I see this parroted a lot (and even saw this in a comment chain on /r/educationalgifs I think). Something doesnβt make sense to me. At 30-35k ft where airplanes fly, air pressure is between 4.4-3.6 ish psi. That means that if the Bernoulli effect were to be PERFECT and there be a complete vacuum above the wing, there would only be about 4 psiβs worth of lift multiplied over the entire wing area. I canβt find relevant numbers, but intuitively I canβt see a mere 4 psi holding the entire weight of a plane up. And of course there will not be a perfect vacuum over the wing, so itβs probably closer to 2-2.5 delta-P.
Furthermore, a symmetric airfoil with zero angle of attack will have zero lift right?
So how much does angle of attack matter compared to the Bernoulli effect in airplane lift?
With an air cannon (a toy made of a barrel that has a round opening on one side and a membrane on the other), you can create a vortex when you hit the membrane.
I have problems understanding the process of creation of the vortex after the air exits the opening of the barrel. Many Internet sources claim that the formation of the vortex is due to the Bernoulli effect, others blame it on the Coanda effect.
Could you explain which is true and why? Thank you!
(As far as I understand, the edge of the outlet opening of the barrel slows down the outer air particles of the outflowing air. The inner air particles retain their high velocity, dragging the outer, slower particles along by internal friction. This entrainment creates a negative pressure at the area around the opening of the barrel (Coanda effect). Air particles from the inner area of the air stream flow into this area to compensate for the pressure differences. This creates the vortex.)
I have 2 functions. In one the user inputs n and it returns a list of the 1st n Bernoulli numbers, recursively generating the Kth number by doing some math on the (k-1)th number. The other function generates and returns only the Nth Bernoulli number. Both functions diverge wildly from what the outputs should be at around n=13 and I'm wondering if this is unavoidable due to rounding errors? I thought errors might be compounding in the 1st function which is why I wrote the second but I'm seeing similar behavior in both. I'm only including the 2nd function here for brevity. Thanks for any insight!
Am I missing something important? Or Mcqueen just literally starts getting old? Aside from saying he's old to race Jackson Storm, are there any reasons why?
There is a question I can't seem to understand regarding fluids.
The question is: "Water is flowing through a circular tube with a cross sectional area of 0.4 m^2 at a rate of 8 m/2. The cross section of the tube decreases to 0.2 m^2 as the tube gains 4 m in height. What is the new velocity of the water?"
The answer provided is:
v1A1 = v2A2 ==> v2 = (8m/s)*(0.4 m^2/0.2 m^2) = 16 m/s
Now we can use the expression for conservation of energy to adjust this velocity for the change in height:
E = Ui + Ki = Uf + Kf
assume initial height is h = 0m... so you can rearrange for vf and get this equation:
vf = sqrt(vi^2 - 2gh)
Then, for vi, 16 m/s is plugged in.
The math in the solution makes sense but I am struggling to understand why we solved the problem this way I guess. I am confused about 2 things:
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How are we able to use the typical kinetic and potential energies for something like water? It's mass isn't really fixed...
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Why is 16 m/s used in the equation for vf? wouldn't the initial velocity be the velocity at the base of the tube?
At first I thought that the dotted line was the reference point and therefore z1= postitive l and z2= negative l, made sense. However if z2 was postive and z1 was negative, the final differential equation would be wrong?
Additionally, I don't understand why velocity would be the negative change in l with respect to time?
Thank you in advance for any tips
https://preview.redd.it/uwtu1i7etka81.png?width=797&format=png&auto=webp&s=30b0d4fe1658522f40b958ad2749e0d45e7eef9a
The Wachowski's Speed Racer (2008) was a critical and commercial failure, but it has always had a special place in my heart. Sure it's campy, the effects are hit and miss in places, and the constant technicolor strobing could give an epileptic a seizure, but I felt it had heart and some really fun racing sequences.
This clip is an edit I did of the final race, the Grand Prix. The original clip was about 12 minutes long. I cut it down to 7:30 by removing most of the dialogue (I left in some of the VOs), and I felt there were a few unnecessary reaction shots and some action shots that just made an already chaotic scene more confusing that needed to go. When you watch the clip, it might not be easy to tell but I truly cut this thing to ribbons (as evidenced by this screenshot of the timeline).
Anyway, I think the final clip really tightened up an already crazily fast-paced scene and made it a little easier to follow. Hope you enjoy and please share any feedback!
link (fyi: this link will disappear in 14 days)
Consider the system in which a pump in a lake increases the pressure in a tube in order to spray water out of a nozzle.
An image with a diagram and my workings.
The pump is supplied with 500W and increases the pressure of water to 1.39 bar. A mass flow rate of 1.1318kg s^-1 is recorded.
Applying the law of thermodynamics and Bernoulli's principle, equation 1 is obtained. Expanding and then upon further simplifying, equation 2 is obtained.
This is where I get stuck. I was told to assume that velocity at A and B are negligible. However I have trouble understanding how that can be possible. Is it correct to neglect the velocities at these points?
Neglecting the velocities give a total energy loss of 448.6W. Which brings the pump efficiency to about 10%.
Is this correct?
I have an issue with Bernoulli's equation, in a venturi pipe. From the general equation used, I've solved the equations for p(1) - p(2), with the areas and without them, with just the pressure and velocities. Now I have to eliminate velocity (v(1) from the equation 1/2*rhoo*(A(1)^2/A(2)^2 - 1) * v(1)^2. I'm supposed to used the equation q(V) = A(1)*v(1) and get the equation for q(V)^2 (so squared). How is this written out using symbols for delta p, rhoo, A(1) and A(2)?
If you can explain how you got there with equations or words, great. Sorry if this is super confusingly written.
Bernoulli's Principle states that for a fluid undergoing steady flow, the pressure is lower where the fluid is flowing faster.
If the fluid is flowing faster wouldn't that result in a higher pressure?
I imagine myself standing in a really large pipe that has fluid flowing through it. I experience pressure. I then move further down to where the pipe is narrower, so the velocity of the fluid increases. I am being hit by the same fluid, but faster. This results in a greater force, and the surface area it is acting on, my surface area, stays the same. Pressure increased. That's my thinking at least. Where's the mistake in my thinking?
I have started watching the show for the first time in a while and I had to rewind a few times to double check, but I believe when Professor Slater says "the Bernoulli distribution is the number of successes in a sequence of independent yes-no experiments", she meant to say the binomial distribution. A small issue, but as a maths student, it really bugged me.
Idk if this is the place to ask but was wondering if anyone could help me get my head around this.
Timoshenko Beam Theory takes into account shear deformation so is more accurate for shorter, bigger cross sectioned beams than Euler Bernoulli that doesn't.
For a simple cantilever with a point load on the end, Euler Bernoulli's equation is (PL^3)/3EI and Timoshenko's equation is (PL^3)/3EI + PL/kAG where all symbols are what you'd expect them to be and k is the shear coefficient whicj for rectangular cross sections is only a function of poissons ratio (sources Wikipedia).
This hence shows that the only difference between the two is the PL/kAG term which is only effected by L/A with the other variables being constants.
Yet this decreases as the cross section increases wrt the length of the beam meaning that Timoshenko approaches the Euler Bernoulli value as the beam becomes shorter and bigger cross sectioned????
What is going on here. Where is the hole in my logic.
doesnt bernoulli show that flow rate is always the same????
So when there is a sudden contraction in a pipe, water flowing through the smaller diameter portion will increase in velocity because volumetric flow rate stays the same. Bernoulli's Principle states that this velocity increase is accompanied by a pressure drop in that region. If the pressure drops low enough, you can get steam bubbles and thus cavitation in the smaller diameter section of the pipe shortly after the contraction.
I think I understand this from an equation perspective using Bernoulli's equation: Since the total pressure is constant, when the dynamic pressure increases due to the jump in velocity, the static pressure term must decrease, which is the pressure drop we see.
I can accept the math, but I'm failing miserably to internalize the truth it is stating. To do that, I need an explanation that paints an imaginary image in my mind of the water molecules zipping through the pipe, and why some of those molecules would change to the gas phase when the molecules start moving faster through the pipe.
Allow me to present an example that acts as a metaphor for the type of explanation I'm trying to get:
Looking at a pipe contraction, A1V1 = A2V2. If A2 is smaller than A1, then V2 must be bigger than V1. To understand that is to understand the math, and that's as far as I'm at with Bernoulli's Principle.
But now let's think about the logic behind A1V1 = A2V2. If I want to move the same amount of fluid volume the same amount of distance in the same amount of time but through a smaller space, the fluid will have to move faster in order to make it through the distance in time. This is the type of explanation I'm looking for with Bernoulli's Principle.
I feel like I've watched every video and read so many web pages but I still don't get it, maybe I'm retarded or something but I would appreciate it if someone could get Bernoulli's Principle through my thick skull.
Thank you!
