# Flow and pressure relationship

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. 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. Consider a tank with high pressure, if we open the tap means water flows be the pressure because force is directly proportional to pressure by relation P=F/A.

### How Does Pressure Relate to Fluid Flow? | Sciencing

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.

## The Relationship Between Pressure and Flow in a Compressed Air System

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. The two most common methods are the Darcy-Weisbach equation and the Hazen-Williams equation.

For example, if you use your fingertip to apply a mild downward force to a cucumber, nothing happens. If you apply that same force with the blade of a sharp knife, you slice through the cucumber.

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

The force is the same but the edge of the blade has a much smaller surface area, and thus the force per unit area -- in other words, the pressure -- is much higher.

Flowing Forces Pressure applies to both fluids and solid objects. You can understand the pressure of a fluid by visualizing water flowing through a hose. The moving fluid exerts a force on the inside walls of the hose, and the pressure of the fluid is equivalent to this force divided by the interior surface area of the hose at a given point.

Sciencing Video Vault Confined Energy If pressure equals force divided by area, pressure also equals force times distance divided by area times distance: Area times distance is equivalent to volume, and force times distance is the formula for work, which in this situation, is equivalent to energy. Thus, the pressure of a fluid can also be defined as energy density: For the simplified case of a fluid that does not change elevation as it flows, total energy is the sum of the energy of the pressure and the kinetic energy of the moving fluid molecules.