Fluid dynamics: laminar and turbulent flow

where Q is flow, ΔP is pressure gradient, r is radius, η is fluid viscosity and l is length.

From this equation, it can be seen that flow is directly proportional to the pressure gradient and the fourth power of the radius. Therefore, doubling the diameter of the tube will increase flow by 16 times (2⁴). Flow is inversely proportional to the viscosity of the fluid and the length of the tube.

Turbulent flow is rough and disordered. Eddy currents and parallel mixing occur within the fluid stream.

The Reynolds number is a dimensionless number that is defined as the ratio of inertial and viscous forces. It is used to predict which type of flow is likely to be present. A Reynolds number <2000, where viscous forces predominate, predicts flow to be laminar. Between 2000 and 4000, both laminar and turbulent flow are anticipated. Above 4000, flow is likely to be completely turbulent because inertial forces are dominant. Critical flow is the point above which turbulent flow commences, which occurs at a Reynolds number of around 2000.

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