- Volume flow rate and equation of continuity
- What is volume flow rate?
- Bernoulli's equation derivation part 1
- Bernoulli's equation derivation part 2
- Finding fluid speed exiting hole
- More on finding fluid speed from hole
- Finding flow rate from Bernoulli's equation
- What is Bernoulli's equation?
- Viscosity and Poiseuille flow
- Turbulence at high velocities and Reynold's number
- Venturi effect and Pitot tubes
- Surface Tension and Adhesion
A fluid’s motion is affected by its speed, density, and viscosity, and weight, as wells as drag and lift. Use an example of a pipe with different sized openings on either end to observe and quantify laminar flow of liquids. Learn about the concept of flux, and how it is used to calculate the power of a system with moving fluid. Created by Sal Khan.
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- can you please tell me what does a venturi meter mean?(16 votes)
- A venturi meter is a way to measure flow in a pipe. The venturi is a section of pipe where the diameter is gradually reduced to some smaller area then gradually increased to the initial diameter
To measure the flow in the pipe you measure the pressure at the inlet and then again at the narrowest section of the venturi.
Assuming no friction. Conservation of energy tells you that the pressure in the reduced area will be lower because the velocity is increased (speeding a fluid up lowers it pressure, some what counter intuitive because we think of pressure in terms of force not potential energy)
Flow rate (Q) = velocity * Area
Q1 = Q2 v1 * A1 = v2 * A2
Potential Energy + Kinetic Energy remains constant. P1 + (1/2density *v1^2) = P2 + (1/density *v2^2)
you can solve these 2 equations for Q (refer to http://en.wikipedia.org/wiki/Venturi_effect)
- You appear to be saying that volume in = volume out only applies if laminar flow exists. Does this mean that fluid is lost or gained in the case of turbulent flow?(13 votes)
- Regardless of whether a flow is laminar or turbulent, if it is incompressible then volume in will always be equal to volume out. Since we're dealing with an incompressible liquid, this is always the case.
The example about emptying a bottle is a little confusing, because in that case the incompressible water is being replaced by air, which is very much compressible.(6 votes)
- Could you please tell me what kind of Flux Sal meant?because if he meant Momentum flux, the rate of transfer of momentum across a unit area, or Volumetric flux, the rate of volume flow across a unit area,why its far from his explaination about flux which he said its volume over time and its unit is m^3/s(10 votes)
- Hi there, I believe Sal has mixed up his terminology here.
He says that V/t is flux, but actually it is Volume Flow Rate, Q (units m^3/s).
Volumetric Flux is actually this flow rate per unit area, i.e. V/t.A, symbol q (units m^3/s.m^2).(14 votes)
- Is this the equation of continuity(5 votes)
- It is better known as 'Conservation of Mass'. Mass in = Mass out.
Since in the case Sal showed us there is mass flow (or mass flux), the flow into the nozzle must be equal to the flow out of the nozzle (because the flow can't go anywhere but out the other end). The flow at the entrance and the flow at the exit is given by the same equation (density)*(area)*(velocity).(11 votes)
- At2:07, we should consider the time taken as dt 'coz the velocity changes as soon as the cross sectional area changes but for dt time we can assume that to be constant.(7 votes)
- He is simplifying the problem. He is considering the inlet velocity to be constant over the time of interest.(5 votes)
- Minute4:43. I think it is actually in-viscid flow not laminar flow. As with laminar flow you can still have viscosity effects,...?(5 votes)
- Laminar flow is when a fluid flows in parallel layers with no disruption between the layers. Unless the wals of the container are frictionless the fluid next to the wall of the container that it is flowing through causes it to flow slower than the middle of the container causing a difference in velocity of the fluid. With low velocity and/or viscosity you can have laminar flow, above a critical velocity which is inversely dependent on the viscosity the flow will become turbulent. This ratio of a fluids velocity vs viscosity is related to the Reynolds Number for the fluid.(4 votes)
- how do we know that water is leaving from the entire output area of the cylinder as shown in the diagram? there aren't any forces pushing the water up so shouldn't the depth of the water in respect to the bottom of the cylinder remain constant throughout the cylinder?(5 votes)
- The pipe is tilting downward but according to the equation Ai*Vi=Ao*Vo shouldn't the liquid decelerate instead. How is that possible?(1 vote)
- He is not considering gravity. You interpret this problem as happening in a space station. Or that the pipe section shown is not vertical, but horizontal, so we see the pipe from above.(8 votes)
- Could you tell me how to deal with the question if the tube splits into two paths with smaller radii? Thanks.(3 votes)
- Volume flow rate would still remain constant. The sum of the flow rates in the two tubes is still equivalent to the flow rate in the original tube.(3 votes)
- Why did the sal said: time same time?6:09(1 vote)
- he meant that we are considering as much time as the liquid took iniatialy.It means that if the fluid take 2 seconds to cover the initial volume (which sal drew in pink) then we will consider the same 2 seconds for the exit volume. was it helpful?(5 votes)
Everything we've done so far has been stationary fluids, or static fluids, and we've been dealing with static pressure. We were trying to figure out what happens when everything's in a steady state. Now let's work on what happens when the fluid is actually moving. Let's imagine a pipe. Let's say one end of the pipe has a larger area than the other end, or at least a different area. So this is one end of the pipe, and this is the other end of a pipe. It's filled with some fluid, some liquid, actually, in our example, so there's just a bunch of liquid in this fluid. Let's say this area at the entrance is called the area in. That's the area of the opening into the pipe, and let's call this area out. It's the area of the opening coming out of the pipe. Let's think about what happens if this liquid is actually moving. Let's say it's moving into the pipe with the velocity V in. Let's think about how much volume moves into the pipe after T seconds. After T seconds, if you think about it, you'd have this much area. If you think about what was right here, it will then be moved to the right by how much? We could just go back to our basic kinematic formula: distance is equal to rate times time. The distance something travels equals velocity times time, so after T seconds, whatever fluid was here, it would have an area of about that much. Whatever fluid was there would have traveled how much to the right? It would have traveled-- let's assume that the pipe doesn't change too much in diameter or in radius from here to here. It would have traveled velocity times time, so V in times time. It could be meters or whatever our length units are. After T seconds, essentially this much water has traveled into the pipe. You could imagine a cylinder of water here. Once again, I know I made it look like it's getting wider the whole time, but let's assume that its width doesn't change that much over the T seconds or whatever units of time we're looking at. What is the volume of this cylinder of water? The volume-in over the T seconds is equal to the area, or the left-hand side of the cylinder. Let me draw the cylinder in a more vibrant color so you can figure out the volume. So it equals this side, the left side of the cylinder, the input area times the length of the cylinder. That's the velocity of the fluid times the time that we're measuring, times the input velocity times time. That's the amount of volume that came in. If that volume came into the pipe-- once again, we learned several videos ago that the definition of a liquid is a fluid that's incompressible. It's not like no fluid could come out of the pipe and all of the fluid just gets squeezed. The same volume of fluid would have to come out of the pipe, so that must equal the volume out. Whatever comes into the pipe has to equal the volume coming out of the pipe. One assumption we're assuming in this fraction of time that we're dealing with is also that there's no friction in this liquid or in this fluid, that it actually is not turbulent and it's not viscous. A viscous fluid is really just something that has a lot of friction with itself and that it won't just naturally move without any resistance. When something is not viscous and has no resistance with itself and moves really without any turbulence, that's called laminar flow. That's just a good word to know about and it's the opposite of viscous flow. Different things have different viscosities, and we'll probably do more on that. Like syrup or peanut butter has a very, very high viscosity. Even glass actually is a fluid with a very, very high viscosity. I think there's some kinds of compounds and magnetic fields that you could create that have perfect laminar flow, but this is kind of a perfect situation. In these circumstances, the volume in, because the fluid can't be compressed, it's incompressible, has to equal the volume out. What's the volume out over that period of time? Similarly, we could draw this bigger cylinder-- that's the area out-- and after T seconds, how much water has come out? Whatever water was here at the beginning of our time period will have come out and we can imagine the cylinder here. What is the width of the cylinder? What's going to be the velocity that the liquid is coming out on the right-hand side? Capital V is volume, and lowercase v is for velocity, so it's going to be the output velocity-- that's a lowercase v-- times the same time. So what is the volume that has come out in our time T? It's just going to be this area times this width, so the output volume over that same period of time is equal to the output area of this pipe times the output velocity times time. Once again, I know I keep saying this, but this is kind of the big ah-hah moment, is in that amount of time, the volume in this cylinder has to equal the volume in this cylinder. Maybe it's not as wide, or something like that, but their volumes are the same. You can't get more water here all of a sudden than what's going in, and likewise, you can't put more water into the left side than what's coming out of the right side, because it's incompressible These two volumes equal each other, so we know the area of the opening onto to the left hand of the pipe times the input velocity times the duration of time we're talking about is equal to the output area times the output velocity times the duration of time we're talking about. It's the same time on both sides of this equation, so we could say that the input area times the input velocity is equal to the output area times the output velocity. This is actually called in fluid motion the equation of continuity, and it leads to some interesting things. We'll do some problems with it in a second. One thing that I want to introduce at this point as well is what is the volume per second? Because this is also something we're going to deal with in a second, probably in the next video, because I'm about to run out of time. We said that in T seconds we have this amount of volume coming in and it's the same coming in as coming out. So what is the volume per second? It's this big capital Vi per amount of time, and we call that flux. We'll learn a lot about flux, especially when we start doing vector calculus, but flux is just how much of something crosses a surface in an amount of time. It's how much a volume crosses a surface in an amount of time. So in this case, the surface is the left-hand side of cylinder. And we're saying how much crosses in amount of time? We figured out it's that input volume, which crosses in every T seconds, and this is called flux. You've probably heard of the flux capacitor in Back To The Future, and maybe we can think about what they were trying to hint at. Let's see if we can use flux and these ideas to come up with some other interesting equations. We know that the volume per time is equal to flux. This is a big V. V is equal to flux, and actually the variable people generally use for flux is R. Of course, it's in meters cubed per second. That's its unit. We also know that the input area times input velocity-- that's a lowercase v-- is equal to the output area times output velocity, and this is called the equation of continuity. It holds true whenever we have laminar flow. Actually, I'm about to run out of time. In the next video, I'm actually going to use some of this information to figure out how much power is there in a system where we have fluid going through a pipe. See you soon.