--- title: "Kennedy and Lacey silt theories compared" subject: "Irrigation and Drainage Engineering" chapter: 4 key: "semester_6/irrigation_and_drainage_engineering:kennedy-lacey-theories-compare" source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/kennedy-lacey-theories-compare site: BCT Engineering --- # Kennedy and Lacey silt theories compared Irrigation and Drainage Engineering · Chapter 4: Design of Canals - Asked in: 2075 Baisakh, 8 marks; 2063 Asoj (old course), 8 marks; 2062 Kartik (old course), 6 marks; 2076 Baisakh, 4 marks (asked 4 times) - Video: [Comparison of Lacey's and Kennedy's Theory | Lacey's Sit Theory | Kennedy's Silt Theory](https://www.youtube.com/watch?v=T6j7aHVzgBQ) — Let's GROW! - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/kennedy-lacey-theories-compare - Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-4 ## Question Explain the concept of Kennedy's and Lacey's silt theories and compare them. Why is Lacey's theory superior to Kennedy's theory? ## Short answer Kennedy's theory assumes eddies from the bed only and gives critical velocity V0=0.55mD^0.64, requiring trial design with a roughness formula. Lacey's regime theory uses eddies from the whole wetted perimeter, a silt factor f=1.76√d, and directly computes V, R, P and S from Q and f without trial. Lacey is superior because it directly accounts for silt size via f, needs no roughness coefficient, and is based on wider data. ## Answer #### Kennedy's silt theory (1895) Kennedy studied channels of the Upper Bari Doab canal system in Punjab (India) that were in regime. He stated that silt is kept in suspension by the **vertical eddies** generated at the bed by the flowing water. The upward component of these eddies balances the weight of the silt. Hence there is a **critical velocity** $V_0$ at which the channel neither silts nor scours: $$ V_0 = 0.55\,m\,D^{0.64} $$ where $D$ = depth of water (m) and $m$ = critical velocity ratio $V/V_0$ (depends on silt grade). The mean velocity $V$ is found with Kutter's (or Manning's) formula. A channel is designed by trial so that $V = V_0$; for a given $Q$ and $S$ the depth, width and velocity are fixed. #### Lacey's regime theory (1929-1935) Lacey said that a channel is in **true regime** only if it flows uniformly in unlimited incoherent alluvium of the same grade as it carries, and its section, slope and velocity all adjust themselves. Silt is held in suspension by the **vertical components of eddies generated at all points of the wetted perimeter (bed and sides)**, and the section tends to be semi-elliptical. Using a **silt factor** $f = 1.76\sqrt{d_{mm}}$, he gave: $$ V = \left(\frac{Qf^2}{140}\right)^{1/6},\quad R = \frac{5V^2}{2f},\quad P = 4.75\sqrt{Q},\quad S = \frac{f^{5/3}}{3340\,Q^{1/6}} $$ For a given $Q$ and $f$, every dimension is fixed with no trial and error. #### Comparison | Point | Kennedy | Lacey | |---|---|---| | Source of eddies | Bed only | Whole wetted perimeter | | Silt grade | Only through $m$ (vague) | Silt factor $f$ from grain size | | Basic equation | $V_0 = 0.55mD^{0.64}$ | $V = (Qf^2/140)^{1/6}$ | | Velocity formula | Kutter's, needs $n$ | Regime formulae, no $n$ | | Design variables | $Q,\ S$ known, find $B, D$ | $Q,\ f$ known, find $V, R, S, P$ | | Number of conditions | Two ($V_0$ and Kutter) | Three (regime) | | Procedure | Trial and error | Direct | | Section | Trapezoidal, $B/D$ by trial | Wetted perimeter fixed, $B/D$ follows | #### Why Lacey's theory is superior - It considers eddies from the entire wetted perimeter, which is closer to real flow. - Silt size enters through $f$, so grain size is accounted for directly; Kennedy's $m$ is chosen by judgement. - It gives the slope as an output, and treats $S$, $P$, $R$, $V$ as depending only on $Q$ and $f$, so the design is quick and unique. - It does not need a roughness coefficient, which is hard to estimate. - It defines regime clearly (initial regime, final regime and true regime) and gives a direct relation between the section and the discharge ($P \propto \sqrt Q$). - Its regime relations are based on data from many canals and rivers in different countries, so they apply better outside Punjab. Both are empirical and restricted to alluvial channels carrying fine silt. Lacey's equations give only the regime perimeter and do not indicate the section shape directly, which is the main criticism of his method. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. According to Kennedy, what keeps silt in suspension? A. Vertical components of eddies generated at the channel bed B. Eddies generated on the whole wetted perimeter C. The side slope shear only D. Surface waves on the water Answer: A. Kennedy considered only bed-generated eddies; Lacey used the whole wetted perimeter. (Key point: Kennedy's principle) 2. What is Kennedy's critical velocity equation? A. V0 = (Qf^2/140)^(1/6) B. V0 = 0.55 m D^0.64 C. V0 = 4.75 sqrt(Q) D. V0 = 5V^2/2f Answer: B. V0 depends on depth D and critical velocity ratio m. (Key point: Kennedy's equation) 3. How does Lacey account for silt grain size? A. Through critical velocity ratio m chosen by judgement B. Through Kutter's n C. Through silt factor f = 1.76 sqrt(d in mm) D. Through the side slope Answer: C. f is computed from grain size, whereas Kennedy's m is a judgement value. (Key point: Lacey silt grade) 4. Which is a genuine reason Lacey's theory is preferred? A. It uses Kutter's n for accuracy B. It requires trial and error for greater precision C. It is based on data from Punjab only D. It gives a direct design with no roughness coefficient or trial and error, using eddies from the entire perimeter Answer: D. Lacey's relations give V, R, P, S directly from Q and f without needing n. 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