Contents preface (VII) introduction 1—37

8.5.1.1. Kennedy’s Method
Kennedy (6) collected data from 22 channels of Upper Bari Doab canal system in Punjab. His observations on this canal system led him to conclude that the sediment in a channel is kept in suspension solely by the vertical component of the eddies which are generated on the channel bed. In his opinion, the eddies generating on the sides of the channel had horizontal movement for greater part and, therefore, did not have sediment supporting power. This means that the sediment supporting power of a channel is proportional to its width (and not wetted perimeter).
On plotting the observed data, Kennedy obtained the following relation, known as Kennedy’s equation.

U = 0.55h^0.64	(8.9)
o

Kennedy termed U_o as the critical velocity¹ (in m/s) defined as the mean velocity which will not allow scouring or silting in a channel having depth of flow equal to h (in metres). This equation is, obviously, applicable to such channels which have the same type of sediment as was present in the Upper Bari Doab canal system. On recognising the effect of the sediment size on the critical velocity, Kennedy modified Eq. (8.9) to

U = 0.55mh^0.64

(8.10)

in which m is the critical velocity ratio and is equal to U/U_o. Here, the velocity U is the critical velocity for the relevant size of sediment while U_o is the critical velocity for the Upper Bari Doab sediment. This means that the value of m is unity for sediment of the size of Upper Bari Doab sediment. For sediment coarser than Upper Bari Doab sediment, m is greater than 1 while for sediment finer than Upper Bari Doab sediment, m is less than 1. Kennedy did not try to establish any other relationship for the slope of regime channels in terms of either the critical velocity or the depth of flow. He suggested the use of the Kutter’s equation along with the Manning’s roughness coefficient. The final results do not differ much if one uses the Manning’s equation instead of the Kutter’s equation. Thus, the equations

	U = 0.55mh^0.64	(8.10)
	Q = AU	(8.11)
and	U =	1	R2/3S1/2	(8.12)
		n

enable one to determine the unknowns, B, h, and U for given Q, n, and m if the longitudinal slope S is specified.
The longitudinal slope S is decided mainly on the basis of the ground considerations. Such considerations limit the range of slope. However, within this range of slope, one can obtain different combinations of B and h satisfying Eqs. (8.10) to (8.12). The resulting channel section can vary from very narrow to very wide. While all these channel sections would be able to carry the given discharge, not all of them would behave satisfactorily. Table 8.4 gives values of recommended width-depth ratio, i.e., B/h for stable channel (5).

¹This critical velocity should be distinguished from the critical velocity of flow in open channels corresponding to Froude number equal to unity.

DESIGN OF STABLE CHANNELS					291