Determine the Head Loss Due To Friction
Determine the head loss due to friction using the Darcy-Weisbach equation. The water is pumped at 3.0 gallons per minute, has a temperature of 60 °F and is pumped through a 1inch schedule-40 steel pipe. The equivalent length of the piping and minor losses is 258 ft.
Steps to solve for the Reynolds Number:
What is the pipe internal diameter? 0.0874 ft
What is the pipe internal area? 0.00600 ft2
What is the velocity of the water flowing in the pipe? 1.11 ft/sec
(3.0gpm)(0.002228 cƒs/gpm) 0.00600 ƒt2
What is the kinematic viscosity? 1.27 × 10-5 ƒt2 /sec
Calculate the Reynolds Number: 8.0 × 103
(0.0874 ƒt)(1.11ƒt /sec) / 1.217 × 10-5 ⁄ ƒt2 sec
Steps to solve for the Relative Roughness:
What is the Specific Roughness of the pipe material? 0.0002
What is the pipe internal diameter? 0.0874 ft
Calculate the Relative Roughness: 0.0002/0.0874 ft = 0.00228
Steps to solve for the friction factor "f": 0.0354 to 0.0361
Apply the Relative Roughness and Reynolds Number to the Moody Diagram or
Darcy Friction Factor table
Calculate the head loss due to friction using the Darcy equation: hƒ = ƒLv2/2Dg
(0.0354)(258 ƒt)(1.11 ƒt /sec)2 /2(0.0874 ƒt)(32.2 ????/sec2) = 2.0 ƒt
(0.0361)(258 ƒt) (1.11 ƒt /sec)2 /2(0.0874 ƒt)(32.2 ƒt /sec2) = 2.04 ƒt