Saturday, January 25, 2014

Comparison of Kennedy's and Lacey's Theories


Here is a brief comparison of Kennedy's theory and Lacey's theory for the design of channels for canal etc.

  • The concept of silt transportation is same in both the cases, both agree that the silt is carried by the vertical eddies generated due to friction of the flowing water against rough surface of canal. Kennedy considered a trapezoidal channel section and, therefore, he neglected eddies generated from the sides. For this reason, Kennedy's critical velocity formula was derived only in terms of depth of flow(y).  Lacey considered that an irrigation channel achieves a cup-shaped section(semi-ellipse) and that entire wetted perimeter of the channel contributes to the generation of silt supporting eddies. He, thus, used hydraulic mean radius(R) as a variable in his regime velocity formulas instead of depth(y).
  • Kennedy stated all the channels to be in state of regime provided they did not silt or scour. But Lacey differentiated between two regime conditions, i.e. initial regime and final regime.
  • According to Lacey, grain size of material forming the channel is an important factor, and should need much more attention than what was given to it by Kennedy. He connected grain size(d) with his silt factor(f) as f= 1.76(dmm)^0.5.
  • Kennedy used Kutter's formula for determining actual generated channel velocity. The value of Kutter's rugosity coefficient(n) is again a guess work. Lacey, on the other hand, has produced a general regime flow, after analyzing huge data on regime channels.
  • Kennedy has not given any importance to bed width and depth ratio. Lacey has connected wetted perimeter(P) as well as area(A) of the channel with discharge, thus, establishing a fixed relationship between bed width and depth.
  • Kennedy did not fix regime slopes for his channels, although, his diagrams indicate that steeper slopes are required for smaller channels and flatter slopes are required for larger channels. Lacey, on the other hand, has fixed the regime slope, connecting it with discharge.