# Bernoulli Definition and 61 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. ### 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.
2. ### 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...
3. ### 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...
4. ### 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...
5. ### I Bernoulli Trials Homework Problem

this is the answer Is this right?
6. ### 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...
7. ### 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 =...
8. ### 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...
9. ### 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...
10. ### Bernoulli! Bernoulli!

Everyone likes to shout "Bernoulli!"
11. ### Pressure in fluids

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...
12. ### 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...
13. ### 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...
14. ### 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?
15. ### 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}##...
16. ### 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...
17. ### Venturi nozzle, Bernoulli

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...
18. ### 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...
19. ### 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...
20. ### Calculate flow

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 =...
21. ### 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 =...
22. ### 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...
23. ### 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...
24. ### 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...
25. ### Valve open to air

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...
26. ### (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. ### 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 (...
28. ### 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...
29. ### 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...
30. ### 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...
31. ### 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...
32. ### 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...
33. ### 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...
34. ### 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...
35. ### 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...
36. ### 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...
37. ### 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...
38. ### Using Bernoulli's Equation

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...
39. ### Question for Syringe

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...
40. ### Flow rate of a syringe

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...
41. ### 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...
42. ### 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...
43. ### 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...
44. ### 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...
45. ### 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...
46. ### Ducted Fan Questions

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...
47. ### 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 ...
48. ### Bending of a Free Beam

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...