fluid dynamics - Does pressure drop across pipe affect flow rate? - Physics Stack Exchange
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 the average velocity of the fluid flow for . In terms of volumetric flow. The relationship between mean flow velocity ⟨v⟩ and volumetric flow rate Q is. This resistance to flow is called head loss due to friction. Forms of Flow The data is given in table form for the different pipe sizes and flow rates. Either method. This pressure drop, follows from, e.g. the Hagen-Poiseuille equation, but for turbulent flow (which you probably have), it relation is similar.
Since all liquids have weight, they also have momentum. This means the liquid will always try to continue moving in the same direction. When the liquid encounters a change in direction such as an elbowits momentum carries the flow to the outer edge of the fitting. Because the liquid is trying to flow around the outer edge of the fitting, the effective area of the fitting is reduced.
The effect is similar to attaching a smaller diameter pipe in the system. The velocity of the liquid increases and the head loss due to friction increases.
Energy Loss Any time a liquid is asked to change direction or to change velocity there is a change in energy. The energy lost by the liquid is converted to heat created by friction. Since the amount of liquid exiting a pipe has to equal the amount entering the pipe, the velocity must be equal. If the velocity is equal, then the velocity energy head must be equal. This only leaves one place for the energy to come from: The measured pressure entering the pipe will be higher than the measured pressure exiting the pipe.
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.
Relationship between Flow Rate and Pressure
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.
Relationship between Flow Rate and Pressure | Physics Forums
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. 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. Based on testing for ten-year old, steel pipe, the tables are divided by the different pipe sizes.
Darcy–Weisbach equation - Wikipedia
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. 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. 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. The change in static pressure across the expansion due to the change in velocity is: