Velocity
EquationV = Q / A
With your numbersV = 1000 cfm / 1.2272 ft² = 815 fpm
The working is shown in the units these equations are defined in. Your results above are converted.
SourceContinuity. A is the actual cross-sectional area, not the equivalent round area.
Friction loss
EquationΔp₁₀₀ = f · (100 / D) · Pv, 1/√f = −2·log₁₀( ε/(3.7D) + 2.51/(Re√f) )
With your numbersQ = 1000 cfm, Dₑ = 15.00 in → V = 815 fpm, Re = 104874, f = 0.01905, Pv = 0.0413 → Δp₁₀₀ = 0.06296 = 0.0630 in. w.g./100 ft
SourceDarcy–Weisbach with the Colebrook–White friction factor. Roughness from the ASHRAE Handbook — Fundamentals duct roughness categories.
Darcy friction factor f = 0.01905 at Re = 104874, relative roughness 2.40e-04 (galvanised steel, ε = 0.00030 ft).