Torricelli Law - Tank With Holes Verse Water Being Poured - Find Velocity of Water (Fluid Mechanics) скачать в хорошем качестве

Torricelli Law - Tank With Holes Verse Water Being Poured - Find Velocity of Water (Fluid Mechanics)

We have a jug filled with water with a hole in the bottom of the jug. The height of the water line from the hole at the bottom is .17 meters. If we were to pour water out of a graduated cylinder at the water line of the jug which we will refer to as point 1. How will the velocity of the graduated cylinder water compare to the velocity of the water coming out of the hole in the bottom of the jug if we measure both velocities at the same height. We will refer to the point where the water is coming out of the jug as point 2. We will be assuming a fluid with not friction or viscosity so we can use the Bernoulli equation. The bernolli equation states that the pressure energy plus the potential energy plus the kinetic energy equals the total energy in the fluid. Being that energy is conserved we can set the total energy or Bernoulli equation at point 1 equal to the bernolli equation at point 2 We first notice that the only pressure acting on these systems is atmospheric pressure. Being that atmospheric pressure is on both sides of the equation it get cancled out and removed from the equation Next we assume at point 1 there is not much movement of the water so relatively speaking there is no kinetic energy. At point 2 we will be setting the height at 0 which makes the potential energy at point 2 zero relatively speaking. We are left with density time gravity times height 1 being equal to one half density time velocity squared. Or in other words potential energy at point 1 equals kinetic energy at point 2 Next we notice that density is on both sides of the equation so it can be canceled out. Now we need to get velocity 2 which we are solving for by itself on one side of the equation. We first divded both sides by one half Then we take the square root of both sides. We are left with the square root of 2 times gravity time height at point 1 being equal to the velocity at point 2. Plugging in all of our givens we get a velocity at point 2 of 1.83 meters per second for both the graduated cylinder example and the jug filled with water example. This problem shows torricelli’s law. Torricelli’s law states that the velocity of the water coming out of the bottom of the tank is equal to the velocity of water if it were left to fall from the height of the water line of the tank Stated another way if you put holes in a tank and let liquid fall from another reservoir from the water line of the tank. The fluid coming out of the holes will have the same velocity (but possibly different direction) as the fluid directly across from it falling from the water line. The velocity of water coming out of the holes or falling out the reservoir is represented by the formula square root 2 times gravity time the vertical height from waterline to center line of the hole or water line to point of interest on stream. Which is simply the projectile motion velocity equation for a free falling object. Disclaimer These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.