### Fluid dynamics and Bernoulli's equation

The equation states that the static pressure ps in the flow plus the dynamic pressure, one half of the density r times the velocity V squared, is equal to a As discussed on the gas properties page, there are two ways to look at a fluid; from the. consider a cylider full of gas. Thus gas is exerting pressure on walls of cylinder while its velocity is zero. Now open the mouth of cylinder, u will. The higher the velocity of a fluid (liquid or gas), the lower the pressure it exerts. This is called Bernoulli's Principle. Fluid pressure is caused by.

- Bernoulli’s Effect – Relation between Pressure and Velocity
- Bernoulli's Equation
- Fluid dynamics and Bernoulli's equation

The total energy of the fluid is the sum of the energy the fluid possesses due to its elevation elevation headvelocity velocity headand static pressure pressure head.

The energy loss, or head loss, is seen as some heat lost from the fluid, vibration of the piping, or noise generated by the fluid flow. Between two points, the Bernoulli Equation can be expressed as: In other words, the upstream location can be at a lower or higher elevation than the downstream location.

If the fluid is flowing up to a higher elevation, this energy conversion will act to decrease the static pressure.

If the fluid flows down to a lower elevation, the change in elevation head will act to increase the static pressure. Conversely, if the fluid is flowing down hill from an elevation of 75 ft to 25 ft, the result would be negative and there will be a Pressure Change due to Velocity Change Fluid velocity will change if the internal flow area changes.

Likewise, drag on an airfoil is defined as the force acting on an airfoil due to its motion, along the direction of motion.

## Bernoulli’s Effect – Relation between Pressure and Velocity

An easy demonstration of the lift produced by an airstream requires a piece of notebook paper and two books of about equal thickness. Place the books four to five inches apart, and cover the gap with the paper.

When you blow through the passage made by the books and the paper, what do you see? Example 1 A table tennis ball placed in a vertical air jet becomes suspended in the jet, and it is very stable to small perturbations in any direction.

Push the ball down, and it springs back to its equilibrium position; push it sideways, and it rapidly returns to its original position in the center of the jet.

**Pressure and velocity in pipes**

In the vertical direction, the weight of the ball is balanced by a force due to pressure differences: To understand the balance of forces in the horizontal direction, you need to know that the jet has its maximum velocity in the center, and the velocity of the jet decreases towards its edges. The ball position is stable because if the ball moves sideways, its outer side moves into a region of lower velocity and higher pressure, whereas its inner side moves closer to the center where the velocity is higher and the pressure is lower.

The differences in pressure tend to move the ball back towards the center.

Example 3 Suppose a ball is spinning clockwise as it travels through the air from left to right The forces acting on the spinning ball would be the same if it was placed in a stream of air moving from right to left, as shown in figure Spinning ball in an airflow.

A thin layer of air a boundary layer is forced to spin with the ball because of viscous friction. At A the motion due to spin is opposite to that of the air stream, and therefore near A there is a region of low velocity where the pressure is close to atmospheric. At B, the direction of motion of the boundary layer is the same as that of the external air stream, and since the velocities add, the pressure in this region is below atmospheric.

The ball experiences a force acting from A to B, causing its path to curve. The second way is to make the pressure at one end of the pipe larger than the pressure at the other end.

A pressure difference is like a net force, producing acceleration of the fluid.

As long as the fluid flow is steady, and the fluid is non-viscous and incompressible, the flow can be looked at from an energy perspective. This is what Bernoulli's equation does, relating the pressure, velocity, and height of a fluid at one point to the same parameters at a second point.

The equation is very useful, and can be used to explain such things as how airplanes fly, and how baseballs curve.

### fluid dynamics - Relation between pressure, velocity and area - Physics Stack Exchange

Bernoulli's equation The pressure, speed, and height y at two points in a steady-flowing, non-viscous, incompressible fluid are related by the equation: Some of these terms probably look familiar If the equation was multiplied through by the volume, the density could be replaced by mass, and the pressure could be replaced by force x distance, which is work.

Looked at in that way, the equation makes sense: For our first look at the equation, consider a fluid flowing through a horizontal pipe. The pipe is narrower at one spot than along the rest of the pipe. By applying the continuity equation, the velocity of the fluid is greater in the narrow section.

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.