# Pressure velocity and flow relationship tips

I need an equation that links ΔP_fan,rise with fan tip speed (or fan RPM)." A fan is used to create velocity (kietic energy) for comfort and pressure for flow. These two observations provide an intuitive guide for analyzing fluid flows, even get closer together, the flow velocity increases, and the pressure decreases. All Sensors Pressure Points are application tips to simplify designing with Reynolds number (Re) is a dimensionless velocity value used to predict flow patterns. Bernoulli's Equation is used to determine fluid velocities through pressure.

The Bernoulli equation states that, where points 1 and 2 lie on a streamline, the fluid has constant density, the flow is steady, and there is no friction.

Although these restrictions sound severe, the Bernoulli equation is very useful, partly because it is very simple to use and partly because it can give great insight into the balance between pressure, velocity and elevation.

How useful is Bernoulli's equation?

### Bernoulli's Equation

How restrictive are the assumptions governing its use? Here we give some examples.

The flow therefore satisfies all the restrictions governing the use of Bernoulli's equation. Upstream and downstream of the contraction we make the one-dimensional assumption that the velocity is constant over the inlet and outlet areas and parallel.

One-dimensional duct showing control volume. When streamlines are parallel the pressure is constant across them, except for hydrostatic head differences if the pressure was higher in the middle of the duct, for example, we would expect the streamlines to diverge, and vice versa.

If we ignore gravity, then the pressures over the inlet and outlet areas are constant. 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.

## What is Bernoulli's equation?

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.

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

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.

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.

### What is Bernoulli's equation? (article) | Khan Academy

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.