The effects of Reynolds number on fluid flows

Abstract

his dissertation investigates the effects of Reynolds number (Re) to fluid flows. Very small . moderate and large Reynolds number efiects are considered and their corresponding significance are discussed. For small Reynolds number. creeping flows are considered. so that the Navier-Stokes equations and the continuity equation for creeping flow are derived. These two equations are fiirther reduced to Laplace equation_ which can easily be solved. This theory is therefore applied to solve problems related to very slow motion flows e.g flow" through porous media. the Helle Shaw flow, the flow" past a sphere and the lubrication theory. However. emphasis has been placed on flow through porous media. For moderate Reynolds numbers. laminar flows and flow‘ through circular pipes; minor and major head losses in pipe flows are also considered. Further. transitions from laminar to turbulent flow" regimes in pipe flows are discussed with reference to the Reynolds number For the large Reynolds numbers flow s. the boundary layer concept is discussed where the boundary layer thickness is calculated. The skin friction coefficient, the drag coefiicient. and lifi coefiicient acting on objects moving within the boundary layer are also considered. in these cases. discussions are made on how these coefficients can be increased or minimised. Finally boundary layer separation and control are discussed and their relevant applications are considered with respect to motion of objects influenced by the existence of boundary layer flows.