# Pressure drop and flow rate relationship

### Darcy–Weisbach equation - Wikipedia

Pressure drop can be defined as the quantity of line pressure, which is lost The measurements can be made to considering certain relationships. Pressure drop is comparative to volumetric flow rate under laminar flow. The relationship between pressure drop and flow rate, where the pressure drop is normalized by the ratio of the viscosity of water to the viscosity of the solution µ . 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.

Friction Loss Tables In an effort to easily predict the head loss in pipes and fittings, there were a number of studies made many years ago. These have been published, as formulas and tables, for different size pipes, fittings, and flow ratings. The most common used are "Darcy, Weisbach" and "Williams and Hazen. The "Darcy, Weisbach" tables are based on the head loss in clean, new pipe.

They are based on the head loss in ten-year old pipe. Their values must be adjusted for different pipe age and materials. The data is given in table form for the different pipe sizes and flow rates. Either method is acceptable as long as you remember what they are based on.

Our company has for years used the "Williams and Hazen" tables and will continue to do so.

The tables are for ten-year old, steel pipe. Variations of this, such as new pipe, plastic pipe, cast iron pipe or other types are addressed through the use of correction factors.

## Darcy–Weisbach equation

These factors apply to the "C" value in the previous equation. Ten-year old, steel pipe has a "C" value of or a multiplier of 1. Clean, new steel pipe has a "C" value above or a multiplier below 1. Older, rougher steel pipe has a "C" value below and a multiplier above 1.

## Relationship between Flow Rate and Pressure

Based on testing for ten-year old, steel pipe, the tables are divided by the different pipe sizes. These are given for different flow rates of liquid through each diameter of pipe. To use these tables: You have now predicted the head loss in that particular pipe.

Pipe Fittings and Valves Pipe fittings and valves disturb the normal flow of liquid, causing head loss due to friction. There are two basic methods currently in use to predict the head loss in pipe fittings and valves.

### Relationship between Flow Rate and Pressure | Physics Forums

They are the "K factor" and the "Equivalent length of pipe in linear feet" methods. K Factor Method The fittings, such as elbows, tees, strainers, valves, etc. These are normally found in pump handbooks including the Hydraulic Institute Data Book. To use this method: You have predicted the head loss through that fitting.

Continue this procedure for each fitting in the system. Add all the fitting losses to the expected losses for the pipe and you now have the head losses due to friction for the entire system.

Equivalent length of pipe in linear feet Le Method The pipe fittings and valves were tested and values assigned for the head loss measured through them. Instead of assigning a factor, as in the "K" Factor method, an "equivalent length of pipe in linear feet" value was assigned.

This means that a particular fitting will have a head loss equal to a given length of straight pipe of the same size.

These tables are found in pump handbooks. This gives you a total effective length of pipe.

**PRESSURE DROP AND FLOW RATE**

You have predicted the head loss due to friction for the system. The friction or resistance to flow due to viscosity also increases. The head loss is related to the square of the velocity so the increase in loss is very quick. When the velocity is reduced there is lower head loss due to friction in the pipe. On the other hand, if the inside diameter of the pipe is reduced, the flow area decreases, the velocity of the liquid increases and the head loss due to friction increases.

The resulting reduction in flow area increases the velocity of the liquid and increases the head loss due to friction. Scale buildup has the added disadvantage of reducing the inside diameter of the pipe. All of these add up to a reduction in flow area, an increase of the velocity of the liquid, and an increase in head loss due to friction. More energy is required to move a high viscosity liquid than for a lower viscosity liquid.

It will be constant for each foot of pipe at a given flow rate. The published tables have head loss values which must be multiplied by the total length of pipe. It must be remembered that fittings disrupt the smooth flow of the liquid being pumped.

The energy loss, or head loss, is seen as some heat lost from the fluid, vibration of the piping, or noise generated by the fluid flow. 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. 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.