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### Course: Physics library > Unit 9

Lesson 3: Fluid Dynamics- 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

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# Turbulence at high velocities and Reynold's number

Explore the concept of Reynold's Number, a key predictor of fluid turbulence. Understand how this dimensionless quantity, calculated using viscosity, fluid density, and tube radius, helps identify the critical speed at which fluid flow becomes chaotic. This knowledge is particularly useful in predicting blood flow turbulence in the aorta.

## Want to join the conversation?

- 1:38I don't quite get the concept of a "unit less" quantity. If blood has a Reynold's number of 2000, it has to, somewhere, be related to something else, doesn't it? Any clarification is appreciated.(10 votes)
- The Reynolds number seems to be a ratio of forces involved in the flow of a fluid. Oftentimes, it gets defined as (inertial forces)/(viscous forces). We can just consider it as an "artificial construct", just like the way mole fractions are used to help determine partial pressures of gases.

Does this help?(14 votes)

- I'd like you to explain how this Reynold's number can affect airflow around an airfoil during flight. And for something like this how do we go about figuring the "radius". Especially when the plane/wings are stalled.(9 votes)
- Airflow accelerates over an airfoil. When the speed of airflow passes the critical speed, turbulent airflow happens and boundary layer separation occurs. The air particles closest to the wing experience more friction, and will therefore stop, this slows down the air particles above it and the process continues. These pockets of air moving at different speeds cause eddies and will cause drag and reduced lift. When a wing is stalled, this happens closer to the leading edge of the wing making the wing ineffective. That's why there are technologies such as vortex generators to prevent such events. This concept is difficult to explain without using Autodesk CFD software.(2 votes)

- What is the difference between turbulent and unsteady flow of a fluid ?(5 votes)
- I would say that unsteady is most likely to mean that its speed is not constant.

Turbulent means it is not laminar.

ok??(4 votes)

- what's the difference between viscosity and density? They both sound like measures of how thick a fluid is but they affect critical velocity in opposite directions(3 votes)
- Density is a measure of mass per volume. Viscosity is a measure of resistance to flow.

Mercury has a high density but very lower viscosity compared to water. Lava has a higher density than water, but also a higher viscosity.(3 votes)

- The Reynold's number is" unit less" and "dimension less". I do not understand this?(2 votes)
- When we say unitless we mean that it is a number like 1 or 2. It doesn't have centimeter attached to it, for example.

Dimension-less means that it is the same in 1d, 2d or 3d.(3 votes)

- Isn't Reynold's number calculated by (ρvD)/μ? What confuses me is that Reynolds number itself depends on v, so how could it be used to find the critical velocity? Thanks!!(1 vote)
- yes (ρvD)/μ is the formula. in the video it is said divide by 2r which is nothing but diameter. if u know which is the critical reynold's number for a flow to be turbulent (i.e the range over which flow becomes turbulent) for a given fluid you can find what is the critical velocity. Then by simply finding the velocity at the end of pipe or apparatus you can say the flow is turbulent or laminar.you dont need to calculate reynold's numer for each time.

OVERALL for simplicity sake it is said to find critical velocity.

doesn't it bother from where will i get these reynold's number??

they have done already experiments for different fluids and find out which is the range for fluid flow to be laminar and turbulent for nearly all existing fluids known to be in use.

hope it helps

correct me if i am wrong anyone it will be more use for me if i am wrong.(2 votes)

- How does volume that will flow per time, given by Poiseuelle's law, relate to the critical speed of the fluid? Is it through the specific values of the non-constants in the critical speed equation like viscosity and radius of tube?(1 vote)
- Poiseulle's law is only valid below a Reynold's number of 2000 which corresponds to laminar flow. The critical speed is the speed, for a given pipe with specific radius, that will achieve a Reynolds number of 2000. Therefore, critical speed is the fastest a fluid can flow where Poiseulle's law accurately describes the flow.(2 votes)

- Everything discussed so far, and to be discussed in the next sections are only for liquids, is that correct?(1 vote)
- 1:30but why that formula works?(1 vote)
- well what is the volumetric flow rate when there is turbulence(again assuming it is a newtonian fluid)?(1 vote)

## Video transcript

- [Voiceover] Okay so we saw that if you have nice laminar streamline flow, Poiseuille's Law told you how much volume per time would flow through a pipe. But how do you know when you're going to have a nice laminar flow? What determines when this
thing becomes chaotic? What determines when these start to cross, these layers of flowing water, or fluid? How you know when they're
going to start to cross, which is going to cause these
vortices and eddy currents. When will this happen? Turns out, there's a way to predict it. It's hard. This is very hard. In fact, not only is
it hard to predict it, once you know that it's going to happen, once you know things are
going to become turbulent, it's even harder to try
to describe the behavior. Typically you have to resort
to a computer simulation rather than an analytical calculation. But there is a number, it's called the Reynold's Number. What this number does is it
gives you a way to predict what's the first speed, what's the critical speed... Where if you went over this speed, if the fluid were to flow
faster than this speed it would become turbulent. The flow would become chaotic. The way you find it is you
take this Reynold's Number-- I'm going to call that R-- you multiply that by the viscosity. Remember eta, this Greek letter we were
using for the viscosity. You divide by two times
the density of the fluid, multiplied by the radius of the tube. This gives you the first speed where you would expect turbulence. Now, if you measure the Reynold's Number to give you an idea for blood, because this comes up a
lot when you're talking about blood flow and the aorta you might worry that
there might be turbulence. For blood, the Reynold's
Number is around two thousand. It's unitless, it has no dimensions. There's no units here,
all the units cancel out. The Reynold's Number is a
unitless, dimensionless quantity. Knowing the Reynold's Number gives you a way to predict what's
the first speed where you might expect turbulence, and therefore the first
speed where you might expect Poiseuille's Law to not
give you an accurate description of the flow of the fluid.