120 Prof. J. Thomson on the Flow of Water in [Dec. 12, 



The great distinction between the mode of flow of a very viscid fluid, 

 such as treacle or tar, and the mode of flow of water in ordinary 

 circumstances in pipes and in open channels, has not been enough 

 generally and enough consistently attended to. The laminar theory 

 constitutes a very good representation of the viscid mode of motion ; 

 but it offers a very fallacious view of the motion in the flow of water 

 in ordinary cases in which the inertia of the various parts of the fluid 

 is not subordinated to the restraints of viscosity. 



In the flow of water in an open channel in ordinary circumstances 

 the earth's attraction is perpetually tending to accelerate the forward 

 motion of the water throughout the whole body of the current in con- 

 sequence of the surface declivity ; or we may say, with more complete 

 expression, in consequence of the fall of free-level* which, in virtue of 

 the surface declivity, occurs to all particles in the current as they 

 advance in their down-stream course. The tendency to increase of 

 velocity, if we neglect the backward or forward force, usually very 

 small, or it may be nothing, applied by the air to the water surface, we 

 may say is counteracted solely by a backward resisting force-system 

 applied by the wetted face of the channel to the water momentarily in 

 contact with it. The wetted channel face, it must be observed, is 

 ordinarily more or less rough with gravel, mud, weeds, or other 

 asperities. It is not a true view to imagine a smooth channel face 

 washed by a thin lamina of water, which imagined lamina of water 

 receives a backward or resisting force-system applied tangentially by 

 the so imagined channel face, and transmits tangential backward force 

 to another lamina of water lying next to itself on the side remote 

 from the channel face. It is not the case that from any layer of water 

 whatever, thick or thin, spread over the channel face, resisting forces 

 are transmitted to the interior of the body of the current in any great 

 degree by mere viscid resistance to change of form in the intervening 

 fluid, as would be the case if it were like treacle or tar. But, very 

 differently, indefinite increase of velocity of the water situated in the 

 interior of the current is prevented by continual transverse flows 

 thereto, and commingling therewith, of portions of water already 

 retarded through their having been lately in close proximity to the 

 resisting channel face; and, jointly with that, by the condition that 

 portions of the fluid which have been flowing forward temporarily in 



* The free-level for any particle of water, in a mass of statical or of flowing 

 water, is the level of the atmospheric end of a column, or of any bar of statical 

 water, straight or curved, having one end situated at the level of the particle, and 

 having at that end the same pressure as the particle has, and having the other end 

 consisting of a level surface of water freely exposed to the atmosphere, or else 

 having otherwise atmospheric pressure there. Or, briefly, we may say that the 

 free-level for any particle of water is the level of the atmospheric end of its pressure- 

 column, or of an equivalent ideal pressure-column. 



