Consider the Colebrook equation for the friction factor in fully developed pipe flow /D 2.51 +...

 

Transcribed Image Text:

Consider the Colebrook equation for the friction factor in fully developed pipe flow €/D 2.51 + 3.7 Rep√ -2 log10 √I where f is the Darcy friction factor, e/D is the relative roughness of the pipe material, and Rep is the Reynolds number based on pipe diameter D. (a) Derive the following fixed-point iteration formula to find f fn+1 = 2 log e/D 2.51 + 3.7 Rep√In * by showing that 2 log €/D 3.7 + 2.51 Rep√ (7)]² (b) Use the fixed-iteration formula in part(a) to find f within 10-6 accuracy when e/D = 0.05, Rep 1000, and using an initial guess of fo = 0.04. = Consider the Colebrook equation for the friction factor in fully developed pipe flow €/D 2.51 + 3.7 Rep√ -2 log10 √I where f is the Darcy friction factor, e/D is the relative roughness of the pipe material, and Rep is the Reynolds number based on pipe diameter D. (a) Derive the following fixed-point iteration formula to find f fn+1 = 2 log e/D 2.51 + 3.7 Rep√In * by showing that 2 log €/D 3.7 + 2.51 Rep√ (7)]² (b) Use the fixed-iteration formula in part(a) to find f within 10-6 accuracy when e/D = 0.05, Rep 1000, and using an initial guess of fo = 0.04. =

Answer rating: 100% (QA)

6 Square both side F frea fmey f ... View the full answer