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Current meter discharge, rating equation

Short answer

Mid-section method: velocities from V = 0.53N+0.05 m/s, strip widths from mid-points, summed to total discharge = 7.71 m³/s.

A current meter (rating equation: V=(0.53N+0.05)V = (0.53N + 0.05) m/s, where N = revolutions per second) was used to measure the velocity at 0.6 depth. If current meter readings at various locations at a cross section are as in the following table, calculate the discharge in the stream.

Distance from right bank (m)0135791112
Depth (m)01.22.12.62.01.71.10.0
No. of revolutions039581129045300
Time (seconds)01001001501001001000

The mid-section method is used. Each vertical represents a strip from the mid-point of the previous vertical to the mid-point of the next vertical:

qi=vi di bi+1−bi−12,Q=∑qiq_i = v_i\,d_i\,\frac{b_{i+1}-b_{i-1}}{2},\qquad Q=\sum q_i

The rating equation v=0.53N+0.05v = 0.53N + 0.05 gives the velocity at 0.6 depth, which is taken as the mean velocity of the vertical (N=N= revolutions / time). The end points (banks) have zero depth.

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)
11.239/100 = 0.3900.2571.51.8000.462
32.158/100 = 0.5800.35724.2001.501
52.6112/150 = 0.7470.44625.2002.318
7290/100 = 0.9000.52724.0002.108
91.745/100 = 0.4500.28923.4000.981
111.130/100 = 0.3000.2091.51.6500.345
Total20.2507.715

Sample calculation at 5 m: N=112/150=0.747N = 112/150 = 0.747 rps; v=0.53×0.747+0.05=0.446v = 0.53\times0.747+0.05 = 0.446 m/s; width =(7−3)/2=2=(7-3)/2 = 2 m; area =2×2.6=5.2=2\times2.6 = 5.2 m2^2; q=0.446×5.2=2.318q = 0.446\times5.2 = 2.318 m3^3/s.

Total area =20.25= 20.25 m2^2 and mean velocity =0.381= 0.381 m/s.

Answer: Discharge Q≈7.71 m3/sQ \approx 7.71\ \text{m}^3/\text{s}.

✓ Answer checked by Claude Sonnet 5.5

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