# Pressure and velocity relationship in fluidstance

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

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Along a streamline on the centerline, the Bernoulli equation and the one-dimensional continuity equation give, respectively, These two observations provide an intuitive guide for analyzing fluid flows, even when the flow is not one-dimensional.

For example, when fluid passes over a solid body, the streamlines get closer together, the flow velocity increases, and the pressure decreases.

Airfoils are designed so that the flow over the top surface is faster than over the bottom surface, and therefore the average pressure over the top surface is less than the average pressure over the bottom surface, and a resultant force due to this pressure difference is produced.

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. 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. The density of a fluid, is generally designated by the Greek symbol rho is defined as the mass of the fluid over an infinitesimal volume.

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

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

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