Hydrodynamically Developing and Fully Developed Laminar Flows in a Semicircular Duct: Analytical and Computational Analyses

Hydrodynamically developing and fully developed laminar flows in a semicircular duct are numerically and analytically investigated, respectively. As part of the analytical approach, scale analysis is used to develop order-of-magnitude estimates for the friction factor–Reynolds number product for developing and fully developed laminar flows in a semicircular duct. Dimensionless axial velocity distribution is determined and presented in terms of the dimensionless pressure drop constant for hydrodynamically fully developed laminar flow. Fully developed laminar frictional characteristics for flow through a semicircular duct are then deduced from the dimensionless axial velocity distribution, from which the location of maximum axial velocity and the ratio of maximum axial velocity to the mean axial velocity are determined. In addition, hydrodynamically developing laminar flow in a semicircular duct is numerically analyzed. Various developing flow region parameters, such as the apparent Fanning friction factor and incremental pressure drop number, for laminar flows in a semicircular duct are determined from the numerical analysis. Furthermore, the fully developed laminar flow results obtained from the numerical analysis are compared with the analytical solution, and good agreement is observed between them.