Master basic hydraulics for adequate irrigation
You define hydraulics as the study of the movement of fluids. In our case, that means the movement of water as it passes through the pipes, fittings, valves and backflow-prevention devices of a typical irrigation system. Basically, hydraulics is simply a tool you can use to help select the correct type and size of pipe or other equipment in an irrigation system. Or you can use the principles of hydraulics to estimate the pressure and flow rate at various locations within an irrigation system. For example, you might want to know how much pressure you can get to a new turf area you are installing. Deciphering such a problem is really simple if you understand the hydraulic principles at work in your irrigation system.
The principles of irrigation hydraulics A hydraulic analysis accounts for changes in energy as water moves from one point to another within an irrigation system's pipes. Water has three forms of energy: velocity (how fast the water moves), elevation (the vertical elevation difference between two locations in a system) and pressure.
Velocity. The velocity is how fast the water moves within a pipe and is usually expressed as the distance water travels in a second (feet per second). For example, we might talk about a velocity of 4.5 feet per second. The amount of energy in the water as a result of velocity is small compared to pressure and elevation. A velocity of 5 feet per second is equivalent to 0.2 psi. A velocity of 10 feet per second (not recommended) is equivalent to 0.7 psi. Because velocity is not very important to us from an energy point of view, we won't go into the technical description of how to compute its equivalent values in this article. If not accounting for this small portion of energy causes some problems in your system, I suspect it al ready is in trouble. In short, then, when accounting for the energy in a typical irrigation system, you'll generally ignore velocity.
Elevation. There are several ways to look at or track the energy that results from changes in elevation. One approach is to determine the elevation of specific points that are above a reference point you choose. "Sea level" is probably the most common reference point. Elevations are expressed in feet above the average sea level. In developing your own topographic map, you can use any conspicuous point at your site as the reference elevation. Then, when referring to the elevations of other points on the site, you would describe them as so many feet above that reference. In a simple problem, it's enough to know what the elevation difference is between two points of interest. In this case, we'll describe the elevation difference as that above or below the reference point expressed in feet. An increase in elevation means a decrease in pressure. A drop in elevation represents a gain in pressure. An easy way to keep this straight is to ask, "Does it take more effort to push a loaded wheelbarrow uphill or downhill?" Elevation is generally expressed in units of feet. However, you also can convert it to units of psi. One foot of water (vertical) is equivalent to 0.433 psi (see boxed information, "Elevation and pressure," page 30).
Pressure. Pressure is the force in pounds per unit of area in square inches. The force is the weight of the water in the system vertically (above the location at which you're making the measurement) divided by the area upon which the weight sits. So, if the water supply to your location is 100 feet higher than your reference point, then the pressure in the water created by the water level is 43.3 psi (100 ft x 0.433 psi per foot).
Putting this all together: The energy in the water at any point in a system is the sum of all three forms of energy: velocity, elevation and pressure. If an irrigation system is not operating and no water is flowing, we call it a static condition. Figure 1 (below) illustrates a static system where the pressure is from a water tank and an elevation difference exists between locations A and B. The system is connected to the water supply at location A and travels to location B at the back of the site.
The elevation and pressures for the static condition are tabulated in Table 1 (above) for locations A and B shown in Figure 1. We've explained that velocity represents little energy in most systems. In the static condition, the velocity is zero and doesn't add any energy to the water. In this problem, we use location B as the elevation reference and, as result, it has zero elevation. Location A has an elevation of 50 feet-50 feet higher than location B. The pressure at A is the result of the height of water above that location (or 150 feet). The pressure at A equals 65 psi (150 feet x 0.433 psi per foot). The energy at A is the sum of all three components (or 86.6 psi).
We can determine the amount of energy at location B by following the same process. Because we used location B as the elevation reference, the problem is simple. B has no elevation with respect to itself. The only form of energy at location B is pressure resulting from the height of water above that location. (It is interesting to note that with a static condition both locations have the same amount of energy.) Location A has more elevation and less pressure than B. Location B has no elevation but more pressure, but the sums of all forms of energy are equal for both locations.
Your next consideration Based on the analysis summarized in Table 1, the apparent answer to our original question is that the pressure at the back of our site (Location B) is 86.6 psi. No problem, right? So, the next question you ask is, "What flow rate can we deliver?" You have 86.6 psi at zero flow. That is not very valuable to you from an irrigation-system operations point of view. What you really need to know is the pressurewith dynamic conditions, or when the water is flowing. So let's look at that next, along with friction loss, flow rate and pipe diameter.
Dynamic conditions. For every flow rate (in gallons per minute), you have a different dynamic pressure. The difference is caused by friction, which you'll often hear referred to as friction losses. Don't take this description literally. It is not a loss of friction but a loss of energy, which results from friction. Another way to think of friction is as a resistance to the flow of water through pipes, valves, fittings and backflow-prevention devices. It simply takes energy to overcome this resistance to flow. What are the factors that influence the amount of friction? They include the length of pipe, the pipe material, flow rate and the diameter of the pipe.
Friction loss. You can compute the friction loss in pipe, or you can use a reference table that has computed that value for you. These charts-typically supplied by sprinkler and pipe manufacturers-offer the friction loss for various flow rates for a 100-foot length of pipe, according to standard pipe sizes and various pipe materials. Table 2 (page 32) summarizes the typical values that these tables include. So, according to the table, if you use Class-200 PVC pipe, this means you'll have a maximum pressure of 200 psi, and with a 1.5-inch pipe and a flow rate of 20 gpm, your friction loss will be 0.78 psi per 100 feet of pipe.
If you have 250 feet of pipe, the actual friction loss will be 250 feet x 0.78 psi divided by 100 feet = 1.95 psi. If you double that length (500 feet), you'd simply double the friction: 3.9 psi. If the length is 125 feet, or half the original 250 feet, the friction will be half as large also: 0.97 psi. As you can see, the total friction is proportional to the length. Triple the length, you triple the friction, with all other things remaining the same. The next question, then is: How is friction affected by changes in the flow rate?
Flow rate. In the example above, the flow rate is 20 gpm. What happens to the friction if you double the flow rate to 40 gpm? Using the friction values from Table 1, you can see that friction increases from 0.78 psi per 100 feet at 20 gpm to 2.82 psi per 100 feet at 40 gpm. The friction increases by 3.6 times (2.82/0.78) by doubling the flow rate. So, the amount of friction is more sensitive to increases in flow rate than increases in pipe length.
Finally, let's look at the effects of changes in the pipe's inside diameter on the amount of friction loss.
Pipe diameter. Using the flow rate of 20 gpm from the original example, let's look at the effect of reducing the pipe size by one-third (or 33 percent), from a 1.5- to a 1-inch diameter pipe. Doing so increases the friction from 0.78 psi per 100 feet for the 1.5-inch pipe to 4.71 psi per 100 feet for the 1-inch pipe. This results in an increase of six times more friction.
The final computation >From the simple comparison of friction loss, you can see the effects of pipe length, flow rate and diameter. It should be fairly apparent that pipe size has the greatest effect on the amount of friction in a system. Thus, a mistake in pipe sizing can easily result in a system with inadequate pressure. If you're still asking, "How much pressure can I get to the new turf area I'm planning?" stop for a second and ask yourself the following: "What is the size and length of pipe serving the area and how much flow rate do I need?" In our example, the answers are: 1,100 ft of 1.5-inch Class-200 pvc pipe and a flow rate of 50 gpm.
So, to determine the missing psi, consider that you have 65 psi at location A, a 50-foot drop in elevation (or a gain in pressure of 21.6 psi), a desired flow rate of 50 gpm (you don't always get what you want!) and a pipe length of 1,100 feet (see Figure 2, above).
The solution at this point is fairly easy. It is a matter of adding gains in pressure and subtracting losses in pressure (representing the friction and elevation if uphill). Starting pressure at location A = 65 psi Gain in pressure/drop in elevation = +21.6 psi Friction (4.26 psi per 100 feet) x 1,100 = -46.9 psi Pressure at location B = 39.7 psi
Now you have the answer for which you've been looking. You can deliver 50 gpm in the 1.5-inch/Class-200 pvc pipe at a pressure of 39.7 psi.
Suppose you have another question: "I really need about 55 psi to account for the friction through control valves and provide enough pressure to allow the sprinklers to operate properly," you say. Why didn't you say so in the first place? Okay then, you still have the tools you need to figure out what pipe size will work.
The simplest thing to do is merely to try using the next pipe size and re-compute the pressure that is available at Location B. You know from your comparison of pipe friction that relatively small changes in diameter result in big changes in the amount of friction. So, let's try a 2-inch-diameter pipe and repeat the computations to determine the amount of pressure available at location B with a flow rate for 50 gpm:
Starting pressure at location A = 65 psi Gain in pressure/drop in elevation = +21.6 psi Friction (1.44 psi per 100 feet) x 1,100 feet = -15.8 psi Pressure at location B = 70.8 psi
The results indicate you have a pressure of 70.8 psi at a flow rate of 50 gpm using a 2-inch Class-200 pvc pipe. So you have more pressure than you need if using the 2-inch pipe, and you don't have enough pressure to use the 1.5-inch pipe. Thus, the correct pipe size is 2 inches. Plus, it will provide some additional capacity that you might need in the future. For now, though, you can eliminate the excess pressure by using a proper adjustment of electric control valves, or possibly a pressure regulator, if one already exists in the system.
Review the process Using the principles of hydraulics, we can estimate the pressure available at any point in an existing system, or we can pick the proper pipe size for a new system to deliver the desired flow rate and pressure.
Again, begin by:
* Choosing a location of known pressure (measured or computed) and work toward the point of interest.
* Determine the starting pressure
* Subtract the friction loss to the point of interest
* Subtract the elevation if uphill
* Add the elevation if downhill.
When using this approach for pipe sizing, simply make an educated guess as to the size you think you need. Compute the pressure at the point of interest. If the pressure is too small, repeat computations using a larger pipe size. If the pressure is too large, repeat the computations using a smaller pipe size. Remember: It is always better to have too much pressure than not enough.
Robert E. Walker is a professor at California Polytechnic State University (San Luis Obispo, Calif.).
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