On-Site Sprinkler Irrigation of Treated Wastewater in Ohio

Bulletin 912

Step 8: Calculate Pressure Losses

For an on-site wastewater irrigation system, water pressure is created by the distribution pump. Calculating pressure losses is necessary for determining the appropriate size pump. The total pressure loss in the system results from the combined losses due to elevation changes and friction.

Losses Due to Elevation Change

Water pressure can be expressed as either “psi” (pounds of pressure per square inch) or “feet of head.” A column of water 1 foot high exerts 0.433 psi at the bottom and therefore 1 psi is equivalent to 2.31 feet of head. This means that for every foot of elevation change from the pump to the sprinkler heads, the corresponding change in pressure will be 0.433 psi.

Losses Due to Friction

As water moves through the irrigation system, pressure losses occur due to water contact with pipes, valves, and fittings. The four factors that determine friction losses in pipe are:

1. The velocity of the water: Water velocity is measured in feet per second. As velocity increases, pressure losses increase. Velocity is directly related to flow rate. An increase or decrease in flow rate will result in a corresponding increase or decrease in velocity. For irrigation systems, the velocity should never exceed 5 feet per second. At velocities greater than 5 feet per second, the friction losses become prohibitive.
2. The size (inside diameter) of the pipe: Smaller pipe causes a greater proportion of the water to be in contact with the pipe, which creates friction. Pipe size also affects velocity. Given a constant flow rate, decreasing pipe size increases the water’s velocity, which increases friction.
3. The roughness of the inside of the pipe: Pipe inside wall roughness is rated by a “C” factor, which is provided by the manufacturer. The lower the C value, the rougher the inside and the more pressure loss due to friction.
4. The length of the pipe: The friction losses are cumulative as the water travels through the length of pipe. The greater the distance, the greater the friction losses will be.

Friction Losses Due to Valves, Fittings, and Other Components

The friction losses for couplings, elbows, and tees are given in Appendix B. Friction loss from these components must be accounted for when calculating friction losses for each section of pipe. Add the equivalent length of pipe for each fitting or valve that occurs in each section of the lateral and main lines.

Consult the manufacturer’s literature for friction losses through valves, regulators, filters, and other components not listed. Several formulas have been developed to calculate friction losses in irrigation systems and, for convenience, friction loss charts based on these formulas are listed.

Friction Losses in Lateral Lines

Using the pipe layout plan with the pipe size and the gpm requirements for each sprinkler head clearly labeled, begin calculating the pressure losses as follows:

Note the gpm flow rate of the next to the last head on this same zone. Add this gpm to the previous head gpm to determine the total amount of water flowing though this section of pipe. Repeat steps 2-6. Continue adding consecutive sprinkler heads and calculating friction losses using steps 2-6 until every section of pipe is accounted for. If the system contains multiple zones, calculate friction losses for each zone but use only the zone with the greatest friction loss to determine total friction losses in the system.

Friction Losses in the Main Line

Use the total gpm flow rate for the zone to calculate the friction loss through the main line using the same procedure as described above. If the mainline size or pipe material is different from the laterals, be sure to use the appropriate Friction Loss Table.

Total Friction Losses

Add the friction losses for all lateral lines, main lines, and other components in the system all the way back to the pump. Add this to the pressure loss due to elevation change from the pump to the highest sprinkler head in the system. This total added to the operating pressure of the sprinkler heads will determine the pump requirements to ensure the proper operation of all the sprinkler heads in the system.

Example: Step 8

Using PVC schedule 40, 3/4 in. plastic pipe.

To calculate the friction loss from A to B:

1st	The gpm of the furthest head (A) is 2.4.
2nd	In the “Flow” column on the friction loss chart 2.4 falls between 2 gpm and 3 gpm.
3rd	At the top of the chart find the 3/4 inch pipe size.
4th	Move down this column and across the row for 3 gpm to the corresponding psi loss, (0.84). Interpolate the figures on the chart for more precise values. The interpolated friction loss value is 0.57. Divide by 100 to get 0.0057 psi/ft.
5th	No fittings or valves are in this section, therefore the effective length is the length of the pipe itself. Multiply the per foot pressure loss value by the length of pipe supplying this sprinkler head. 0.0057 X 38 = 0.22
6th	Record this information on the Friction Loss Worksheet.

To calculate the friction loss from B to C:

1st	Add the gpm flow rate of the last two heads in this zone. 2.4 + 2.4 = 4.8 Repeat steps 2-6.
2nd	Between 4 and 5 gpm
3rd	3/4 inch
4th	2.0/100 = 0.02 psi/ft
5th	0.02 X 38 = 0.76
6th	Record these figures on the Friction Loss Worksheet.

To calculate the friction loss from C to the automatic control valve:

1st	Determine the total gpm for Zone 1. 2.4 + 2.4 + 2.4 = 7.2 Repeat steps 2-6.
2nd	Between 7 and 8 gpm
3rd	3/4 inch
4th	4.24/100 = 0.0424
5th	A 90° elbow occurs in this section. This represents an additional 4.5 feet of pipe length. Add this to the 19 feet of actual pipe to determine the effective pipe length and multiply this number by the per foot pressure loss. 0.0424 X 23.5 = 1.0 psi
6th	Record these figures on the Friction Loss Worksheet.

To calculate losses in the main line:

1st	Use the gpm of the largest zone in the entire system. In this example, Zone 1 and Zone 2 are identical; therefore, it is not necessary to calculate both zones. Repeat steps 2-6.
2nd	Between 7 and 8 gpm
3rd	3/4 inch
4th	0.0424/100 = 0.0424 psi/ft
5th	This section of pipe includes a 90° elbow and a standard T fitting. The elbow adds 4.5 feet and the T fitting adds 3 feet. Therefore, the effective pipe length is 57.5 feet. 0.0424 X 57.5 = 2.44 psi According to the manufacturer’s specifications, pressure loss due to the control valve for this zone is 3 psi.
6th	Record these figures on the Friction Loss Worksheet.

Calculate pressure losses due to changes in elevation:

8 ft X 0.433 psi/ft = 3.46 psi

Total Pressure Losses in the System:

Add up all of the losses that have been calculated and recorded on the Friction Loss Worksheet.

0.22 + 0.76 + 1.0 + 2.44 + 3.0 + 3.46 = 10.88 psi

Interpolating Friction Loss Tables

In this example, the flow rates were between two values listed on the table of Friction Losses. Therefore, the values used in the calculations were interpolated. To interpolate values follow these steps:

The flow rate of the first section of pipe is 2.4 gpm. Calculate friction losses at 2.4 gpm as follows:

1st	Determine the friction loss that occurs in a 3/4 inch pipe between 2 gpm and 3 gpm. 0.84 - 0.39 = 0.45
2nd	2.4 is 4-10ths of the way to 3.0, so multiply 0.45 by 4/10. 0.45 X 0.40 = 0.18
3rd	Add this to the friction loss value for a 3/4 inch pipe with a 2 gpm flowrate. 0.39 + 0.18 = 0.57 psi

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