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Head Loss in Piping Systems

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**The Laws of Nature**

To move a given volume of liquid through a pipe requires a certain amount of energy. An energy or pressure difference must exist to cause the liquid to move. A portion of that energy is lost to the resistance to flow. This resistance to flow is called head loss due to friction.

One form of resistance to flow is due to the **viscosity** of the liquid. Viscosity is the amount of work needed to move one "box" of liquid against another "box" of liquid. Every liquid has its own value for this resistance to flow. SAE 30 motor oil has a lower viscosity and flows much easier than SAE 50 motor oil. The values for water are lower than for the motor oil.

Another characteristic of any liquid is its attraction to a surface. It attaches itself to any surface and cannot be moved. The liquid in the "box" on the very surface of a pipe does not flow or move. It always remains stationary. The liquid in the "box" above it has to slide against it and that requires an amount of energy to overcome friction between the two "boxes." The higher the viscosity of the liquid is, the higher the resistance to flow, therefore, the higher the friction loss.

A layer is formed by this non-moving liquid and reduces the inside diameter of the pipe. This increases the velocity of the liquid passing through it. The head loss from friction is related to the velocity energy (V^{2}/2g) of the liquid squared.

The liquid is not moving at the pipe wall but has a much higher velocity at the center of the pipe.

The **condition of the inside of a pipe** also has a great effect on the head loss of the flow of liquid. The rougher it is, the thicker the layer of non-moving or slow moving liquid near the pipe wall. This reduces the inside diameter of the pipe, increasing the velocity of the liquid. With the increase in velocity comes an increase in friction losses.

Any time a liquid flow changes direction there is resistance. 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 elbow), its 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.

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: pressure energy. The measured pressure entering the pipe will be higher than the measured pressure exiting the pipe.

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." They are good predictors of head loss but have some basic differences. The "Darcy, Weisbach" tables are based on the head loss in clean, new pipe. The formula is:

The "Williams and Hazen" tables take a different approach. They are based on the head loss in ten-year old pipe. Their values must be adjusted for different pipe age and materials. The formula is:

Don't be scared by these formulas, normally you won't have to use them. 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. These factors apply to the "C" value in the previous equation. Ten-year old, steel pipe has a "C" value of 100 or a multiplier of 1.0 because that is what the tables are based on. Clean, new steel pipe has a "C" value above 100 or a multiplier below 1.0, which translates to lower head loss and this makes sense. Older, rougher steel pipe has a "C" value below 100 and a multiplier above 1.0, so the head loss is higher and this also makes sense. Based on testing for ten-year old, steel pipe, the tables are divided by the different pipe sizes. Each of these tables could have values for velocity in ft/sec, velocity head, and head loss per 100' section of pipe. These are given for different flow rates of liquid through each diameter of pipe. To use these tables:

· Determine the type, size, and length of the pipe.

· Find the table for that pipe diameter.

· Find the flow rate you wish to put through that pipe.

· Divide the length of pipe you have by 100 and multiply by the "Head loss per 100'" value.

You have now predicted the head loss in that particular pipe.

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.

The fittings, such as elbows, tees, strainers, valves, etc., have all been tested and assigned "K" factors based on the head loss measured through them. These are normally found in pump handbooks including the Hydraulic Institute Data Book. To use this method:

· Find the chart pertaining to the fitting in question.

· Determine the "K" factor for the diameter fitting.

· Go to the tables for head loss in pipe and find the correct size pipe for this fitting.

· Find the velocity head of the liquid for the flow rate expected through the fitting.

· Multiply the velocity head times the "K" factor.

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.

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. To use this method:

· Find the fitting you wish to use in the appropriate table.

· Find the pipe size and record the equivalent length.

· Continue this for all the fittings in the system.

· Add the fitting equivalent length values to get a total equivalent length of pipe.

· Find the pipe diameter, appropriate flow rate (GPM), and head loss per 100' in the tables.

· Add the total fittings equivalent length of pipe to the total actual length of pipe. This gives you a total effective length of pipe.

· Divide the total effective length of pipe by 100 and multiply the result by the head loss per 100' value from the table.

You have predicted the head loss due to friction for the system.

When the flow rate (GPM) increases, the velocity of the liquid increases at the same rate. 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 inside diameter is made larger, the flow area increases and the velocity of the liquid at a given flow rate is reduced. 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.

As the roughness of the inside pipe wall increases so does the thickness of the slow or non-moving boundary layer of liquid. The resulting reduction in flow area increases the velocity of the liquid and increases the head loss due to friction.

Scale deposits and corrosion both increase the roughness of the inside pipe wall. 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.

The higher the viscosity of the liquid is, the higher the friction is from moving the liquid. More energy is required to move a high viscosity liquid than for a lower viscosity liquid.

Head loss due to friction occurs all along a pipe. 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.

Elbows, tees, valves, and other fittings are necessary to a piping system for a pump. It must be remembered that fittings disrupt the smooth flow of the liquid being pumped. When the disruption occurs, head loss due to friction occurs. At a given flow rate the losses for the fittings will be calculated using a factor that must be multiplied by a velocity head figure, or as the head loss equivalent to a straight length of pipe.

Because of momentum, liquid wants to travel in a straight line. If it is disturbed due to crooked pipe, the liquid will bounce off of the pipe walls and the head loss due to friction will increase. There is no accurate way to predict the effects since "crooked" can mean a lot of things.

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