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