# Density and pressure drop relationship

### Pressure drop evaluation along pipelines -

In fluid dynamics, the Darcy–Weisbach equation is an empirical equation, which relates the head loss, or pressure loss, due to friction along a given length of pipe to ρ, the density of the fluid (kg/m3);: D, the hydraulic diameter of the pipe (for a pipe .. While the Colebrook–White relation is, in the general case, an iterative. points 1 and 2 lie on a streamline,; the fluid has constant density,; the flow is over the bottom surface, and a resultant force due to this pressure difference is. Two phase pressure drop; Simplified friction pressure drop . In using some of these figures, the relationship between viscosity in centistokes . Except for the total composite-fluid density, the bubbles have little effect.

It was developed using sections of pipeline that could be inclined at any angle. The Flanigan Correlation is an extension of the Panhandle single-phase correlation to multiphase flow.

### Darcy–Weisbach equation - Wikipedia

It incorporates a correction for downhill flow. In this software, the Flanigan multiphase correlation is also applied to the Modified Panhandle and Weymouth correlations. The Modified Flanigan Correlation is an extension of the Modified Panhandle single-phase equation to multiphase flow.

It incorporates the Flanigan correction of the Flow Efficiency for multiphase flow and a calculation of hydrostatic pressure difference to account for uphill flow. There is no hydrostatic pressure recovery for downhill flow.

In this software, the Flanigan multiphase correlation is also applied to the Panhandle and Weymouth correlations. The Petalas and Aziz Model is a correlation that was developed to overcome the limitations imposed by using previous correlations. It applies to all pipe geometries, fluid properties and flow in all directions. A mechanistic approach fundamental laws are combined with empirical closure relationships to provide a model that is more robust than other models and can be to used predict pressure drop and holdup in pipes over a more extensive range of conditions.

## Darcy–Weisbach equation

Each of these correlations was developed for its own unique set of experimental conditions or designed using a mechanistic modeling approach, and accordingly, results will vary between them. For multiphase flow in essentially vertical wells, the available correlations are Beggs and Brill, Petalas and Aziz, Gray and Hagedorn and Brown. If used for single-phased flow, these four correlations devolve to the Fanning Gas or Fanning Liquid correlation.

This data is then used to calculate the pressure loss caused by the component for a specified flow rate but the flow rate itself will also be dependent on the pressure loss downstream of the component and so it is very difficult to model component head loss performance without the use of appropriate software such as Pipe Flow Expert.

Animation : Relationship of Pressure with Volume and Temperature

Pressure Loss due to Change in Elevation Flow in a rising pipe If the start elevation of a pipe is lower than the end elevation then on top of friction and other losses there will be an additional pressure loss caused by the rise in elevationwhich measured in fluid head is simply equivalent to the rise in elevation. Flow in a falling pipe If the start elevation of a pipe is higher than the end elevation then as well as the friction and other losses there will be an additional pressure gain caused by the drop in elevation, which measured in fluid head is simply equivalent to the fall in elevation.

Energy and Hydraulic Gradelines The elevation of a fluid within a pipe, together with the pressure in the pipe at a specific point, and the velocity head of the fluid, can be summed to calculate what is known as the Energy Grade Line.

The Hydraulic Grade Line can be calculated by subtracting the fluid's velocity head from the EGL Energy Grade Lineor simply by summing only the fluid elevation and the pressure in the pipe at that point.

## Pressure drop evaluation along pipelines

Pump Head Calculations Within a pipe system there is often a pump which adds additional pressure known as 'pump head' to overcome friction losses and other resistances. The performance of a pump is usually available from the manufacturer, in terms of the pump performance curve, which plots a graph of the flow versus head produced by the pump for a range of flow values. Since the head produced by the pump varies with the flow rate, finding the operating point on the pump performance curve is not always an easy task.

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

### Pressure Loss Correlations

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.