--- title: "Area-velocity method and mid-section method" subject: "Engineering Hydrology" chapter: 4 key: "semester_5/engineering_hydrology:area-velocity-midsection-method" source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/area-velocity-midsection-method site: BCT Engineering --- # Area-velocity method and mid-section method Engineering Hydrology · Chapter 4: Surface Runoff - Asked in: 2073 Shrawan, 3+3 marks - Video: [Discharge (Stream flow) Measurement Methods: [ Mid-Section and Mean-Section Methods ]](https://www.youtube.com/watch?v=QoeX_fyuDCE) — Hydraulics and Hydrology Tutorials - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/area-velocity-midsection-method - Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4 ## Question Explain the procedure of stream flow measurement by area-velocity method. Also, describe the mid section method for discharge computation using sketch and equations. ## Short answer Area-velocity method divides channel into verticals, measuring depth and velocity. Mid-section method: each vertical’s strip extends halfway to neighbours, width w_i=(b_{i+1}-b_{i-1})/2, q_i=v_i d_i w_i, total Q=Σ q_i. ## Answer #### Area-velocity method: procedure The discharge at a river section is $Q = \int v\,dA$, found by measuring velocity at many points of the cross-section. 1. Select a site on a straight reach with stable bed, parallel flow and a gauge nearby. 2. Mark the section with a tagged cable, rope or bridge markings. Record the stage. 3. Divide the width into 15 to 30 verticals so that no strip carries more than 10 % of the flow (closer verticals where depth varies strongly). 4. At each vertical, measure the **depth** (sounding rod or weight) and the **velocity** with a current meter held at 0.6 d (shallow) or at 0.2 d and 0.8 d (deeper) for 40 to 60 s. The velocity $v = aN + b$ from the revolutions $N$ per second. 5. Compute the mean velocity of each vertical, the area of each strip, and sum the partial discharges. #### Mid-section method Each measured vertical is assumed to represent a strip extending half-way to the verticals on either side. ```text water surface ___|_____|_____|_____|___ \ | d1 | d2 | d3 | / \ | | | |/ b(i-1) b(i) b(i+1) <--w_i--> ``` Width of strip $i$: $$ w_i = \frac{b_{i+1}-b_{i-1}}{2} $$ Partial discharge: $$ q_i = v_i\,d_i\,w_i = v_i\,d_i\,\frac{b_{i+1}-b_{i-1}}{2} $$ Total discharge: $$ Q = \sum_{i=1}^{n} q_i $$ where $v_i$ is the mean velocity in the vertical and $d_i$ the depth at that vertical. The end verticals at the banks have zero depth. This is the method normally used because it is simple and does not need a separate area calculation. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The area-velocity method computes discharge as A. Q = integral of v dA B. Q = v / A C. Q = A / v D. Q = h x L Answer: A. Discharge is the integral of velocity over the cross-sectional area. (Key point: Basic principle) 2. How many verticals are chosen so that no strip carries too much flow? A. Exactly 5 B. 15 to 30, no strip over about 10 % of the flow C. 2 to 3 D. 100 or more Answer: B. 15 to 30 verticals are used, closer where depth varies strongly. (Key point: Number of verticals) 3. In the mid-section method, what is the width of the strip assigned to vertical i? A. The full distance between the two banks divided by the number of verticals B. The distance b(i+1) - b(i) C. Half the distance between the verticals on either side, (b(i+1) - b(i-1))/2 D. The distance b(i) - b(i-1) Answer: C. Each vertical represents a strip from the mid-point of the previous interval to the mid-point of the next, so w = (b(i+1) - b(i-1))/2. (Key point: Strip width in mid-section method) 4. The partial discharge in the mid-section method is A. q = d w / v B. q = v + d + w C. q = v / (d w) D. q = v d w Answer: D. q_i = v_i d_i w_i, summed over all verticals for Q. 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