Implications of Froude’s work

It seems to me that Froude showed us something fundamental about the flow of fluids that had not been demonstrated before. In this chapter I wrote this (and I reproduce it in red because it is easier than scrolling back to find it):-

 

The obvious effect of the motion of this swim head bow is to push water forwards and upwards and it is evident from the bubbles in the picture that the wave in front of the bow is close to rolling just as it might in an open channel. It also follows that water must flow under the boat and that somewhere there is a horizontal division between water that will go upwards and forwards and water that will go backwards under the hull. The momentum in the vertical direction of the two flows must be equal and opposite because there can be only one value for the net force between them. The result is that the water with higher speed flowing under the boat will experience a drop in pressure as evidenced by the trough on the side of the boat.[1] (Had this been a channel we would have talked of constant specific energy.) The rise in the water level ahead of the bow will increase the static pressure all over the head by an amount equal to  and this pressure acting on the area of the front of the bow will produce an additional force on the boat that has a component that resists the motion. The rise in level  where  is the speed of the boat.

 

One way or another this will happen for bows of any shape whether they are sharp like a warship, blunt like a tanker or fitted with a bulbous bow. A rise in level will occur and it will alter the pressure acting on some difficult-to-define area around the bow to produce the resisting force. The central argument of model testing is that, if the value of  is proportional to the length, the pressures will be in proportion to the square of the speed and the areas that are affected will be the same shape and proportional to the square of the length. Then if two hulls of the same shape but of different sizes running with the same trim at the corresponding speeds the resistances will be proportional to the cubes of their length.

 

The curves in graph 11-4 are so totally similar that there can be no doubt that the pressures do rise over the hulls in the same way and that the pressures do act on the various areas of the hull in the same way to produce forces that can be related by simple scientific methods. The fluid flow over hulls is repeatable and by extension will be repeatable for aeroplanes, rivers, water turbines and every other similar application.

 

A direct consequence of this is that if you choose a category of ship, for example an oil tanker, the goals of designers are always the same and the resulting designs will tend to a best shape that will be substantially the same, if not identical, for all tankers regardless of size. The service speed and the power requirements will change with size in a predictable way. We have potential for a systematic storage of design data. The same thing will be true for other devices that are made in a range of sizes.

 

This is important and it came about through the skill and persistence of one man. It is appropriate that his name is immortalised in the non-dimensional parameter that bears his name.