Fluids in Motion: Crash Course Physics #15
TLDRThis video explains fluid dynamics concepts like the continuity equation, Bernoulli's principle, and Torricelli's theorem. It imagines a simplified fictional world to make fluid calculations easier, assuming fluids have no viscosity or compressibility. The continuity equation states that in any pipe system, the mass flow rate is the same everywhere. Bernoulli's principle builds on continuity by showing that when a pipe narrows, fluid speed increases but pressure decreases. Torricelli's theorem calculates fluid speed coming out of a container's spout based on the container's height, using conservation of energy. The episode aims to help viewers grasp key fluid motion principles while acknowledging real-world complexities.
Takeaways
- 😀 To understand fluid dynamics, we make simplifying assumptions like fluids being incompressible and having no viscosity
- 😯 The mass flow rate of an incompressible fluid is the same everywhere in a pipe according to the equation of continuity
- 🔍 You can calculate mass flow rate using density, area and velocity instead of mass and time
- 🌊 Where a pipe narrows, fluid velocity increases to maintain the same mass flow rate
- 📉 Faster flowing fluids have lower pressure on pipe walls as stated in Bernoulli's principle
- 🤓 Bernoulli's equation combines conservation of energy and different energy densities in a flowing fluid
- 💧 Torricelli's theorem relates outlet velocity to the theoretical velocity of a falling drop from the fluid surface level
- 👆 Turning the outlet to point upwards would make the stream reach the initial fluid level under ideal conditions
- 📐 Understanding relationships between pressure, velocity and pipe structure is key in fluid dynamics
- 🎥 The episode was produced with help from Thought Cafe and filmed in the Dr. Cheryl C. Kinney Studio
Q & A
Why do we make assumptions and pretend certain things are not happening when studying fluid dynamics?
-Because fluids in motion are dynamic and there are many complex factors at play. By making simplifying assumptions like fluids being incompressible and having no viscosity, we can grasp the essential concepts more easily.
What is the equation of continuity and what does it state?
-The equation of continuity states that the mass flow rate of a fluid is the same at any point along a pipe. Specifically, it says that density × area × velocity is a constant.
How does Bernoulli's principle relate velocity to pressure in a fluid flow?
-Bernoulli's principle states that within a fluid flow, higher velocity corresponds to lower pressure, and lower velocity corresponds to higher pressure.
What forms of energy are included in Bernoulli's equation?
-Bernoulli's equation includes pressure energy, kinetic energy, and gravitational potential energy.
What is Torricelli's theorem?
-Torricelli's theorem states that the velocity of fluid flowing from a spout is the same as the velocity a single droplet would reach falling from the fluid surface height in the reservoir.
How can you use Bernoulli's equation to derive a kinematic equation?
-By setting the pressure terms equal on both sides and eliminating gravitational potential energy, Bernoulli's equation simplifies down to a kinematic equation relating velocity, height difference, and acceleration due to gravity.
What causes the change in velocity as a fluid flows from a wider to narrower pipe cross-section?
-The continuity equation requires that if area decreases then velocity must increase to maintain the same mass flow rate.
Why does the pressure decrease as the fluid flows through a narrower section of pipe?
-According to Bernoulli's principle, as velocity increases in the narrower pipe the pressure exerted on pipe walls decreases.
What practical use does knowing the velocity of water from a rain barrel spout serve?
-Knowing the velocity allows calculating the volume flow rate, which helps determine how much water is delivered for gardening over a time period.
How high would the water spout reach if aimed vertically upward?
-Thanks to conservation of energy, it would reach exactly as high as the water level in the reservoir tank before falling back down.
Outlines
😄 Fluid Dynamics Concepts and Continuity Equation
Introduces basic fluid dynamics concepts like mass flow rate, equation of continuity relating fluid velocity, density and pipe area. Explains how these concepts allow calculating mass flow rate at any point in a pipe based on area and velocity.
😃 Bernoulli's Equation and Torricelli's Theorem
Explains Bernoulli's equation as an energy conservation principle applied to fluids. Breaks down the terms for pressure energy, kinetic energy and potential energy. Describes Torricelli's theorem as a special case relating velocity of fluid from a tank spout to free fall under gravity from the tank height.
Mindmap
Keywords
💡Fluid dynamics
💡Equation of continuity
💡Bernoulli's principle
💡Torricelli's theorem
💡Kinetic energy
💡Potential energy
💡Pressure
💡Density
💡Viscosity
💡Mass flow rate
Highlights
Describing the rules of the universe sometimes requires us to pretend that certain things aren’t happening.
The same is true when we talk about fluids. Because, fluids in motion are dynamic and there are many, many things going on in and around them all at once.
The mass flow rate is the same for every point in the pipe.
Where the pipe is narrower, the fluid will have to flow faster, in order to compensate.
The higher a fluid’s velocity is through a pipe, the lower the pressure on the pipe’s walls, and vice versa.
As a fluid flows through a pipe, it won’t gain or lose any energy.
Bernoulli divided all these terms by volume, because when it comes to fluids, it’s just easier to talk about things in terms of density than it is to talk about mass.
The velocity of the fluid coming out of the spout is the same as the velocity of a single droplet of fluid that falls from the height of the surface of the fluid in the container.
It’s exactly the same equation as the one we just found by using Bernoulli’s equation.
Torricelli’s theorem tells you that if a droplet of water fell from the same height as the top of the barrel, when it reached the level of the spout, it’d have the same velocity as the water coming out of the spout.
If the water from this spout could shoot straight up, the stream would get exactly as high as the water at the top of the barrel, before falling down to the ground.
Lawn mowers are loud.
Fluids that don’t flow as easily, like honey, have a higher viscosity.
The water at the top of the barrel isn’t going to be moving very much. In fact, we can say that its velocity is basically zero.
You also learned that lawn mowers are loud.
Transcripts
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