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. Turbulent Flow in Pipes – Newtonian Fluids Determination of Friction Factor - Laminar Flow Relationship between shear stress and friction factor: Pipe flow under laminar conditions: Therefore, Newtonian fluids flow in pipe under laminar flow conditions: Hence, This equation will be used to calculate the friction factor of Newtonian fluids flow in pipe under laminar flow conditions. Turbulent Flow in Pipes – Newtonian Fluids Determination of Laminar/Turbulent Flow If Re 4,000 Turbulent Note that this critical Reynolds number is correct only for Newtonian fluids 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 the mean motion of the fluid. 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. Then we can figure out the critical flow rate.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: Power law constant (consistency factor), Ka = 6.63ĭetermine the critical annular velocity by substituting factors into this equation. Power law constant (flow behavior index), na = 0.51 Please follow the step-by-step calculation to learn how to determine the critical flow rate. Ka = power law constant (consistency factor)Īfter we get the critical velocity, we can figure out the critical flow rate by the following equation. Na = power law constant (flow behavior index) Μea = effective viscosity in the annulus, centi-poise The critical annular velocity equation is listed below: The Reynolds number equation for critical velocity is listed below: The effective viscosity equation for critical velocity is listed below: With this relationship, we can determine the critical velocity by rearranging the Reynold Number and Effective Viscosity equation. To get the point at the transition period, the critical Reynold Number for laminar flow must be around 3470 – 1370na. The first step of the critical flow rate determination is to figure out the critical velocity and then substitute it into the annular flow rate. Critical flow rate is the flow rate at the transition point between laminar and turbulent flow.
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