fluid dynamics - Relation between pressure, velocity and area - Physics Stack Exchange
Because of their ability to flow, fluids can exert buoyant forces, multiply forces in a The formula that gives the P pressure on an object submerged in a fluid is: The density of sea water is X 10 3 kg/m3 and the atmospheric pressure is. The concept of pressure is closely related to the important You can understand the pressure of a fluid by visualizing water flowing through a hose. Thus, the pressure of a fluid can also be defined as energy density: the. The density of a liquid will change with temperature and pressure. The density of water versus temperature and pressure is indicated below: Water density vs.
How does pressure affect density of fluid?
For example, if you use your fingertip to apply a mild downward force to a cucumber, nothing happens. If you apply that same force with the blade of a sharp knife, you slice through the cucumber. The force is the same but the edge of the blade has a much smaller surface area, and thus the force per unit area -- in other words, the pressure -- is much higher.
Flowing Forces Pressure applies to both fluids and solid objects. You can understand the pressure of a fluid by visualizing water flowing through a hose. The moving fluid exerts a force on the inside walls of the hose, and the pressure of the fluid is equivalent to this force divided by the interior surface area of the hose at a given point. Sciencing Video Vault Confined Energy If pressure equals force divided by area, pressure also equals force times distance divided by area times distance: Area times distance is equivalent to volume, and force times distance is the formula for work, which in this situation, is equivalent to energy.
Thus, the pressure of a fluid can also be defined as energy density: For the simplified case of a fluid that does not change elevation as it flows, total energy is the sum of the energy of the pressure and the kinetic energy of the moving fluid molecules. Is the pressure higher or lower in the narrow section, where the velocity increases?
Your first inclination might be to say that where the velocity is greatest, the pressure is greatest, because if you stuck your hand in the flow where it's going fastest you'd feel a big force. The force does not come from the pressure there, however; it comes from your hand taking momentum away from the fluid. The pipe is horizontal, so both points are at the same height. Bernoulli's equation can be simplified in this case to: The kinetic energy term on the right is larger than the kinetic energy term on the left, so for the equation to balance the pressure on the right must be smaller than the pressure on the left.
It is this pressure difference, in fact, that causes the fluid to flow faster at the place where the pipe narrows. A geyser Consider a geyser that shoots water 25 m into the air. How fast is the water traveling when it emerges from the ground? If the water originates in a chamber 35 m below the ground, what is the pressure there? To figure out how fast the water is moving when it comes out of the ground, we could simply use conservation of energy, and set the potential energy of the water 25 m high equal to the kinetic energy the water has when it comes out of the ground.
Another way to do it is to apply Bernoulli's equation, which amounts to the same thing as conservation of energy.
Let's do it that way, just to convince ourselves that the methods are the same. But the pressure at the two points is the same; it's atmospheric pressure at both places. We can measure the potential energy from ground level, so the potential energy term goes away on the left side, and the kinetic energy term is zero on the right hand side.
This reduces the equation to: The density cancels out, leaving: This is the same equation we would have found if we'd done it using the chapter 6 conservation of energy method, and canceled out the mass. To determine the pressure 35 m below ground, which forces the water up, apply Bernoulli's equation, with point 1 being 35 m below ground, and point 2 being either at ground level, or 25 m above ground.
Let's take point 2 to be 25 m above ground, which is 60 m above the chamber where the pressurized water is. We can take the velocity to be zero at both points the acceleration occurs as the water rises up to ground level, coming from the difference between the chamber pressure and atmospheric pressure.
The pressure on the right-hand side is atmospheric pressure, and if we measure heights from the level of the chamber, the height on the left side is zero, and on the right side is 60 m. Why curveballs curve Bernoulli's equation can be used to explain why curveballs curve.
Let's say the ball is thrown so it spins. As air flows over the ball, the seams of the ball cause the air to slow down a little on one side and speed up a little on the other.
The side where the air speed is higher has lower pressure, so the ball is deflected toward that side. To throw a curveball, the rotation of the ball should be around a vertical axis. It's a little more complicated than that, actually.
Fluid dynamics and Bernoulli's equation
Although the picture here shows nice streamline flow as the air moves left relative to the ball, in reality there is some turbulence. The air does exert a force down on the ball in the figure above, so the ball must exert an upward force on the air.
This causes air that travels below the ball in the picture to move up and fill the space left by the ball as it moves by, which reduces drag on the ball.