Turbulent Flow in Pipes/Annuli – nonNewtonian Fluids Equivalent Diameter for Annular Geometry – From Momentum Equation From the momentum equation, frictional pressure drop for Newtonian fluid in the annulus is Turbulent Flow in Pipes/Annuli – NonNewtonian Fluids Equivalent Diameter for Annular Geometry – Hydraulic Diameter Method Hydraulic diameter is defined as:Įquivalent diameter by using hydraulic diameter method: Solve this equation for the Fanning friction factor: f = 0.00666 Thus the frictional pressure loss can be obtained by 2ĭp f v 0.00666* 9 *11.162 p f D D *10000 756psi dL 25.8d 25.8 * 3.826 Turbulent Flow in Pipes – Newtonian Fluids Example From table 4.5, the absolute roughness for commercial steel pipe is e = 0.000013 inches. For smooth pipe, the relative roughness e/d 2,100, the flow is under turbulent flow conditions. Turbulent Flow in Pipes – Newtonian Fluids Determination of Friction Factor - Turbulent Flow For turbulent flow, the friction factor can be calculated by using Colebrook correlation. This equation will be used to calculate the friction factor of Newtonian fluids flow in pipe under laminar flow conditions. Newtonian fluids flow in pipe under laminar flow conditions: Turbulent Flow in Pipes – Newtonian Fluids Determination of Friction Factor - Laminar Flow Relationship between shear stress and friction factor: Note that this critical Reynolds number is correct only for Newtonian fluids fluid velocit y,ft /s d pipe I.D.,in μ viscosit yof fluid, cp. Μ where ρ fluid densit y,lbm/gal u avg. Turbulent Flow in Pipes – Newtonian Fluids Determination of Laminar/Turbulent Flow _ Laminar occurs at low Reynolds number, where viscous forces are dominant, and is characterized by smooth, constant fluid motion turbulent flow occurs at high Reynolds number and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities. Reynolds number is used to characterize different flow regimes, such as laminar or turbulent flow. Turbulent Flow in Pipes – Newtonian Fluids Definition of Reynolds Number Reynolds number, Re, is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces. This irregular, fluctuating motion can be regarded as superimposed on ![]() Turbulent Flow: In turbulent flow, there is an irregular random movement of fluid in transverse direction to the main flow. Laminar flow systems are generally represented graphically by streamlines. ![]() There is no microscopic or macroscopic intermixing of the layers. Turbulent Flow in Pipes – Newtonian Fluids Introduction Laminar Flow: In this type of flow, layers of fluid move in streamlines. Drilling Engineering – PE 311 Turbulent Flow in Pipes and Annuliįrictional Pressure Drop in Pipes and Annuli When attempting to quantify the pressure losses in side the drillstring and in the annulus it is worth considering the following matrix:
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