Bernoulli's equation (part 1) | Fluids | Physics | Khan Academy

TL;DR

This video discusses the conservation of energy in fluid flow and explores the work, potential energy, and kinetic energy involved in a pipe system.

Transcript

Let's say we have a pipe again-- this is the opening-- and we have fluid going through it. The fluid is going with a velocity of v1, the pressure entering the pipe is P1, and then the area of this opening of the pipe is A1. It could even go up, and the other end is actually even smaller. The fluid-- the liquid-- is exiting the pipe with velocity v2... Read More

Key Insights

• 💐 The conservation of energy principle applies to fluid flow systems.
• 💦 Work is calculated by multiplying pressure, area, velocity, and time.
• 💆 Potential energy is determined by mass, gravity, and height.
• 🤪 The total energy going into the system equals the sum of work, potential energy, and kinetic energy.
• 🔠 Energy components on the output side are similar to those on the input side.
• ❓ Mass remains constant in the system.
• 👮 The video emphasizes the importance of the law of conservation of energy.

Questions & Answers

Q: How is the work being put into the system calculated?

The work input is calculated by multiplying the input pressure, volume of fluid moved, and time, which can be expressed as the input pressure times the input area times the input velocity times time.

Q: What determines the potential energy of the system?

The potential energy is determined by multiplying the mass of the fluid by gravity and the initial height of the fluid, denoted as the input height (h1).

Q: How can the total energy going into the system be calculated?

The total energy going into the system is equal to the work done (input pressure times the mass divided by density), potential energy (mass times gravity times input height), and kinetic energy (mass times input velocity squared divided by 2).

Q: What are the energy components on the output side?

On the output side, the energy components include the work out (output pressure times the mass divided by density), potential energy (mass times gravity times output height), and kinetic energy (mass times output velocity squared divided by 2).

Summary & Key Takeaways

• The video introduces a pipe system with fluid flowing through it, emphasizing the velocities, pressures, and areas of both the input and output of the pipe.

• The law of conservation of energy is applied to the system, stating that the energy input must equal the energy output in any closed system.

• The video provides calculations for the work being done, potential energy, and kinetic energy in the system.