Question

g If experimentally you measure the hydraulic gradient, Δp/L = 0.6832 m H2O/m, with a tube diameter = 3.00 mm and a mean measured flow velocity through the tube = 1.043 m/s; and rho= 997.0 kg/m3 and μ = 9.140 x 10-4 (N-s)/m2, what is the corresponding value of the friction factor, f ? Do not calculate this based upon a theoretical prediction, but from the definition of the friction factor and using these experimentally determined values

Answer 1

Fanning friction factor = 0.009232

Darcy's friction factor = 0.03693

Step-by-step explanation:

Fanning friction factor is given by

f = τ ÷ (ρv²/2)

where

τ = wall shear stress

ρ = density of the fluid = 997 kg/m³

v = mean measured flow velocity through the tube = 1.043 m/s

τ = (R/2) × (ΔP/L)

R = radius of the pipe = 0.0015 m

(ΔP/L) = 0.6832 m H2O/m = (0.6832 × 997 × 9.8) Pa.m = 6,675.3 Pa.m

Note that: ΔP = ρgh

τ = (0.0015/2) × (6,675.3) = 5.01 N/m²

f = τ ÷ (ρv²/2)

f = 5.01 ÷ (997 × 1.043²/2)

f = 0.009232

Darcy's friction factor = 4 × fanning friction factor

Darcy's friction factor = 4 × 0.009232

= 0.03693

Hope this Helps!!!