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The equation for head loss in pipes, also referred to as slope, S, expressed in "feet per foot of length" vs. in 'psi per foot of length' as described above, with the inside pipe diameter, d, being entered in feet vs. inches, and the flow rate, Q, being entered in cubic feet per second, cfs, vs. gallons per minute, gpm, appears very similar.
PO gpm = pump output in gpm (gallons per minute) 1 gallon = 0.0238095238 barrels; ID 2 = inside diameter of the wellbore or casing, squared; OD 2 = outside diameter of the drill pipe or tubing, squared; 1029.4 = A conversion factor constant used to calculate the volume between the outside of a tube within the inside of another tube, using barrels.
Note that the cited sources recommend that flow velocity be kept below 5 feet / second (~1.5 m/s). Also note that the given f D in this table is actually a quantity adopted by the NFPA and the industry, known as C, which has the customary units psi/(100 gpm 2 ft) and can be calculated using the following relation:
where is the density of the fluid, is the average velocity in the pipe, is the friction factor from the Moody chart, is the length of the pipe and is the pipe diameter. The chart plots Darcy–Weisbach friction factor f D {\displaystyle f_{D}} against Reynolds number Re for a variety of relative roughnesses, the ratio of the mean height of ...
D H is the hydraulic diameter of the pipe (the inside diameter if the pipe is circular) (m), Q is the volumetric flow rate (m 3 /s), A is the pipe's cross-sectional area (A = πD 2 / 4 ) (m 2), u is the mean velocity of the fluid (m/s), μ (mu) is the dynamic viscosity of the fluid (Pa·s = N·s/m 2 = kg/(m·s)),
, the hydraulic diameter of the pipe (for a pipe of circular section, this equals D; otherwise D H = 4A/P for a pipe of cross-sectional area A and perimeter P) (m); v {\displaystyle \langle v\rangle } , the mean flow velocity , experimentally measured as the volumetric flow rate Q per unit cross-sectional wetted area (m/s);