# Irrigation Chapter 7 - Flow Measurement and Basic Water Calculations

Managing our water resources begins with knowing how much water is being used for irrigation and comparing that with how much the crop uses. This can help identify water losses and improve application efficiency, which can reduce pumping costs and protect or conserve natural resources. These water use measurements can be used to:

- check irrigation efficiency
- determine pumping plant efficiency, and
- detect well and pump problems

Methods of measuring irrigation water can be grouped into three categories: direct, velocity-area, and constricted flow. Method selection will depend on the volume of water to be measured, the degree of accuracy desired, whether the installation is permanent or temporary, and the financial investment required.

Author: Chuck Burr, University of Nebraska Lincoln Extension Educator in Phelps and Gosper counties.

## Direct Measurement Methods

To measure small flow rates such as from individual siphon tubes, sprinkler nozzles or individual outlets in gated pipe, use a stop watch or other timing device to see how long it takes to fill a container of a known volume. Ordinarily one-gallon or five-gallon containers will be adequate. It is recommended that the measurement be repeated three or preferably five times to determine a reliable flow rate per unit of time. For example, if you collect five gallons of water from a siphon tube in 30 seconds, the flow rate would be 10 gallons per minute.

## Velocity-Area Methods

Commercial flow meters measure the total volume of water flowing through a pipe and are extremely accurate if properly installed and maintained (*Figure 7.1*). Most meters include an indicator which estimates the instantaneous flow rate (*Figure 7.2*). Measurement accuracy is greatly improved by recording the totalizer readings over a given time, perhaps 10 minutes. This will provide an average flow rate measurement.

Since most meters use the units of acre-inches, gallons, or cubic feet for the totalizer, you will need to convert to gallons. Some helpful conversions are:

1 acre-inch = 27,154 gallons

1 cubic foot (cu. ft.) = 7.48 gallons

## Example 7.1

A propeller type flow meter is used to estimate the gallons per minute being delivered to a pivot irrigated field. During a 10-minute interval, the accumulator reading changed from 10,973 cubic feet to 12,109 cubic feet. Determine the average flow rate.

* Answer:*

Final reading 12,109 cu.ft.
Initial reading – __10,973 cu.ft.__
Volume pumped in 10 minutes 1,136 cu.ft.

Flow rate = __ 1,136 cu.ft. x 7.48 gallons/cu.ft.__
10 minutes

Flow rate = 850 gpm

## Installation of Flow Meters

Proper installation of flow meters is important to obtain accurate readings. Spiraling and turbulent flow in the meter section caused by valves, pumps, reducers, increasers, tees and elbows will reduce the accuracy of the reading. Because of this, most manufacturers recommend a minimum of five straight diameters (inside measurement of the pipe) without obstructions ahead of the propeller, and at least one straight pipe diameter without obstructions downstream from the meter. For an 8-inch diameter pipe, you need 40 inches upstream and 8 inches downstream of straight, unobstructed pipe. For better results, ten diameters or more is preferred upstream.

If space does not allow for ten diameters upstream, straightening vanes can be installed in the pipe section ahead of the meter. These vanes will reduce the turbulence of the water within the pipe near the meter propeller(*Figure 7.1*). The position of the saddle, the base of the meter that attaches to the pipe, is also very important since the propeller shaft needs to be in the center of the pipe. It also is necessary that the pipe be flowing full to obtain accurate readings. Sometimes a piece of pipe that looks like an upside down “U” is installed downstream of the meter. This insures a full pipe at the meter.

Periodic meter inspection and maintenance are essential for dependable service and accurate readings. At a minimum the meter should be inspected every three years. First, remove the meter from the pipe and check the propeller surface for any cracks, rodent damage or excessive wear. Replace the propeller if needed and recalibrate. Check the propeller for excessive wobbling which would indicate worn bearings. Replace the bearings if needed. Grease the propeller bearings with a lubricant recommended by the meter manufacturer.

Inspect the meter head for moisture accumulation. A wet or foggy appearance on the inside of the plastic cover indicates a break in the seal and possible moisture damage to the register. Replace the meter register and seal the canopy with the proper gaskets or sealant. Be sure the meter saddle is sealed properly to the irrigation pipe.

## Ultrasonic Flow Meters

Ultrasonic flow meters are easy to install, non-intrusive, and becoming increasingly popular in the irrigation industry. If installed properly, they are quite accurate. The ultrasonic flow meter normally is used as a rate meter but can total the volume when desired. In contrast to ultrasonic meters, most conventional flow meters require installation in the pipe, which requires shutting down the line to install the meter. A head loss is almost always associated with conventional meters. The ultrasonic flow meter has several advantages over conventional in-line meters. First, there is no head loss associated with the ultrasonic meter because the installation is on the outside of the pipe. Installation of the clamp-on transducers eliminates the need for line shutdown. As a result, ultrasonic meters can be used in several locations for different applications. Since the pipeline is not broken, measurements are leak free.

Because of the relatively high cost, ultrasonic meters typically are not used for permanent flow measurements in irrigation. Rather, they are used as test meters by water management agencies, researchers, and consultants to get a “snapshot” of the flow rate of the irrigation system.

Like most flow measuring devices, proper application and installation is important. For example, the pipeline must be flowing full where the meter is installed. Also there must be a similar adequate distance of straight pipe, free of obstructions, upstream from the point of measurement.

## Constricted Flow Methods

Methods employing a constriction of pre-determined dimensions are frequently used for measuring flow in irrigation canals and ditches. Weirs and flumes are the most common constricted-flow devices.

Basically, a weir measures flow by causing the water to flow over a “V” or trapezoidal notch of pre-determined shape and dimensions. This method is quite accurate when properly constructed, installed and maintained. Weirs do have some limitations. First, they require considerable drop (difference in elevation) between the upstream and downstream water surfaces which often is either unavailable in flat grade ditches or undesirable. Second, it is often necessary to construct a pool or stilling area above the weir so the water velocity slows. Unless the water appears practically still, flow rate readings will be inaccurate. Weir installations in earthen ditches can be particularly troublesome. The stilling area in the ditch above the weir frequently tends to “silt in” while excessive erosion may occur immediately downstream of the weir.

Generally, only one or two measurements of water depth flowing over the weir are required where the dimensions of the constriction are known. Using these measurements, rate of flow is determined from either a table, graph or by calculation. Due to the wide variety of types and sizes of constricting devices, flow tables are not included in this publication. Most weirs and flumes purchased from the manufacturer include a table or graph.

## Example 7.2

A canal system is used to deliver water to several fields. A 90^{o} triangular notch weir is used to measure the flow rate. The manufacturer provided the following formula to determine flow rate:

Q = 2.49 x H^{2.48}

Where : Q = Flow rate in cubic feet per second (cfs)

H = Head in feet (or depth of water flowing through the weir)

Calculate the flow rate if the head is 2.0 feet.

* Answer:*

Q = 2.49 x (2.0 ft)^{2.48}

Q = 13.89 cfs

A flume measures flow by restricting the flow through a channel of pre-determined dimensions. Flumes can operate with less difference in elevation between upstream and downstream water surfaces than can weirs. Like weirs, when properly installed and maintained, flumes are quite accurate. Recently smaller flumes have been developed to measure flow rate in an individual furrow. They are normally used in conducting research.

Flow measuring devices estimate the average flow rate. To calculate total volume pumped, the flow rate must be multiplied by the length of time the pump is operated.

## Example 7.3

A pump supplies water to a gravity system. The propeller type flow meter indicates that the average flow rate is 900 gallons per minute. Calculate the total number of gallons and acre-inches applied during a 12-hour set time.

* Answer:*

Total volume = 900 gpm x 12 hr x 60 min/hr

Total volume = 648,000 gallons

Total acre inches = 648,000/27,154

Total acre inches = 23.86

## Basic Water Calculations

The easiest and most common calculation used by irrigators is gross irrigation application. Gross application is simply the average water depth applied over a unit area. To calculate gross application, determine flow rate, length of time water was applied and area irrigated.

Many flow measurement devices provide a reading in gallons per minute (gpm). To convert to acre-inches per hour, use the following conversion factor:

1 acre-inch/hr = 453 gallons per minute (gpm)

When meters use units of gpm, divide the gpm by 453 to convert units to acre-inch/hr.

Multiply the flow rate (now in units of acre-inch per hour) times the number of hours irrigated and divide by the number of acres irrigated. The result is the average depth applied across the whole field. This conversion factor could be written on the lid of the meter for easy reference.

## Example 7.4

An irrigation pump delivers 900 gpm to a 40-acre furrow irrigated field. If the pump runs for 48 hours, determine the gross depth of water applied.

* Answer:*

Flow rate in __acre-inch__ =
hr

__ 900 gpm x 1 acre-inch/hr__
453 gpm

Flow rate = 2.0 acre-in/hr

Depth = __2 acre-inch/hr x 48 hrs__
40 acres

Gross depth = 2.4 inches

Some flow meters have an output reading in cubic feet per second (cfs). Cubic feet per second is nearly equal to acre inch per hour and the labels can be used interchangeably.

1 cfs = 1 acre-inch/hr

To calculate the area of a field, multiply the length in feet by the width in feet and divide by 43,560 ft^{2}/acre. The resulting area is in the unit of acres. The area of fields with a shape other than a square or rectangle can be determined using geometric calculations.

## Example 7.5

Calculate the set size of an area to be irrigated. The field is 1,320 feet long and 80 rows wide. The row spacing is 30 inches.

* Answer:*

Area = __1,320 feet x 80 rows x 30 inches/row__
12 inches/ft x 43,560 ft^{2}/acre

Area = 6 acres

## Example 7.6

A pivot is used to irrigate a 130-acre field. If the irrigation pump delivers 1.85 cfs and it takes three days to complete the circle, calculate the average depth applied.

* Answer:*

1.85 cfs = 1.85 acre-inches/hr

Depth =__1.85 acre-inches/hr x 72 hrs__
130 ac

Gross depth = 1.02 inches

Flow meters also can help determine the amount of water applied during a growing season. The totalizer reading on the meter should be read at the beginning and end of the irrigation season. The volume of water is then divided over the acres irrigated to determine the gross depth for the season. Most totalizer readings have units of acre-inches, gallons, or 1,000 ft^{3}. When buying a new meter, choose one that uses acre-inches. The following formula may be useful for those totalizers that use 1,000 ft^{3} as the unit of measurement:

1 acre-inch = 3,630 ft^{3}

## Example 7.7

A furrow-irrigated field is 80 acres. Knowing the beginning reading of 12,978.4 (1,000 ft^{3}) and the ending reading of 17,624.8 (1,000 ft^{3}), calculate the gross depth per acre for the season.

* Answer:*

* *Final reading 17,624.8 (1,000 ft^{3})*
*Initial reading –__ 12,978.4 (1,000 ft__^{3})* ** *Volume of water used 4,646.4 (1,000 ft^{3})

Volume = __4,646,400 ft____ ^{3} x 1 acre-inch__
3,630 ft

^{3}

* *Volume = 1,280 acre-inch

* *Depth = __1,280 acre-inch__ * *
80 acres

Depth applied = 16.0 inches

## Example 7.8

A pivot irrigated field has a flow meter with totalizer units in acre-inches. The field is 130 acres. The beginning reading is 2,980 acre-inches and the ending reading is 4,540 acre-inches. Calculate the application depth for the season.

* Answer:*

* *Final reading 4,540 acre-inch*
*Initial reading –__ 2,980 acre-inch__*
*Volume used 1,560 acre-inch

* *Depth = __1,560 acre-inch__ * *
130 acres

* *Depth applied = 12 inches