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Figure 32 Moody diagram (From Engineering Data Book, 2d ed, Hydraulic Institute, Parsippany, NJ, 1990, p 37)
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Piping System Friction
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Reynolds number chart (From Engineering Data Book, 2d ed, Hydraulic Institute, Parsippany, NJ, 1990, p 42)
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Piping System Friction Piping System Friction 53
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flowing through this pipe, the velocity is 833 ft/s, and the velocity head is 108 ft
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Computing the kinematic viscosity first in square feet per second from Eq 22
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At 30 F, 67197 85 10 6795 At 130 F, 67197 14 10 6608
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The data have now been collected to compute the Reynolds number at the two temperatures At 30 F, R At 130 F, R 833 0505 0142 10 5 296 105 V D 833 0505 0841 10 4 500 104
The friction factors can now be selected from the Moody diagram (Fig 32) At 30 F and a Reynolds number of 500 104, the friction factor f is 0022 At 130 F and a Reynolds number of 296 105, the friction factor f is 0017 The friction in feet per 100 ft can now be calculated from the Darcy Weisbach equation (Eq 33) At 30 F, Hf At 130 F, Hf 0017 100 108 0505 364 ft/100 ft 0022 100 108 0505 471 ft/100 ft
This example demonstrates the use of Reynolds number and the Moody diagram It also emphasizes the variation in pipe friction with viscosity In this case, the friction at 130 F was 77 percent of that at 30 F Also, this demonstrates that the friction for water at 60 F from Table 35 of 357 ft /100 ft should not be used in calculating friction losses for this glycol solution
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Piping System Friction 54 The Basic Tools
333 Use of the Darcy Weisbach equation
For those who wish to study pipe friction further or use the Darcy Weisbach equation for generating their own computer program for pipe friction, the preceding example provides a guide for doing so Also, the two figures from the Hydraulic Institute s Engineering Data Book (Figs 32 and 33) should clarify the use of Reynolds number for the calculation of pipe friction Another source for Darcy Weisbach data is Cameron Hydraulic Data, published by the Ingersoll Rand Company Like the data book of the Hydraulic Institute, it is an excellent source for pipe and water data and is a necessary reference manual for any serious designer of piping Both these sources do not include any allowance in their tables for pipe aging, variation in pipe manufacture, or field assembly The Hydraulic Institute recommends that 15 percent allowance be made for these factors; I consider this factor adequate for loop-type systems such as hot or chilled water systems It is not adequate for cooling tower water, which is exposed to air in the water; it is recommended that a factor of 20 percent be added for this service if steel pipe is used This possible increase in friction for steel pipe may demonstrate the application for plastic pipe on cooling tower water; its use is limited by size and structural capability
334 Use of the Williams-Hazen formula
The Williams-Hazen formula is very popular in the civil engineering field and can be used for HVAC piping design if it is understood properly This formula gives accurate values for liquids that have a viscosity of around 11 cSt, such as water at 60 F It is therefore acceptable for chilled water and even condenser water It will show an error as much as 20 percent high if used for hot water over 200 F This formula is based on design factors that relate to the roughness of the pipe involved These design factors are called C factors that appear in the preceding equation and range from 80 to 160, 80 being for the roughest pipe and 160 for the smoothest pipe Table 36 is taken from an older edition of Cameron Hydraulic Data and includes the C factors for various types of pipe If a C factor of 140 is used with the Williams-Hazen formula, it will yield friction data for steel pipe that is somewhat comparable with the Darcy Weisbach formula with the 15 percent aging factor as recommended previously This is adequate for closed piping such as chilled water but should not be used with cooling tower piping Cooling tower piping should be calculated with a C factor of 130 for steel pipe when using the Williams-Hazen formula
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