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Many irrigation manuals and books have chapters on valve operation. Weathermatic's Turf Irrigation Manual is a good source for information on valve operation especially their reverse flow type of valve. You could also check with the National Irrigation Association website and check through their library of books etc. The basic principals of valve operation are the same for most all valves. The bottom of the valve , where the source water is, is separated from the upper chamber by a rubber diaphragm. When the valve is in a closed position there is water in both the upper and lower chambers. The reason the valve stays closed is because the water exposed surface area on the upper part of the diaphragm is larger than the water exposed surface area on the lower part of the diaphragm. Therefore, there is more force acting on the upper part of the diaphragm which keeps it closed. When the controller sends a signal to open the valve the solenoid plunger is lifted up which exposes a water exhaust port which sends the water in the upper chamber to the downstream outlet of the valve. When this happens, you lose the hydraulic advantage in the upper chamber because the water has someplace to go. The water at the bottom of the valve diaphragm pushes it open and the water now goes through the valve. Likewise , when the electric current is stopped to the solenoid, the plunger drops down, closing off the exhaust port. The pressure will then begin to build up again in the upper chamber and the diaphragm will slowly close as it reaches that hydraulic advantage again. If you want to understand through the use of a formula, use P(pressure) = F(force) / A(area). As you will see, at a given pressure if you change the area the force will change.

Go tohttp://www.hunterindustries.com/support/how-does-irrigation-valve-work for a decent Hunter video. Look on the bottom left for a PowerPoint illustration.

If you want to drift into the weird, irrigation valves are used in potato guns. There's an interesting video on Youtube at http://www.youtube.com/watch?v=XfukXLK7jUU.
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