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River discharge with current meter constants a and b

Short answer

Applying mid-section method with current meter equation v = 0.51N + 0.03 at 0.6d. Segment width equals half distance to adjacent verticals. Summing v × depth × width gives Q ≈ 8.77 m³/s.

With the following data, compute discharge for a river.

Distance from left bank (m)01471013161920
Depth (m)011.251.752.151.801.201.050
Revolution at 0.6d0304030403525200
Duration of observations (sec)01001005050501001000

Calibrated value of constants for current meter: a = 0.51 and b = 0.03

Mid-section method. The current-meter equation is v=aN+b=0.51N+0.03v = aN + b = 0.51N + 0.03 (m/s), with NN = revolutions per second, measured at 0.6 d (mean velocity of the vertical).

qi=vi di bi+1−bi−12q_i = v_i\,d_i\,\frac{b_{i+1}-b_{i-1}}{2}
Distance (m)Depth d (m)N = rev/time (rps)v (m/s)Width w (m)Area w dw\,d (m2^2)q=v w dq = v\,w\,d (m3^3/s)
1130/100 = 0.3000.18322.0000.366
41.2540/100 = 0.4000.23433.7500.878
71.7530/50 = 0.6000.33635.2501.764
102.1540/50 = 0.8000.43836.4502.825
131.835/50 = 0.7000.38735.4002.090
161.225/100 = 0.2500.15833.6000.567
191.0520/100 = 0.2000.13222.1000.277
Total28.5508.767

Total area =28.55= 28.55 m2^2; mean velocity =0.307= 0.307 m/s.

Answer: Discharge Q≈8.77 m3/sQ \approx 8.77\ \text{m}^3/\text{s}.

✓ Answer checked by Claude Sonnet 5.5

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