# Pressure and flow velocity relationship

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

To understand the relationship between the pressure drop across a pipeline and the flow rate through that pipeline, we need to go back to one. The relationship between velocity and pressure for incompressible flow ( constant fluid density) is given by Bernoulli's Law. Where v is flow velocity, rho is . Reynolds number (Re) is a dimensionless velocity value used to predict flow Bernoulli's Equation is used to determine fluid velocities through pressure.

This is the source of lift on an airfoil. Lift is defined as the force acting on an airfoil due to its motion, in a direction normal to the direction of motion. Likewise, drag on an airfoil is defined as the force acting on an airfoil due to its motion, along the direction of motion.

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.

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.

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

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.

If the spin was counterclockwise, the path would have the opposite curvature. The appearance of a side force on a spinning sphere or cylinder is called the Magnus effect, and it well known to all participants in ball sportsespecially baseball, cricket and tennis players.

Stagnation pressure and dynamic pressure Bernoulli's equation leads to some interesting conclusions regarding the variation of pressure along a streamline. Consider a steady flow impinging on a perpendicular plate figure There is one streamline that divides the flow in half: Along this dividing streamline, the fluid moves towards the plate.

### What is the relationship between pressure and velocity for a liquid and gas? | How Things Fly

To understand the relationship between the pressure drop across a pipeline and the flow rate through that pipeline, we need to go back to one of the most important fundamental laws that governs the flow of fluid in a pipe: Total Fluid Energy Daniel Bernoulli, a Swiss mathematician and physicist, theorized that the total energy of a fluid remains constant along a streamline assuming no work is done on or by the fluid and no heat is transferred into or out of the fluid.

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.

### Bernoulli’s Effect – Relation between Pressure and Velocity - Nuclear Power

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. For example, if the pipe size is reduced, the velocity will increase and act to decrease the static pressure. If the flow area increases through an expansion or diffuser, the velocity will decrease and result in an increase in the static pressure.