Kennedy Theory

Kennedy, as described earlier, did pioneering research for obtaining a stable non-silting, non-scouring irrigation canal system. On the basis of observations made in certain reaches of Upper Bari Doab Canal system in Punjab, which were found to be fairly stable i.e., required no silt clearance for about three decades, Kennedy concluded that, (i) The flowing water is to counteract friction against the bed of the channel resulting in generation of vertical eddies rising up gently to the water surface and work up against the depth of channel. These eddies keep most of the silt in suspension. The vertical component of the eddies tend to move the sediment up, and the weight of sediment tends to bring it down, thereby keeping the sediment up, and the weight of sediment tends to bring it down, thereby keeping the sediment in suspension (ii) The silt supporting power of a channel cross section is mainly dependent on these eddies. Some of the eddies may start from the sides of the channel but these are for most of their part horizontal and as such of no silt supporting power. The silt supporting power of the channel is, therefore, proportional to the bed width, (iii) A velocity sufficient to generate these eddies keeps the sediment in suspension thereby avoiding silting up of the channel. He designated it as critical velocity $(V_0)$ defined as the mean velocity which just keeps the channel free from silting or scouring. The silt supporting power of a channel is proportional to $V_0^5{}^/{}^2$,(iv) Safe velocity against erosion for canals in Punjab soil in 1 m/sec corresponding to a depth of not more than 3 m, (v) The amount of silt held in suspension is proportional to the upward acting force of vertical eddies and varies as bed width and some power of the velocity of flow in the channel, (vi) A regime channel is that which neither silts nor scours, (vii) Coefficient of roughness n average for all irrigation channels is 0.0225. Later he founnd out that this value is not constant and suggested value of 0.02 for large canals and 0.025 for small channels.

Kennedy concluded that the channels of various sizes with velocities based on this formula did not silt or scour their beds. However, the formula gives correct tesults only when correct shape of the channel is chosen.

Kennedy later, a smore data became available, recognized that the sediment size played a significant role in this relationship and regarded the silt of Upper Bari Doab Canal as the standard silt. Since critical velocity in a channel depends upon the grade of silt, he introduced another factor, Kennedy critical velocity ratio, CVR, Denoted by symbol 'm' in the equation. It is the ratio of critical velocity in a channel to the critical velocity obtained at Upper Bari Doab Canal only. The factor was utilized to define the grade of silt and silt charge carried in the canals whose regime differed from that given byt the kennedy formula. The modfied equation is as under:

V$=0.55mD^0{}^.{}^6{}^4$

where, V=velocity (m/s), m=critical velocity ratio $(V/V_0)$, eith values varying from 1.1 to 1.2 for sand coarser than the standard and 0.8 to 0.9 for finer sands.

The non-silting velocity by the above formula is relevant to channels which have silt of the same character as that in the observed cahnnels of UBDC by Kennedy but different for silt charge of different size and grade. The suggested values of constant C and m for different silt charge in the genral form of the formula $V_0 = CmD^n$ are as under:

Kennedy Equations applicable in different regimes are as under:

$V_0 = 0.391D^0{}^.{}^5{}^5$, Godavari delta

$V_0 = 0.530D^0{}^.{}^5{}^2$, Krishna Western delta

$V_0=0.567D^0{}^.{}^5{}^7$, Lower Chenab canal

$V_0=0.283D^0{}^.{}^7{}^3$, Egyptian canals

A general feature of these formulae was that the value of C is proportional to the size of the be dmaterial.

Kennedy later (1904) recognized that the ratio of bed width to depth varied with the size of the channel. He stated that the proportion of bed to depth will, of course, vary with the size of the channel.