# Pressure velocity relationship bernoulli equation

### Fluid dynamics and Bernoulli's equation

This inverse relationship between the pressure and speed at a point in a fluid is Bernoulli's equation relates the pressure, speed, and height of any two points. The Bernoulli Equation can be considered to be a statement of the effect" is the lowering of fluid pressure in regions where the flow velocity is increased. . with spin will curve because one side of the ball will experience a reduced pressure. In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler who derived Bernoulli's . The above equations use a linear relationship between flow speed squared and pressure.

It might be conceptually simplest to think of Bernoulli's principle as the fact that a fluid flowing from a high pressure region to a low pressure region will accelerate due to the net force along the direction of motion.

The idea that regions where the fluid is moving fast will have lower pressure can seem strange. Surely, a fast moving fluid that strikes you must apply more pressure to your body than a slow moving fluid, right? Yes, that is right. But we're talking about two different pressures now. The pressure that Bernoulli's principle is referring to is the internal fluid pressure that would be exerted in all directions during the flow, including on the sides of the pipe.

This is different from the pressure a fluid will exert on you if you get in the way of it and stop its motion.

I still don't get the difference. Imagine firefighters are spraying a building with steady streamline water from a firehose. The pressure that exists inside the stream of water pushing outward against air pressure as it flies toward the building is different from the pressure caused when the water strikes the building and changes momentum due to a collision.

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.

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

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.

**Bernoulli's equation explained - Understanding the relation between velocity and pressure**

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.

## What is Bernoulli's equation?

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. Since the flow cannot pass through the plate, the fluid must come to rest at the point where it meets the plate.

Bernoulli's equation along the stagnation streamline gives where the point e is far upstream and point 0 is at the stagnation point.

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

It is the highest pressure found anywhere in the flowfield, and it occurs at the stagnation point. It is called the dynamic pressure because it arises from the motion of the fluid. The dynamic pressure is not really a pressure at all: Pitot tube One of the most immediate applications of Bernoulli's equation is in the measurement of velocity with a Pitot-tube.