Modelling and Numerical Investigation of Pressure Drop of Viscous Fluid in Elbow Pipe using Colebrook-White Equation
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Date
2026
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Department of Civil Engineering, University of Ilorin
Abstract
Elbows constitute resistance to flow, increase energy losses, and increase pumping power. This current study presents a mathematical model for
analyzing pressure drop in elbow pipes for viscous fluids with flow conditions in turbulent flow regimes. The selected pipes were two 90º 100 mm nominal diameter schedule 40 commercially available steel elbow pipes of different geometries. The mathematical model developed was validated with experimental results, and numerical simulation for the model was conducted using MATLAB with varying parameters such as velocity and friction factor. Results showed that for low viscous flow with velocities ranging from 0.33 to 6 m/s, the pressure drop values obtained were between 0.0128 and 6.1669 kPa and 0.0087 and 4.2195 kPa for short-radius elbows and long-radius elbows, respectively. For higher viscous fluids with velocities ranging from 46.26 to 100 m/s, pressure drop values obtained were between 431.6507 and 3919.1 kPa and 295.34 and 2681.5 kPa for short-radius and long-radius elbows, respectively. The results of the study can function as a guide in the choice of 90° elbow pipe used in manufacturing and process industries for the transport of the viscous fluids treated.
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Keywords
Colebrooke-White equation, elbow pipe, friction factor, pressure drop, turbulent flow, viscous fluids.