Appendix 2
The behaviour of the flow over a body moving through a viscous liquid such as water is governed by the ‘Reynold’s Number’ defined as:
Length × Velocity/ (Kinematic Viscosity of the liquid) Reynold’s Number governs the viscous resistance which, per unit area, is highest at low Reynold’s Number and hence small changes of Reynold’s Number have the greatest effect at low Reynold’s Number. At very low values of Reynold’s Number the flow is ‘laminar’ – very smooth. Laminar flow is unlikely to occur to any great extent on a ship but may occur on a model, making it difficult to scale the result to full size. At higher values the flow is ‘turbulent’, full of eddies.
In scaling viscous resistance from model to ship it is usually sufficient to use an overall value of Reynold’s Number based on ship length. However, in the case of a submerged submarine the resistances of the appendages – bridge fin, rudder, hydroplanes, flooding holes etc – form a major part of the overall resistance. Strictly, each should be scaled independently using its own value of Reynold’s Number based on chord length or as appropriate. This approach was lengthy and difficult with the methods available until about the 1960s. It was probably first applied as Dreadnought was completing, when there were several ‘rival’ estimates of her speed.
Reynold’s Number also governs the scaling of viscous flow over a propeller, and hence cavitation effects, where it is even more difficult to define the appropriate length. Early studies used diameter, but this gave misleading results. Clearly something related to chord length was needed but which chord? For quite sound reasons the chord at 0.7 radius was regarded as typical though the author in some fairly successful approximations used a mean value, dividing the area of the face of the blade by the radius of the propeller. The next problem with a propeller is the choice of the appropriate velocity over a blade that is rotating as well as moving forward. It is possible to combine rotational velocity with forward motion but the former varies with radius. Again the magical 0.7 radius seems to work as a mean.1 The problem is still not over, as the action of the propeller increases the speed of the water ahead of it and, strictly, this effect should be included. It was and, in the author’s opinion, still is too difficult and any errors are reduced by an appropriate ‘fudge factor’.
Reynold’s Number is a convenient shorthand telling fellow engineers that viscous effects predominate and scaling from model to ship needs care and experience.
1 For most propellers, half the total water flow through the propeller disk takes place outside 0.7 radius.