Pipe Turbulent Flow and Convection from First Principles and Disc Drag

This article involves laminar and turbulent flow in pipes and pipe wall convection also, along with torque of rotating discs. The conventional definition of dynamic viscosity, originally presented by Newton, assumes that the shear force is as a result of friction and is proportional to the elemental velocity change. The author adds a second term, where he assumes that the shear force is also due to inertia and is proportional to velocity squared via pressure, as opposed to shear force. The shear force, resulting velocity, inertial pressure, and resulting flow rate are calculated using a single equation each, by integration. A comparison is made with the conventional frictional factor, and with measurements also. The convection is simulated purely as conduction, where a velocity term is added to the conduction coefficient equation, and the results are reasonably accurate, when compared to the convection coefficient calculated from Nusselt number. Sample temperature profiles are given. Measurements are made of shear force and pressure in turbulent flow around a rotating disc. Two different apparatuses were used. Drag on the rotating disc is measured and accurately simulated. It is shown that the drag is independent of flow thickness.