(.5/24)^2 * PI = .0013635 ft^2. This is the Area in square feet of a circle with a diameter of 1/2". It is inch diameter divided by 12 = ft diameter, divided by 2 = ft radius. I know cake are square, pie are round, but for sprinkler work: Area=the radius squared times PI. So far we have ft * ft, so if we had ft/sec, the velocity of the flow, we would have ft * ft * ft/sec. That is cubic ft per sec, and since there are 7.48 gallons per cubic feet and 60 seconds per minute we could get gal/min-- GPM, if we knew ft/sec. Evangelista Torricelli figured that out in the first half of the 1600s: Torricelli's Theorem- v=SQRT(2gh). g is the (constant) acceleration due to gravity although I don't know what it was called then because Newton wasn't born yet, it was just the number that made the Theorem work. I use 32.2 ft/sec/sec. h is 'feet of head', or, how many feet above your head is the water level? If a gauge screwed to your nose said 100 PSI, it means the h is 100/.433=230.9 ft above. This is because water weighs 62.4 lbs/ft^3, lbs is force, pressure is force divided by area, and 62.4/144=.433.
We can all argue about PEX, but whom amongst us will argue: Q=14.816 P=7.0 K=5.6 ? When I first started screwing up on hydraulic calculations 40 years ago the manufacturer's data showed K Factors like 5.56, 5.80, 5.this and that, based on actual bucket test type U.L. measurements. Thank Goodness it all boiled down to it's fine to use NOMINAL 1/2" diameter with Coefficient of Discharge=.75. That just means between the actual I.D. of a "1/2 HEAD" and Torricelli, about 3/4 is delivered. So, .0013635 ft^2 * .75 = .001023 ft^2. Now the 'size of Cecil's hole' is set, and will not change under any conditions. We could assume any pressure and calc the flow, or any flow and calc the pressure. Doing the latter: 14.816/7.48/60=.033 ft^3/sec. .033 ft^3/sec / .001023 ft^2 = 32.27 ft. 32.27 ft. Rearranging Torricelli: h=v^2/2g=16.17 ft. 16.17 ft * .433 = 7.00 lbs/ft-- "PSI". It's Friday on the Forum so trip to the liquor store and back to the PEX debate. Thanks Steve, May you have a happy weekend too. b
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