Water and Sanitation Technologies: A Trainer's Manual (Peace Corps, 1985)
 Sessions
 Session 31 - Gravity water systems: Part I
 (introduction...) Attachment 31A: General explanation of pressure, head, HGL, and friction losses

### Attachment 31A: General explanation of pressure, head, HGL, and friction losses

Pressure Exerted by a Column of Water

A column of water exerts a force due to the weight of the water. The pressure, or force per unit area, is dependent on the height of the column of water. Therefore, head or water pressure is usually expressed in terms of the equivalent height of water needed to exert that pressure. The pressure under static conditions is not dependent on pipe diameter. See Figure 1.

Figure 1

The pressure at the bottom of each column of water is the same. It is 10 meters of head, or 1.0 kg/cm2. The pressure midway in each column would be 5 meters of head or 0.5 kg/cm2.

Pressure in a Static System

In a system under static conditions, the pressure at any point is dependent on the difference in height between the point in question and the highest point in the system. If an opening is made in the pipe in any part of the system and a tube connected to it then the water level will rise until it is the same as the highest point. See Figure 2.

Figure 2

The system in Figure 2 is static and no flow occurs. The pressure or head at points B. C, F and H is the same; i.e., 10 meters. The pressure or head at point E is 5 meters or the difference in height between points A and E. If the pipeline were opened and a tube connected to it at point C or F. then the water would rise 10 meters and be at the same level as points A, D and G.

Pressure in a Flowing System

When water in the pipeline is flowing, then the pressure is no longer dependent solely on the height difference with respect to the highest point. There is a loss of pressure or head due to friction between the water and the pipe. The pressure or head at any point is equal to the static head (relative height difference) minus the head loss due to friction. This is then called the dynamic head level. Because of the head loss, the water will not rise to the same level as the highest point but only as high as the pressure or head at that point. Head loss occurs only when water is flowing. See Figure 3.

Figure 3

Under flowing conditions, the pressure is no longer the same and the pressure at point C or C1 is not sufficient to raise the water level to points D or F. The height difference between points D and E or points F and G is the head loss due to friction in the pipeline. If the flow were stopped, the water level would return to points D and F.

Factors Influencing Head Losses

The amount of head loss is influenced by the following factors:

a. The length of pipe

The longer the pipeline, the greater the head loss. This loss is directly proportional to the length; i.e., the head loss for 200 meters of pipe would be twice that for 100 meters under the same conditions.

b. The diameter of the pipe

The smaller the diameter of the pipeline, the greater the friction will be for the same flow of water. The differences are not proportional.

c. The flow of water in the pipe

The higher the flow of water in a given pipe, the greater the head loss due to friction. Friction increases as the square of the velocity.

d. The pipe material

The smoother the inner surface of the pipe, the lower the head loss. Thus, since PVC pipe is smoother than steel or cast iron, it has a lower head loss for identical conditions.

e. The number of fittings or bends in the pipeline

A straight pipeline would have a lower head loss than one of the same length with fittings or bends.

Pipe Design

In designing a gravity flow pipeline, three factors are of primary importance; design flows, pipeline distances, and available head. The latter two are obtained from field measurements. The design flow is calculated by the designer to fit the number of people being served and the projected per capita consumption. A pipe size is then chosen with a head loss less than the available head at that section of the pipeline. When doing the calculations it is important to list the known values of the system and plot the profile from there. Known values would be:

- Design flows
- Length of entire pipeline
- Length of specific reaches of pipe (lengths of pipe without breaks)
- Available head for the entire system
- Available head for specific reaches of pipe
- Frictional head loss factors from tables

The Hydraulic Gradient Line (HGL)

The hydraulic Gradient Line (HGL) is defined by subtracting the head loss in the pipeline from the static head. The difference between the ground profile and the HGL is the pressure in the pipeline while the water is flowing, or the residual head. If an opening were made in the pipeline and a tube connected to it, then the water would rise to the level of the HGL. The HGL should always lie above the profile, If it does not, then the water may still flow but at sections where the profile lies above the gradient, there is a negative pressure which can cause air or pollution to enter the pipeline. Those sections of the pipeline where negative pressures occur should be redesigned to eliminate them. Figures 4 and 5 illustrate this.

Figure 4

If the pipeline followed ground profile A, then the choice of pipe with the given HGL is acceptable. If the pipeline followed ground profile B. then negative pressure would exist in section C, so the pipeline should be redesigned. See Figure S.

Figure 5

The pipe diameters have been changed, thus changing the HGL. Use of a larger diameter pipe near the source ensures that the HGL lies entirely above the ground profile and is acceptable. Note that two pipe diameters are now used between the source and reservoir. For each diameter the HGL has a different slope. The slope is directly dependent on the head loss, so a smaller diameter pipe has a steeper slope.

Pipeline Design Sample Problems

Plotting the pipeline profile is a process of trial and error. The calculated values for head losses from different sizes of pipe are compared to the available head on the profile drawing. The smallest diameter pipe, with a calculated head loss less than the available head, is chosen for each continuous section of the pipeline.

Problem 1

A spring with a flow of 0.5 1/s is 1,000 meters from the village and the available head is 20 meters. It is planned to convey the entire flow to a small reservoir in the village. What size pipe is recommended? On the water flow charts, a flow of 0.5 1/s and a length of 1,000 meters using 1.5 inch pipe indicates a head loss of 11 peters. For 1.25 inch pipe the head loss is 26 meters. Thus, the required flow will not be obtained with a 1.25 inch pipe, and a 1.5 inch pipe is too large.

The most economical solution is a combination of two pipe sizes. By trial and error it is found that 500 meters of 1.5 inch GI pipe with a flow of 0.5 1/s has a head loss of 6 meters, and 500 meters of 1.25 inch GI pipe has a head loss of 13 meters. Thus, the total head loss for the 1,000 meter pipeline is 19 meters, which closely matches the available head. The pipeline profile and HGL are plotted in Figure 1.

Figure 1

Calculated head losses for various pipes are as follows: Use for problems 1 and 2

 Length (meters) Flow (1/s) Pipe Diameter (inches) Head Loss (incl.10%) (extra meters) Available Head (meters) 1,000 2 3 5 20 1,000 2 2.5 11 20 1,000 2 2 33 20 1,000 0.5 2 3 20 1,000 0.5 1.5 11 20 1,000 0.5 1.25 26 20

Problem 2

A water source is 1,000 meters from Village One and it is 1,000 meters further to Village Two. The available head between the source and Village One is 20 meters, and between Village One and Village Two, it is also 20 meters. The design flows are 2.0 1/s from the source to Village One and 0.5 1/s from Village One to Village Two. What are suitable pipe diameters?

A suitable selection of pipe would be 2.5 inch pipe for the first 1,000 meters, and 1.25 inch pipe for the second 1,000 meters. The total head loss is then 37 meters, which closely matches the total available head of 40 meters. Note that the second 1,000 meters has a head loss of 26 meters and an available head of only 20 meters. This is allowable because there is excess head available from the first 1,000 meters of the pipeline and the HGL is always above the pipeline profile. See Figure 2.

Figure 2

Problem 3

A spring with a flow of 3 1/s is 500 meters from the Village and the school is 1,000 meters further. A flow of 1 1/s will be used to serve the Village and 2.0 1/s for the school. The available head is 10 meters between the spring and village and 20 meters between the village and the school. What pipe sizes are recommended?

Some calculated head losses are as follows (Use for Problem 3):

 Length (meters) Flow (1/s) Pipe Diameter (inches) Head Loss (incl.10%) (extra meters) Available Head (meters) 500 3 3 5 10 500 3 2.5 12 10 500 3 2 36 10 1,000 2 3 5 20 1,000 2 2.5 11 20 1,000 2 2 33 20 500 2 2.5 6 - 500 2 2 16 -

If 2.5 inch pipe is used for the entire 1,500 meters, the total head loss is 23 meters, which is less than the total available head of 30 meters. Thus, the desired amount of water may flow. However, the HGL as plotted in Figure 3 falls below the pipeline profile and this is not allowable.

Figure 3

An acceptable alternative solution would be to use 500 meters of 3 inch pipe followed by 1,000 meters of 2.5 inch pipe. The total head loss would then be 16 meters and excess available head would be 14 meters. A more economical solution would be 500 meters each of 3, 2.5, and 2 inch pipe, which would convey the full design flows. The HGL for these two solutions are plotted in Figure 4.

Figure 4

REFERENCE: Practical Design Notes for Simple Rural Water Systems; A Scott Faiia, CARE, Indonesia, 1982.