An Improvement in the Calculation of Turbulent Friction in Rectangular Ducts

Abstract

Frictional pressure drop in rectangular ducts is examined. Using correspondence between theory and experiment in laminar flow as a means for acceptance of published data, turbulent flow data for smooth rectangular ducts were compared with smooth circular tube data. Data for ducts having aspect ratios between unity and 39:1 were obtained in the literature and, in conjunction with new experimental data, were examined for deviations from the smooth circular tube line (smooth Moody). It was found that at constant Reynolds number based on hydraulic diameter the friction factor increases monotonically with increasing aspect ratio. It was thus concluded that the hydraulic diameter is not the proper length dimension to use in the Reynolds number to insure similarity between the circular and rectangular ducts. Instead, it was determined that if a modified Reynolds number Re* was obtained so that geometric similarity was provided in laminar flow by the relation f = 64/Re* for all geometries, that this Reynolds number also provided good similarity in fully developed turbulent flow within a ∼ 5 percent scatter band about the smooth tube line. By using this “laminar equivalent” Reynolds number, Re*, it is demonstrated that circular tube methods may be readily applied to rectangular ducts eliminating large errors in estimation of friction factor.

Reynolds number dependence of mean flow structure in square duct turbulence

“…The skin friction coefficients, obtained averaging in time and along the streamwise direction, are in good agreement with the empirical formula: f − 1 2 = 2 log 10 (2.25 Re b f 1 2 ) − 0.8, f being the skin friction factor defined by f = 8u 2 τ /U 2 b (Jones 1976). At this level, it is important to mention that the above given empirical formula estimates that the length of the edge of the square in wall units spans the range 2 h + ∈ [160, 450] for the considered interval of Reynolds numbers (i.e., Re b ∈ [1077, 3500]).…”

Aeolian deposition of dust over hills: the effect of dust grain size on the deposition pattern

“…The airflow in the wind tunnel during the experiments was fully turbulent as the tunnel Reynolds number during the tests (106 000) was well above the critical value of 3900 (threshold value for a rectangular tunnel of 120 cm wide and 60 cm high; see Jones (1976) and Obot (1988) …”

Numerical methods for hydraulic fracture propagation: A review of recent trends

“…It is a function of both the local Reynolds number of the flow Re = ρD eq V /µ (where D eq is an equivalent hydraulic radius for plane flow) and the fracture relative roughness k/w (where k is a characteristic scale of the fracture roughness -typically related to the rock grain size). As first discussed in Jones (1976), the definition of the equivalent hydraulic radius can be directly obtained such that the laminar parallel plate flow relation (Poiseuille law) for a Newtonian fluid is recovered when using the laminar expression of the Fanning factor for pipe flow f = 16/Re Deq , i.e. D eq = 4/3w.…”