--- title: "Slope area method of discharge" subject: "Hydro Power" chapter: 2 key: "semester_6/hydro_power:slope-area-method" source: https://www.bctengineer.com/q/semester_6/hydro_power/slope-area-method site: BCT Engineering --- # Slope area method of discharge Hydro Power · Chapter 2: Introduction to Hydrology - Asked in: 2071 Magh, 6 marks - Video: [Discharge Measurement By Slope Area Method tutorial | Slope Area Method for discharge measurement](https://www.youtube.com/watch?v=re3ZXvFBoII) — Civil Guys - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/hydro_power/slope-area-method - Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-2 ## Question How the discharge of a stream or river can be computed by slope area method? ## Short answer The slope-area method computes flood discharge from high-water marks and surveyed cross-sections. Using Manning’s equation, energy equation, and conveyance, discharge is found by trial as Q = K√(hf/L), where friction slope hf/L is corrected for velocity head changes. ## Answer The **slope-area method** is an indirect method of finding discharge, mainly used for **flood peaks** when direct current-meter measurement is not possible. Discharge is computed from the water surface slope (from high flood marks) and the channel cross-sections, using Manning's equation. #### Field work 1. Select a fairly straight, uniform reach (length $L$, about 75 m or more, fall ≥ 0.15 m). 2. After the flood, survey **high water marks** (silt lines, debris) at two (or more) sections 1 and 2. 3. Survey the cross-sections to get area $A$, wetted perimeter $P$ and hydraulic radius $R$ at each section. 4. Estimate Manning's $n$ from bed and bank conditions. ```text Sec 1 Sec 2 ___ HFL ___ Dz (fall) | ------____ | y1 L ----___ HFL |____________________________y2_| =========== bed ============> ``` #### Computation Energy equation between sections 1 and 2: $$ h_f = (Z_1 - Z_2) + \left(\frac{V_1^2}{2g} - \frac{V_2^2}{2g}\right) - h_e $$ where $Z$ = water surface elevation, $h_e$ = eddy loss $= K_e\left|\frac{V_1^2}{2g} - \frac{V_2^2}{2g}\right|$ ($K_e \approx 0$–0.1 for contracting, 0.3 for expanding reach). Conveyance $K = \dfrac{1}{n}AR^{2/3}$ at each section; average $K = \sqrt{K_1K_2}$. $$ Q = K\sqrt{S_f}, \qquad S_f = \frac{h_f}{L} $$ Since $V$ depends on $Q$, solve by **trial**: 1. First take $h_f = Z_1 - Z_2$ (fall), find $S_f$ and $Q$. 2. Compute $V_1 = Q/A_1$, $V_2 = Q/A_2$; correct $h_f$ with the velocity head and eddy loss terms. 3. Repeat until $Q$ stops changing (usually 2–3 trials). Limitations: accuracy depends on the choice of $n$ and on reliable flood marks; the reach must be free of backwater and sudden changes. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. When is the slope-area method mainly used? A. To estimate flood peaks when direct measurement is not possible B. To calibrate a current meter C. To measure low flows with a weir D. To compute rainfall Answer: A. It is an indirect method for flood peaks, using high flood marks after the flood. (Key point: Purpose of the method) 2. Which field data are needed for the slope-area method? A. Rainfall at each gauge B. High water marks at two sections, cross-sections and Manning's n C. Revolutions of a current meter D. Sediment concentration only Answer: B. High water marks give the surface slope; cross-sections give A, P and R; n is estimated from channel conditions. (Key point: Field data) 3. How is discharge computed? A. Q = K x Sf, with K = AR B. Q = K x Sf^2 C. Q = K sqrt(Sf), with K = (1/n) A R^(2/3) D. Q = A / Sf Answer: C. Manning's equation gives Q = K sqrt(Sf), where Sf = hf/L. (Key point: Conveyance and discharge) 4. Why is the slope-area solution done by trial? A. Because n is unknown B. Because the sections are not surveyed C. Because L changes each time D. Because velocity head in hf depends on Q, which is not yet known Answer: D. hf includes velocity head terms depending on Q, so Q is assumed from the fall, then corrected until it stops changing. 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