By E. W. Billington and A. Tate

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**Example text**

At flow rates above 168,040 bbl/day the Reynolds number exceeds 4000 and the flow will be in the turbulent region. Thus, for this 16 in. pipeline and given liquid viscosity of 250 cSt, flow will be fully turbulent at flow rates above 168,040 bbl/day. As the flow rate and velocity increase, the flow regime changes. With changes in flow regime, the energy lost due to pipe friction increases. At laminar flow, there is less frictional energy lost compared with turbulent flow. 4 Flow Regimes In summary, the three flow regimes may be distinguished as follows: Laminar: Reynolds number<2000 Critical: Reynolds number>2000 and Reynolds number<4000 Turbulent: Reynolds number>4000 As liquid flows through a pipeline, energy is lost due to friction between the pipe surface and the liquid and due to the interaction between liquid molecules.

Sometimes an R value of 2100 is used as the limit of laminar flow. 16) where Q=Flow rate, bbl/day D=Internal diameter, in. 15) after performing conversions to commonly used pipeline units. R is still a dimensionless value. 17) where Q=Flow rate, gal/min D=Internal diameter, in. 18) where Q=Flow rate, m3/h D=Internal diameter, mm ν=Kinematic viscosity, cSt As indicated earlier, if the Reynolds number is less than 2000, the flow is considered laminar. This means that the various layers of liquid flow without turbulence in the form of laminations.

This variation in the velocity of the liquid layers results in a velocity gradient. 6) where dV/dy represents the rate of change of velocity with distance or the velocity gradient. Newton’s law states that the shear stress between adjacent layers of a flowing liquid is proportional to the velocity gradient. The constant of proportionality is known as the absolute (or dynamic) viscosity of the liquid. Shear stress=(Viscosity) (Velocity gradient) Copyright © 2004 by Marcel Dekker, Inc. 16 Chapter 2 The absolute viscosity of a liquid is measured in lb-s/ft2 in English units and pascal-s in SI units.