<P> The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface . These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension (L in the above equation). This dimension is a matter of convention--for example radius and diameter are equally valid to describe spheres or circles, but one is chosen by convention . For aircraft or ships, the length or width can be used . For flow in a pipe or a sphere moving in a fluid the internal diameter is generally used today . Other shapes such as rectangular pipes or non-spherical objects have an equivalent diameter defined . For fluids of variable density such as compressible gases or fluids of variable viscosity such as non-Newtonian fluids, special rules apply . The velocity may also be a matter of convention in some circumstances, notably stirred vessels . </P> <P> In practice, matching the Reynolds number is not on its own sufficient to guarantee similitude . Fluid flow is generally chaotic, and very small changes to shape and surface roughness can result in very different flows . Nevertheless, Reynolds numbers are a very important guide and are widely used . </P> <P> Osborne Reynolds famously studied the conditions in which the flow of fluid in pipes transitioned from laminar flow to turbulent flow . In his 1883 paper Reynolds described the transition from laminar to turbulent flow in a classic experiment in which he examined the behaviour of water flow under different flow velocities using a small stream of dyed water introduced into the centre of clear water flow in a larger pipe . </P> <P> The larger pipe was glass so the behaviour of the layer of the dyed stream could be observed, and at the end of this pipe there was a flow control valve used to vary the water velocity inside the tube . When the velocity was low, the dyed layer remained distinct through the entire length of the large tube . When the velocity was increased, the layer broke up at a given point and diffused throughout the fluid's cross-section . The point at which this happened was the transition point from laminar to turbulent flow . </P>

Reynold's number is a ratio of inertia force to