# 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. ### I Why Does Differential Pressure Vary As The Square Of The Flow?

Can someone explain to me Bernoulli's principle as to why the pressure across a restriction varies as the square of the velocity? I'm looking for an understanding (conceptual) as to why this is without a gazillion math examples please. Thanks.
2. ### Bernoulli equation for calculation of water flow

Hello everyone; Please need some help to check if my calculation are correct (and if possible some explantation) Bernoulli's equation between point 1 and 3 is given by: P_1+1/2 ρv_1^2 + ρgh_1 = P_3+1/2 ρv_3^2 + ρgh_3 P_1 = P_(atm ) v_1= 0 m/s h_1= 0.875 m P_3 = P_(atm ) v_3= ? m/s h_3= 0...
3. ### Misc. Bernoulli effect on new vent design

First off don't quit reading if you understand basic Bernoulli effect. I am nowhere close to the caliber of minds on this forum but I have a problem and lack understanding that science may help answer. Preface: Temperature extremes are stressing wildlife populations. I happen to be an advocate...
4. ### I Bernoulli and Momentum Disconnect?

I was playing around, and I found something unexpected. If we are analyzing a simple fluid jet: We can apply Bernoulli's (which is Conservation of Energy) and arrive at: $$P_{1_{B}} = \frac{1}{2} \rho \left( v_2^2 - v_1^2 \right) = \frac{1}{2} \rho ( v_2 - v_1 ) ( v_2+ v_1)$$ It would...
5. ### Order of Magnitude Difference: Solving with Torricelli & Bernoulli

Solving with Torricelli I get Vt = 6x10^-3 m/s Solving with Bernoulli I get Vt = 6x10^-4 m/s, a whole order of magnitude smaller. How can it be correct? I know that Torricelli is an approximation, but the solution given by the book uses Torricelli which doesn't seem right to me.
6. ### 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...
7. ### I Conflicting Conventions for Bernoulli Numbers?

In the Wikipedia article https://en.wikipedia.org/wiki/Bernoulli_number on Bernoulli’s numbers, it explains that there are two conventions which differ only at m=1. Then it says… Under “explicit definitions”, it gives, for m>1 So, it seems pretty straightforward that they are saying that...
8. ### Derive the Venturi Meter eqn from the Bernoulli eqn

Advanced apologies for this format; I am posting my question as an the image b/c the Latex is being very buggy with me, and I lost a kind of lengthy post to it. Can anyone show me what I am doing wrong? I have attached a pdf version for easier reading if need be.
9. ### Bernoulli equation / fluid flow / finding height

Hi, everyone! Doing some fluid flow/Bernoulli tasks. Ok, so the task is: «A hose with a radius of 0,035m is connected to a nozzle, which reduces the radius of the hose to 0,018m (2). The hose carries (qv) 0,0075 m3/sec and the totalpressure (3) in the wide section (1) is 211 kPA. The density of...
10. ### Engineering Fluid mechanics question and the Bernoulli Equation

Good afternoon, I am struggling to find the solution at Q2 and Q3. For Q2 the absolute pressure at point 1 is at the bottom of the tank, so do i need to use the formula P=Patm+qgh ? If using this formula I've got a bigger number than 100Pa. Same issue for Q3, isn't the pressure at point 2...
11. ### The Traditional Bernoulli Eqn Derivation of Rocket Exhaust Velocity

If you've seen it, they chose one point in the combustion chamber and the other in the exhaust nozzle. I think they're assuming that we have a gas both places. They say that the pressure in the nozzle is atmospheric pressure, or it you're in outer space, zero. That makes perfect sense...
12. ### I Help Regarding Application of Bernoulli in a Boundary Layer

Hey all, I recently took an aerodynamics exam that included the question "Please Explain how the Bernoulli Equation can be Applied Inside a Boundary Layer". Now, it is my belief that the Bernoulli equation, defined by my textbook as P+0.5ρV2=ℂ, requires inviscid flow to be properly applied...
13. ### A Bernoulli, lift and cause & effect

Dear all, for a book I'm writing I'm trying to understand the generation of lift by wings on a conceptual level. Some papers I used are given at the end. I won't talk about all the misunderstandings out there concerning the generation of lift. I'm interested, also from a pedagogical level, in...
14. ### I Series for coth(x/2) via Bernoulli numbers

Hello, I've been using "Guide to Essential Math" by S.M. Blinder from time to time to stay on top of my basic mathematics. I'm currently on the section on Bernoulli Numbers. In that section he has the following (snippet below). Is the transition to equation 7.61 just wrong? The equation just...
15. ### Hagen-Poiseuille vs Bernoulli

I am trying to calculate the exit velocity of a nozzle (0,25Ø) that is connected to a high pressure syringe (10 BAR), however I cannot understand why Hagen-Poiseuille will have a higher exit velocity then Bernoulli when HP take viscosity into account.
16. ### Solve the Bernoulli differential equation

kindly note that my question or rather my only interest on this equation is how we arrive at the equation, ##v(x)=ce^{15x} - \frac {3}{17} e^{-2x}## ...is there a mistake on the textbook here? in my working i am finding, ##v(x)=-1.5e^{13x} +ke^{15x}##
17. ### Bernoulli Equation — Discharging water from a partially-filled sealed tank

Hi there, I'm doing a past exam paper Q and i'd like some help. Assumptions are: The velocity in the tank is negligible and the hydrostatic head is 4m. Pressure in the vessel: Gauge pressure 1 bar g = 10^5 Pa 0.2 bar g = 20,000 Pa Hydrostatic Pressure: (4)(9.81)(978) = 38,376.72 Pa Absolute...
18. ### Bernoulli and Bayesian probabilities

Summary:: Hello there, I'm a mechanical engineer pursuing my graduate degree and I'm taking a class on machine learning. Coding is a skill of mine, but statistics is not... anyway, I have a homework problem on Bernoulli and Bayesian probabilities. I believe I've done the first few parts...
19. ### Does Fluid Dynamics Explain Pressure Gradients in a Frictionless Tube?

Let's start with a horizontal tube with a constant diameter. I'm not sure if it's important, but let's assume it's frictionless. I will have some fluid flowing in this tube and if it's important, we can make the fluid incompressible, inviscid, irrotational, etc. To create a flow in the tube...
20. ### 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:$$p_1=p_2+h\rho_{air} g$$...
21. ### Flow of air through an open tube with a balloon

I hope you guys don't mind a bizarre question from a novice. I've learned just enough about fluid dynamics to be dangerous. Assume that we have a straight, rigid tube with a constant inner diameter. It's not long, let's say it's around a foot (in case that matters). We cut a chunk out of the...
22. ### Lift, Drag, Magnus, Bernoulli, Tennis ball fuzz, etc.

Hello, My background is not fluid mechanics. Yet, I am trying, very late in life (near retirement) to understand some things, now that I have time. I have always been confused about the qualitative descriptions about the role of dimples on golf balls and fuzz on tennis balls. Sometimes, the...
23. ### I Bernoulli Trials Homework Problem

this is the answer Is this right?
24. ### Sticky card Application of Bernoulli / Pressure incorrect?

After doing what the instruction did, I noticed that the card stuck to the spool, and generated the hypothesis that it was the same effect as when putting two papers together and blowing through them, the lower pressure of the faster speed of the wind makes the higher pressure outside move the...
25. ### Calculate pump height by using the Bernoulli Equation

Really need to help getting started with this one. They've given NPSH = (Ps - Pvp)/qg Where Ps = Suction pressure at pump inlet Pvp = vapour pressure of liquid at temp of pumping q = density of liquid g = acc due to grav They've also provided Darcys friction Equation The examiners tip (its a...
26. ### The Venturi Effect cannot explain how an eductor works

I've google all the keywords like "eductor", "ejector", "Venturi pump". All of them are the mechanism or applications that utilize "Venturi Effect". All of them are trying to explain the "suction effect" by saying that restriction area makes the fluid's velocity higher and hence lower pressure...
27. ### I Bernoulli Equation with weird integral

Part of me thinks this is could be a u-sub b/c x^3's derivative is 3x^2, a factor of 3 off from what e is raised to...but it is not a traditional u-sub...any thoughts if this is a u-sub or by parts, and what u should be?I know that there is more to solving the equation after this ( z =...
28. ### Bernoulli equation in a closed loop system

P1 = 5psi P2= 15psi , Z2-Z1 = 0, i assume V2 =V1 because velocity of water is the same everywhere in a pipe of constant diameter is H friction = H pump = 10psi ? Please help
29. ### Crane Arm Model using beam theory

Can a Bernoulli or Timoshenko model be reasonable for a crane arm, on ships? Yes, the arm might have a truss element, yes there is a hydraulic force to lift the arm (or cables). But to some extent, can one model the crane arm as one of a simple beam (either Timoshenko or Bernoulli -- and...
30. ### Water Pressure at the tap and practical Bernoulli equation

Hello, I think I understand how Bernoulli equations works but I am clearly uncertain on some aspects of its application. For example, let's look at the figure below: 1) The static pressure is ##60## ##psi## from the city water supply. There is not flow (tap closed) so the pressure at the...
31. ### MHB Merged Bernoulli process

Consider two Bernoulli processes X1 and X2 such that X1[k] is a Bernoulli random variable with P=0.5 and X2[k] is a Bernoulli random variable with P=0.7 for all k>=0 Let Y be a random process formed by merging X1 and X2, i.e. Y[k] =1 if and only if X1[k] = X2[k] = 1 and Y[k] = 0 otherwise. a.)...
32. ### Bernoulli equation and negative pressure

In one pipeline with pressure P1 area A1 decrease to A2 we want to find P2 in area A2 we have bernoulli equation p1+1/2 ρv^2=p2+1/2ρv^2 with low of conservation of mass A1V1=A2V2 that we can write V2=A1/A2 V1 if we keep in bernouli equation we have P2=P1+1/2V2(1-(A1/A2)^2) my quation is...
33. ### Dialysate flow rate when pulling through a jug

Friendly argument at work (both non physics majors) with what tube would fill up faster with a flow rate (siphon like) that remains the same through two different diameter tubes. The dialysate jug is open to atm pressure. One tube is about .5 inches in diameter and the other is .25. We were...
34. ### Bernoulli! Bernoulli!

Everyone likes to shout "Bernoulli!"
35. ### Understand Pressure in Fluids: Conceptual Guide

I'm looking for a conceptual understanding of pressure in fluid. According to what I've gathered, in static fluid, the pressure at any point in the fluid depends on the depth within the fluid, because there is more fluid weighing down on an object the deeper into the fluid it is. However, for...
36. ### Deriving Bernoulli's Equation Using Euler's Law of Motion

Hi all, I have attached an image of a page out of the book I am using for context. The blue arrow in Figure 12-3 describes the motion of the particle. I figured the net force would need to be in the same direction, but apparently the net force opposes the motion. So, in Figure 12-3 the pressure...
37. ### Hole Sizing to Drain Fluids [Pressurized Container]

Hello, I want to size my system to be able to get rid of fluids without any head buildup within the container. I am just a bit confused as to what formula I should use. My problem is summed up in the following schematic. Note that P1>P2, I have assumed H=10^(-4)m and my flow rate is 0.1 m3/s...
38. ### B Expectation of the number of successes in Bernoulli trial

I'm trying calculate the expected number of steps in one node in a random walk , ##\langle s\rangle=\sum sp^s##. By deduction I have a possible solution (for rational probabilities ##p=n/m,\ n< m##) in ##\bar{s}=\langle s\rangle= nm/(m-n)^2##, which looks pretty weird but I have not found a...
39. ### Bernoulli Principle from a molecular scale

Good evening everyone. Can you tell me if it is possible to mathematically derive the Bernoulli principle from a microscopic analysis? In particular, in the hypothesis of an incompressible stationary flow, at a constant altitude, it states that: P + 0.5ρV^2 = cost Well, in textbooks this...
40. ### Bernoulli Principle vs. Coanda Effect

In the past couple of days I've been watching video demonstrations on YouTube that use the Bernoulli Principle to explain what is happening (e.g. the hairdryer and ball experiment) Then, I saw this one video using the Coanda Effect as the explanation (they were also using the hairdryer and ball...
41. ### How can I calculate the drop in pressure across an orifice?

I know the inlet pressure, temperature and density along with the massflow rate across the orifice and the orifice cross section. Is there a way for me to calculate the drop in pressure across the orifice?
42. ### Need help with a Bernoulli(?) expression

Hello! So this is my problem here, there's a question I've been studying for an exam in which I really can't understand the answer. Basically it has multiple choices and I'm very undecided. So this is it: Expression: "What does this expression reflect? PV + mgh + 0,5mv^2 = constant " a)...
43. ### MHB Differential Equations - Bernoulli equation

Afternoon, anyone that would like to take a look at this Differential Equation problem it would be very helpful. I have tried separating the problem, but I am only working with one known term. Consider the logistic equation $$\dot{y}=y(1-y).$$ (a) Find the solution satisfying $y_1(0)=6$ and...
44. ### MHB Success runs in Bernoulli trials

I tried to understand the following problem: Consider a sequence of Bernoulli trials with success probability $p$. Fix a positive integer $r$ and let $\mathcal{E}$ denote the event that a run of $r$ successes is observed; recall that we do not allow overlapping runs. We use a recurrence...
45. ### Pressure and heights of a manometer -- Find the fluid flow rate

Homework Statement Find the flow rate of water. The fluid in the manometer is mercury. ##d_{1},d_{2}## are the diameters in the figure Homework Equations Bernoulli, continuity equations The Attempt at a Solution We know that ##p_{1}=p_{1Top}+\rho_{water}gh_{2}##...
46. ### Autocorrelation of a Bernoulli Coin Flipping Experiment

I am confused at one point. The coin flipping Bernoulli Process has a probability of p of getting HEADS and a probability of 1-p of getting TAILS. Let's define a random variable x[n], which takes the value +1 when it is a HEADS, and -1 when it is a TAILS. The mean or estimation of x[n] becomes...
47. ### Bernoulli, Binomial & Poisson: What is pi?

Homework Statement Hi, I have a confusion in knowing Pi in the equations attached. Eq are related to the Topic Discrete Random Variables in the context of Probability lecture I also can't understand what is P(Y=y|Pi)? Homework Equations Eq are attached The Attempt at a Solution I can't...
48. ### The math around the windbag or Bernoulli bag experiment

What is the math behind this experiment? If the mass flow rate of the air coming out of the guy's mouth is M1, then what is the mass flow rate, M2, of of the air going into the bag? I know that this is related to compressible flow. The explanations I have found on the internet are that since...
49. ### Bernoulli Equation and gauge pressure

Homework Statement What gauge pressure is required in the city mains for a stream from a fire hose connected to the city mains to reach a vertical building of height 15m? Homework Equations Bernoulli Equation The Attempt at a Solution I have tried this sum. My confusion is regarding choice of...
50. ### A Two Bernoulli distribution- test hypothesis for biased coins

I'm simplifying a research question that I have at work. Assuming I have 2 coins each with a different probability of head, let's call heads a success (p). Those are biased coins each with a different p, and I do not know the probability of success of each coin, but I do got a sample: Coin 1 -...