Pressure Drop of Fully-developed, Laminar Flow in Rough Microtubes

The characteristics of fully-developed, laminar, pressure-driven, incompressible flow in rough circular microchannels are studied. A novel analytical model is developed that predicts the increase in pressure drop due to wall roughness in microtubes. The wall roughness is assumed to posses a Gaussian isotropic distribution. The present model is compared with experimental data, collected by other researchers and good agreement is observed. Nomenclature a = mean radius of rough microtube, m C = Darcy’s friction coefficient, fReD D = microtube inside diameter, m f = Darcy’s friction factor, [−] f∗ = normalized friction factor, f/f0 L = microtube length, m ṁ = mass flow rate, kg/s p, q = random variables, m Ra = arithmetic average wall roughness, m r = radius, m ReD = Reynolds number, ρuD/μ Rf = frictional resistance, m−1s−1 R∗ f = normalized frictional resistance, Rf/Rf,0 Rq = RMS wall roughness, m T = mean fluid temperature, ◦C u = mean fluid velocity, m/s z = measured values of surface heights, m 1Post-Doctoral Fellow. Mem. ASME. Corresponding author. Email: [email protected]. 2Distinguished Professor Emeritus. Fellow ASME. 3Associate Professor and Director of MHTL. Mem. ASME. Greek 2 = relative roughness, ≡ σ/a ρ = fluid density, kg/m μ = fluid viscosity, kg/m.s σ = roughness standard deviation, m ∆P = pressure gradient, Pa Subscripts 0 = reference value, smooth microtube θ = in angular direction x = in longitudinal direction