# Relationship between reynolds number and pressure drop

### Pressure Loss in Pipe – Neutrium Finally this article discusses which correlation for pressure loss in pipe is the loss or flow rate through pipe knowledge of the friction between the fluid drop as a fluid moves through a pipe are Reynolds Number of the fluid. Pressure drop in pipes is caused by: Friction, Vertical pipe difference or The friction factor for laminar flow condition is a function of Reynolds number only. Calculating the Reynold's Number from the fluid density, fluid viscosity and pipe diameter. and hence they produce a smaller frictional loss than those pipes with a greater internal roughness, such as concrete, cast iron and steel. Therefore friction occurs between layers within the fluid. Pipe Pressure Drop Calculations.

The difference between the two friction factors is that the value of the Darcy friction factor is 4 times that of the Fanning friction factor. In all other aspects they are identical, and by applying the conversion factor of 4 the friction factors may be used interchangeably.

### Pressure drop vs Reynolds number

Unless stated otherwise the Darcy friction factor is used in this article. Methods of Determining the Darcy Friction Factor The Darcy friction factor may be determined by either using the appropriate friction factor correlation, or by reading from a Moody Chart. The Darcy friction factor is a dimensionless number; the pipe roughness and the pipe diameter which are used to determine the friction factor should be dimensionally consistent e.

There are many relationships available to determine the Darcy friction factor. Here we discuss the practicality and accuracy of applying these methods. Different methods of determining the friction factor as used depending on the flow regime of the fluid, as determined by the Reynolds Number.

Laminar Flow In the laminar flow regime the Darcy Equation may be used to determine the friction factor see 2. Transitional Flow In the transitional flow regime the inconsistency of the flow patterns make the prediction of friction factor impossible. No relationships are available to adequately describe this flow regime. The only drawback to using this equation is that it is implicit, and will require iteration to solve.

## Pressure drop vs Reynolds number

Where iteration is possible and there are no constraints on computation speed, calculation via the Colebrook equation is appropriate. It should be noted that more accurate approximations of the Colebrook equation have been proposed but generally the increased accuracy is not required. Friction Factor Equations Here we detail some of the most common relationship for the Darcy friction factor for reference. For a discussion of the most appropriate relationships to use see above. Darcy Equation The Darcy equation describes the Darcy friction factor for laminar flow. This equation was developed taking into account experimental results for the flow through both smooth and rough pipe. It is valid only in the turbulent regime for fluid filled pipes.

It is widely accepted and most of the relationships discussed in this article are merely explicit approximations for this relationship. Due to the implicit nature of this equation it must be solved iteratively. A result of suitable accuracy for almost all industrial applications will be achieved in less than 10 iterations. 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. 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: 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.