--- title: "Principle and procedure of slope-area method" subject: "Engineering Hydrology" chapter: 4 key: "semester_5/engineering_hydrology:slope-area-principle-procedure" source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/slope-area-principle-procedure site: BCT Engineering --- # Principle and procedure of slope-area method Engineering Hydrology · Chapter 4: Surface Runoff - Asked in: 2069 Chaitra, 3+3 marks - Video: [Slope Area method | Hydrology | BE Civil | Prashant YT | 4th Sem | Unit:3 | Surface Runoff |](https://www.youtube.com/watch?v=yUxuC_eatug) — Prashant YT - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/slope-area-principle-procedure - Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4 ## Question Describe the principle of slope-area method for the measurement of flood discharge in a stream. Explain the procedure to compute peak discharge using the method. ## Short answer The slope-area method estimates flood peak discharge indirectly using Manning's equation and the energy slope from high-water marks and channel geometry. It computes conveyance from cross-sections and roughness, then iteratively finds discharge by correcting friction slope for velocity head and eddy losses. ## Answer #### Principle The slope-area method is an indirect method for estimating flood peak discharge in a stream reach from the high-water marks and the channel geometry, used when direct measurement is impossible. It assumes steady non-uniform flow in a reach and applies Manning's equation with the friction slope from the energy equation: $$ Q = K\sqrt{S_f},\qquad K = \frac{1}{n}AR^{2/3},\qquad S_f = \frac{h_f}{L} $$ $$ h_f = (h_1-h_2) + \left(\frac{\alpha_1v_1^2}{2g}-\frac{\alpha_2v_2^2}{2g}\right) - h_e $$ where $h_e = k_e|\Delta(\alpha v^2/2g)|$ is the eddy loss, with $k_e=0.3$ for expansion and $0.1$ for contraction. ```text E.G.L ----\_____ W.S. -----\___ \__ h_f bed ------------------ [1]<--L-->[2] ``` #### Procedure 1. Select a straight reach with a fairly uniform cross-section and clear high-water marks (flood marks) on both banks. 2. Survey 2 to 3 cross-sections and the water-surface levels at each section; measure the reach length $L$. 3. Compute $A$, $P$ and $R=A/P$ for each section; choose Manning's $n$ from the bed material and vegetation. 4. Compute conveyance $K_1$, $K_2$ and $K_m=\sqrt{K_1K_2}$. 5. First trial: $Q=K_m\sqrt{(h_1-h_2)/L}$. 6. Compute $v_1=Q/A_1$, $v_2=Q/A_2$, velocity heads, $h_e$ and $h_f$. 7. Compute the new $Q=K_m\sqrt{h_f/L}$; repeat until $Q$ converges. This is the peak flood discharge. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the slope-area method? A. An indirect method using Manning's equation and the energy slope from high-water marks and channel geometry B. A direct method using a current meter at many verticals C. A method using only the rainfall over the catchment D. A method using the stage-discharge curve at the site Answer: A. It estimates flood peak discharge without measuring flow, from flood marks, sections and roughness. (Key point: Principle) 2. How is the friction slope Sf obtained? A. Sf = bed slope of the whole river B. Sf = hf/L, where hf comes from the energy equation between two sections C. Sf = h1/h2 D. Sf = Manning's n divided by L Answer: B. hf is the fall plus the change in velocity head minus eddy loss, and Sf = hf/L. (Key point: Friction slope) 3. How is the final discharge found? A. Take the first trial value as the answer B. Average the discharges at the two sections C. Start with Q = Km sqrt((h1-h2)/L), recompute velocity heads and hf, and repeat until Q converges D. Multiply conveyance by reach length Answer: C. Velocity heads depend on Q, so iteration is needed until Q stops changing. (Key point: Trial procedure) 4. What eddy loss coefficients apply? A. 0.1 for expansion and 0.3 for contraction B. 0.5 for both C. Zero for both always D. 0.3 for expansion and 0.1 for contraction Answer: D. Expanding reaches lose more energy to eddies, so ke = 0.3 for expansion and 0.1 for contraction. 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