# Relationship between pressure velocity volume and temperature

### Bernoulli's Equation

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. To understand the relationship between the pressure drop across a a change in velocity, and the energy lost to heat, noise, and vibration. It puts into a relation pressure and velocity in an inviscid incompressible flow. no work is done on or by the fluid,; no heat is transferred to or from the fluid, The dimensions of terms in the equation are kinetic energy per unit volume.

An easy demonstration of the lift produced by an airstream requires a piece of notebook paper and two books of about equal thickness.

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

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.

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

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.

**Pressure and velocity in pipes**

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. It is the highest pressure found anywhere in the flowfield, and it occurs at the stagnation point.

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

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.

If the pipe diameter is constant, the velocity will be constant and there will be no change in pressure due to a change in velocity. As an example, if an expansion fitting increases a 4 inch schedule 40 pipe to a 6 inch schedule 40 pipe, the inside diameter increases from 4.

If the flow rate through the expansion is gpm, the velocity goes from 9. The change in static pressure across the expansion due to the change in velocity is: In other words, pressure has increased by almost 0.

Pressure Change due to Head Loss Since head loss is a reduction in the total energy of the fluid, it represents a reduction in the capability of the fluid to do work. Head loss does not reduce the fluid velocity consider a constant diameter pipe with a constant mass flow rateand it will not be effect the elevation head of the fluid consider a horizontal pipe with no elevation change from inlet to outlet.

Therefore, head loss will always act to reduce the pressure head, or static pressure, of the fluid. There are several ways to calculate the amount of energy lost due to fluid flow through a pipe.