INTRODUCTION 3 



sections along the channel, and remains constant with respect to time. 

 The discharge divided by the area at a section gives the average velocity 

 at the section, or more briefly, the velocity. Open channel flow is 

 turbulent except in very small channels, so that the velocity of the 

 different filaments in a section will usually show considerable variation, 

 both in magnitude and in direction. 



The velocity head at a section is equal to the square of the average 

 velocity, divided by twice the acceleration of gravity. It is equal to the 

 distance through which a freely falling body would have to fall from rest, 

 under the influence of gravity alone, in order to acquire a velocity equal 

 to the average velocity. The velocity heads of the individual filaments 

 will vary considerably above and below the velocity head based on the 

 average velocity, and it should be noted that the average of the velocity 

 heads will be somewhat greater than the average- velocity head. This is 

 important in precise investigations of energy loss, but is unimportant 

 for practical hydraulic work, except in the few cases where the velocity 

 distribution is markedly non-uniform. 



The sum of the elevation head, measured above a fixed datum plane, 

 and the pressure head, measured above atmospheric, is often called the 

 static head. The static head at every point in a cross section of an open 

 channel in which the flow is essentially parallel will be the same, even 

 though the velocity head varies from filament to filament. 



Another derived variable of great significance in open channel flow is 

 that which represents the energy of the flow.^ As a matter of con- 

 venience it is customary to approximate the energy of the stream by the 

 total head, which is equal to the depth of flow plus the velocity head 

 corresponding to the average velocity. The total head may be referred 

 to the bottom of the channel, if it is a uniform channel, or to a convenient 

 horizontal datum, if it is an irregular channel. A longitudinal profile of 

 the elevation of the total head is called the total head line, or energy 

 line. 



* Use of the word " energy " in this connection is not logical and is likely to be 

 misleading, but it has been well established by custom. The erroneous implication 

 is that elevation head, pressure head, and velocity head each represent energy. 

 Though a certain quantity of water may actually possess energy (the ability to do 

 work) by virtue of its elevation or velocity, it cannot of itself possess energy because 

 of being under pressure. The energy corresponding to its pressure head is only 

 available when the situation is such that the surrounding fluid will close in, constantly 

 maintaining full pressure, as the water is being removed to a region of lower pressure. 

 Compare, for example, the work that could be obtained in releasing a pound of water 

 from behind a dam with that obtainable in releasing a pound of water from a strong 

 steel container which it completely fills, the initial and final pressures being the same 

 in each case. 



