# Fluid flow and pressure relationship

### Fluid dynamics and Bernoulli's equation

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 .. Note that the relation of the potential to the flow velocity is unaffected by this transformation: ∇ Φ = ∇φ. To understand the relationship between the pressure drop across a In reality, the flow of fluid between two points cannot be achieved without. The equation for the flow rate of water coming out of the hole is the proportional relationship between the pressure and the flow rate squared.

Between two points, the Bernoulli Equation can be expressed as: In other words, the upstream location can be at a lower or higher elevation than the downstream location. If the fluid is flowing up to a higher elevation, this energy conversion will act to decrease the static pressure.

If the fluid flows down to a lower elevation, the change in elevation head will act to increase the static pressure.

## Bernoulli's principle

Conversely, if the fluid is flowing down hill from an elevation of 75 ft to 25 ft, the result would be negative and there will be a 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: 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.

### Bernoulli's principle - Wikipedia

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.

Conserved Energy The fundamental relationship between pressure and fluid velocity is captured in the Bernoulli equation, which states that the total energy of a moving fluid is conserved. In other words, the sum of energy due to pressure and kinetic energy remains constant even when the flow volume changes.

By applying the Bernoulli equation, you can demonstrate that pressure actually decreases when fluid is traveling through a constriction. The total energy before the constriction and during the constriction must be the same.