--- title: "Tractive force method of channel design" subject: "Hydraulics" chapter: 10 key: "semester_4/hydraulics:tractive-force-method-explain" source: https://www.bctengineer.com/q/semester_4/hydraulics/tractive-force-method-explain site: BCT Engineering --- # Tractive force method of channel design Hydraulics · Chapter 10: Flow in mobile boundary channel - Asked in: 2081 Chaitra, 4 marks; 2072 Magh, 3 marks; 2072 Asoj, 3 marks (asked 3 times) - Video: [ST-020 Tractive force method](https://www.youtube.com/watch?v=2rH7-WvrfH4) — Dr. Philip De Groot - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/hydraulics/tractive-force-method-explain - Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-10 ## Question Describe how a mobile boundary channel is designed based on the tractive force method. ## Short answer The tractive force method ensures bed shear τb ≈ γyS0 and side shear τs ≈ 0.75γyS0 remain below permissible values. For coarse material, τc = 0.06(γs−γ)d from Shields; side critical stress is Kτc. Find permissible depth from bed and side limits, then use Manning’s equation to solve for base width b carrying the discharge. ## Answer The **tractive force method** (Lane, USBR) designs a mobile boundary channel by ensuring the shear stress (tractive force) of the flowing water on the bed and banks is less than the critical shear stress of the boundary material. #### Basic ideas - Tractive force on the boundary: $\tau_0 = \gamma R S_0$ (average). For a trapezoidal channel the maximum values are about $\tau_b \approx \gamma y S_0$ on the bed and $\tau_s \approx 0.75\gamma y S_0$ on the sides. - Critical shear stress on a level bed, $\tau_c$: from the Shields diagram, $\tau_c = \tau_*(\gamma_s - \gamma)d$ (about $0.06(\gamma_s - \gamma)d$ for coarse material), or from Lane's charts for a given $d_{75}$. - On the side slope, the critical shear stress is reduced to $\tau_{cs} = K\tau_c$, with $K = \sqrt{1 - \sin^2\theta/\sin^2\phi}$. #### Design procedure 1. From soil data find the grain size $d$ (or $d_{75}$) and the angle of repose $\phi$. 2. Select the side slope $z$ (with $\theta = \tan^{-1}(1/z) < \phi$) and compute $K$. 3. Find $\tau_c$ on the level bed; apply a reduction for sinuosity or a safety factor if required. 4. Find the permissible depth from the **side-slope** condition and the **bed** condition: - bed: $\gamma y S_0 \le \tau_c$ - sides: $0.75\gamma y S_0 \le K\tau_c$ and take the smaller $y$. 5. With that $y$, use Manning's equation ($n$ from the material) to find the base width $b$ that carries $Q$: $$ Q = \frac{1}{n}A R^{2/3}S_0^{1/2},\qquad A = (b + zy)y $$ 6. Check the Froude number (the flow should be subcritical) and add freeboard. If $b/y$ is far from the assumed range, repeat with a modified side slope. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the basic stability condition in the tractive force method? A. Shear stress of flow on bed and banks must be less than the critical shear stress of the material B. Mean velocity must be less than 1 m/s C. Froude number must be exactly 1 D. Hydraulic radius must be maximum Answer: A. The method keeps tractive force below the critical value on both bed and banks. (Key point: Principle) 2. Which pair of conditions is used to find the permissible depth? A. Bed: 0.75 gamma y S0 <= tau_c; Sides: gamma y S0 <= K tau_c B. Bed: gamma y S0 <= tau_c; Sides: 0.75 gamma y S0 <= K tau_c C. Bed: gamma y S0 <= K tau_c; Sides: gamma y S0 <= tau_c D. Both: gamma y S0 <= tau_c Answer: B. Bed carries up to gamma y S0 and sides 0.75 gamma y S0 but side critical stress is reduced to K tau_c. (Key point: Bed and side checks) 3. After computing the depth allowed by bed and by sides, which is adopted? A. The larger depth B. The average C. The smaller depth D. The bed depth always Answer: C. The smaller value satisfies both conditions. (Key point: Choosing depth) ## Related in Hydraulics - [Mobile boundary design: three approaches](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Adesign-three-methods-mobile-boundary) — Hydraulics, chapter 10 - [Rigid versus mobile boundary design principle](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Arigid-vs-mobile-boundary-design-principle) — Hydraulics, chapter 10, asked 3× - [Tractive force design in coarse alluvium, 20 m³/s](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Atractive-force-trapezoid-20m3s-d75-2cm) — Hydraulics, chapter 10 - [Derive tractive force ratio (shear reduction factor)](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Atractive-force-ratio-derivation) — Hydraulics, chapter 10, asked 5× - [Tractive force design for 15 cumecs, 5 cm particles](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Atractive-force-15-cumecs-5cm-particles) — Hydraulics, chapter 10, asked 2× - [Tractive force design for 10 cumecs, 3 cm particles](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Atractive-force-10-cumecs-3cm-particles) — Hydraulics, chapter 10, asked 2× ## Related in other subjects - [Tractive force design: Q 30](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Atractive-q30-slope-13700) — Irrigation and Drainage Engineering, chapter 4, asked 3× - [Tractive force design: Q 45](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Atractive-q45-slope-14500) — Irrigation and Drainage Engineering, chapter 4, asked 3× - [Tractive force design: Q 50](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Atractive-q50-slope-15000) — Irrigation and Drainage Engineering, chapter 4, asked 3× - [Sediment transport and tractive force approach](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Asediment-transport-tractive-force) — Irrigation and Drainage Engineering, chapter 4