight sided and flat across the exit. Option 1...
  14. K

    Expected value of bernoulli random variable.

    "Let X be a Bernoulli random variable. That is, P(X = 1) = p and P(X = 0) = 1 − p. Then E(X) = 1 × p + 0 × (1 − p) = p. Why does this definition make sense? By the law of large numbers, in n independent Bernoulli trials where n is very large, the fraction of 1’s is very close to p, and the...
  15. Destroxia

    Bernoulli Binomial Distribution

    Homework Statement Derive the bernoulli binomial distribution by generalizing the probability of a coin flip. ## P(k, n) = \binom{n}{k}p^{k}q^{(n-k)} ##, q = p - 1 Homework Equations Combination: ## \binom{n}{k} = \frac {n!} {k!(n-k)!} ## Prob. of coin flip: ## \frac {\binom{n}{k}} {2^n}...
  16. V

    Examples of Beginning of Bernoulli

    Hi i need a examples of beginning of bernoulli, i will do a presentation of this, i need a original example (object, which have to be a utility in our lives) of Bernoulli, my classmates, they already have a other examples like, aircraft, sailing, atomizer. So i need other one, easy to explain...
  17. T

    Bernoulli principle and fluid particle

    Hello, Bernoulli principle describes the flow of a fluid for steady, incompressible flow along a streamline. But it is said for a particle of a fluid along a streamline. My question is a particle of fluid refers to a molecule or a group of molecules? Thank you
  18. F

    Bernoulli's equation and (mostly) sealed containers.

    (This is more of a conceptual question than a real homework question; thank you all so much for your help though!) :D 1. Homework Statement Let's say that I have a large soda bottle. I drill a small hole through the side of it, put my finger over it to seal the hole, and fill the bottle up...
  19. nuuskur

    Bernoulli differential equation, Cauchy problem

    Homework Statement Observe a Cauchy problem \begin{cases}y' + p(x)y =q(x)y^n\\ y(x_0) = y_0\end{cases} Assume ##p(x), q(x)## are continuous for some ##(a,b)\subseteq\mathbb{R}## Verify the equation has a solution and determine the condition for there to be exactly one solution. Homework...
  20. C

    MHB Bernoulli Equation Checking the solution

    Dear Everyone, I need someone to check the solution, The question identity and then solve, The Equation is Bernoulli To Solve: $(ye^{-2x}+y^3)dx-e^{-2x}dy=0$ $\frac{1}{dx}(ye^{x}+y^3)dx=\frac{1}{dx}(e^{2x}dy)$ $ye^{-2x}+y^3=e^{-2x}\d{y}{x}$ $e^{-2x}y^{\prime}-ye^{-2x}=y^3$ Let...
  21. R

    What causes the liquid to rise in this picture?

    This is a diagram of a pitot-static tube. My question is however not related to its applications but rather, what causes the liquid to rise up the static tube? The static tube is at right angles to the fluid flow. I understand that this is a very basic question but I can't seem to get my head...
  22. S

    Overexertion of pump impeller?

    Does diameter reduction on the pressure side shortly after the pump induces overexertion of the impeller? This is the setup: suction line: 8" - length: 20' ; high pressure centrifugal pump powered by a engine at approx. 2000 rpm ; pressure line: 6" at a length of 18" directly followed by a...
  23. JuanC97

    Bernoulli's equation confusion?

    Some days ago I got confused trying to solve an exercise about fluid dynamics. Trying to simplify the problem here is a similar situation: I have a cistern connected to a tube containing a fluid as shown in the picture below. Assumming that the fluid is incompressible... I know from the law...
  24. Q

    Nonlinear Mass Spring Damper with Euler Bernoulli Beam

    I'm trying to find a solution to a system in which a clamped free Euler-Bernoulli Beam system rests on top of a mass-spring-damper system. The MSD system has nonlinearities in both the spring and the damper and is of the form: I have extended the nonlinear restoring force to its 3rd term and...
  25. A

    Calculating Pressure Difference w/ Bernoulli Law for Bay Inlet

    I have a container with one inlet and one outlet. I have the area of the inlet, Ai, velocity vi of the air coming in, and mass flow mi (assume a plane with an air inlet to a bay). I don't know anything about the outlet (just that there is one). What I need to do is calculate the size of an extra...
  26. U

    Bernoulli vs conservation of momentum (Reynolds transport theorem form)

    So I've found several instances in which Bernoulli and Conservation of momentum (in Reynolds transport theorem form) give different answers for the study of an inviscid fluid. Let's consider a simple situation as described in my diagram attached. Basically a tap/faucet is releasing fluid, which...
  27. ManicPIxie

    Bernoulli, Fluid Dynamics, and ships

    Homework Statement The Plimsoll line is a line marked on the side all ships that effectively indicates the safe maximum load the ship can carry in that type of water at that temperature.You have been asked to stand on the dock and collect the tickets of the passengers boarding a cruise ship...
  28. B

    Ducted Fan Pressure Differential: Questions Answered

    Hi guys, I recently completed a fluid dynamics practical at Uni and submitted a report on it, however, I still have some burning questions which I need to be answered. Firstly, the data that we collected shows that as the flow rate in the duct increases, the pressure differential of the fan...
  29. C

    Interpreting Bernoulli Equation

    Homework Statement The photo below shows a stream of water in steady flow from a kitchen faucet. At the faucet, the diameter of the stream is 0.960 cm. The stream fills a 0.125cm3 container in 16.3 s. Find the diameter of the stream 13.0 cm below the opening of the faucet. Homework Equations...
  30. Poetria

    Moivre-Laplace theorem (homework)

    < Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > I have no idea what I am doing wrong. Here is my problem: S(n) - the number of successes in 10 Bernoulli trials, each with probability 0.7 I am supposed to use normal approximation to compute ...
  31. spovolny

    Free Beam Bending: Find Complete Answer & More

    Consider a beam with an upwards concentrated force applied to its center. This is equilibrated by a distributed downwards force. There are no displacement boundary conditions. I've tried approaching this with simple beam theory, but I can't get a complete answer (shear, moment, slope...
  32. danielng245

    Please help calculate flowrate frm blower to push water down

    How to calculate how much flowrate from blower i can push water pool 2,75m*1,8m down by 1,25m in 1 sec? Note : Blower Pressure 0.03 bar - 0.035 bar There is an empty room above the water pool with dimension of 2.75m*1.8m*1.7m This process happen in a closed chamber...
  33. R

    How can the Bernoulli Equation be applied to solve a challenging problem?

    Hey everyone ! I'm new here and found that this forum was very useful. Would really appreciate it if you could help me out with this problem ! Have been scratching my head for hours now :( Question: Thank you very very much once again !
  34. Jewish_Vulcan

    Low pressures at high velocities

    Why does pressure decrease as velocity increases, I think it is because pressure is defined as particles hitting the edge of the medium so when velocity increases the particles hit the edge of the medium less but how?
  35. T

    Surge Pressure Stagnation Pressure Static Pressure Bernoulli

    I have trouble understanding why Stagnation Pressure equals Total Pressure when we apply Bernoullis theorem to a constriction. Two different scenarios Scenario 1.A pipe has pressure p_1 , its flow is velocity v_1 and a diameter a_1 ,it has no restriction along its length. Total Pressure Tp_1...
  36. H

    Uniform & Non-Uniform Gravitational Fields Explained

    HEy what is uniform and non-uniform gravitational field...
  37. A

    Estimate pipe diameter based on flow rate

    I'm designing a testing unit where I need to estimate the smallest diameter of a short complex pipe (around 1 meter, three bends and some diameter viariations). Since the pipe is being cooled down in a water bath after production, my idea is to force water with a known pressure in one end of the...
  38. I

    Does the shape of a car produce lift or downforce?

    I have a few questions related to downforce in cars. Please forgive any fundamental misunderstanding of aerodynamics. Does the shape of a car, say a Volkswagen Golf, driving on a road produce lift or downforce? Is the Coanda Effect at play there? How does the height of the car above the ground...
  39. E

    Does the flow rate and pressure decrease as the exit height of a pump increases?

    OK, So I have been having an on and off debate with my family about this. I saw a pump at Home Depot that said it has a 30 ft head. Then it went on to show that the flow rate varied as the output of the pump changed in height. Now I thought that this was wrong. I just finished a course in...
  40. C

    How Does Changing Height Affect Bernoulli's Equation Values?

    It's just a simple question. How does the height effect the other values if the height increases or decreases. What happens when the height increases and what happens when the height decreases?
  41. W

    Solving the Fluids Straw Problem: Compute Water Fraction in Ideal Gas Model

    Homework Statement This problem pertains to the drinking straw trick. You decide to place your finger over a 20.0cm straw. 95.0% of the straw is filled with water, while the top is full of air. Treating the straw as an ideal gas, compute fraction of the straw that is filled with water when the...
  42. AdityaDev

    Bernoulli's equation and velocity

    What happens when you have more than one hole in a vessel containing liquid? Can you help me finding the velocities at different holes if they are at some height from level of liquid at a particular instant? I know what happens when you put a small hole in a tank containing liquid at a height h...
  43. U

    Measuring Velocity based on change in Pressure

    Homework Statement There is an air-tight 1L Canister filled with 90% water and 10% N2O. This canister is attached to some clear tubing which is not entirely air-tight. At the end of this tubing are some tungsten particles averaging ~1µm in diameter with total mass of 60mg. The contraption is...
  44. C

    Bernoulli equation application

    Why is the water level in the object above the water level of the current? How to apply Bernoulli equation in this case?
  45. J

    Hypothetical Bernoulli situation with Pascals Law(Efflux torcellis result)

    Homework Statement : There is tank with a certain depth with water that is exposed to air. There is a hole at the bottom of the tank. Using Bernoulli's equation, we can find the efflux speed. density of the water * gravity * depth = 1/2density of water * velocity ^2. This will give us the...
  46. G

    Bernoulli Principle and fluid velocity

    I have been trying to fully understand this concept of Bernoulli's Principle , the Venturi effect and fluid velocity and energy. I need to grasp this to develop an idea that I have been working on. 1. As water is forced down a narrowing pipe, as the pipe gets more narrow, it means it losses...
  47. Corin511

    What is the relationship between water stream diameter and distance from faucet?

    Homework Statement Daphne goes to the kitchen for a glass of water. She turns on the faucet so the stream of water is laminar flow. She notes that the diameter of the water steam decreases with distance below the faucet assuming that the water exits the faucet of diameter D with speeds v0...
  48. D

    Differential Equations: Bernoulli Equation

    Homework Statement Find the general solution: y'-3y=(y^2) Homework EquationsThe Attempt at a Solution divide both sides by y^2 y'(y^-2) -3(y^-1) = 1 we know v=y^(n-1) v=y^-1 v'=d/dx(y^-1) v'=-(y^-2) y' plug it back into y'(y^-2) -3(y^-1) = 1 -v'-3v=1 this is where I think I am making a...
  49. Y

    Bernoulli equation - pitot tubes

    Homework Statement Homework Equations P1+pV12/2+pgh1=P2+pV22/2+pgh2 The Attempt at a Solution My thinking: since the pitot tubes measure the stagnation pressure (static + dynamics pressure) and the height of the tubes are the same. By Bernoulli's equation, the total pressure along a...
  50. D

    MHB Y=-X if X ~ Ber(1/4): Solving the Mystery

    If \(Y = -X\) and \(X\sim Ber(1/4)\), then what is Y? I know that \[ X\sim \begin{cases} 1 - p, & x = 0\\ p, & x = 1 \end{cases} \] where \(p = 0.25\) in this case. What is the negative of \(X\) though. It doesn't make any sense making the probabilities negative.
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