How is velocity computed at 0.8 m?

N = 12/48 = 0.25 rps, v = 0.05 + 0.3(0.25) = 0.125 m/s

2079 Bhadra · 8 marks

Discharge from current meter, V=0.05+0.3N

Short answer

Mid-section method: velocity v = 0.05 + 0.3N (N in rps) measured at 0.6d depth. Segment discharges are v × depth × width between adjacent midpoints. Total discharge Q ≈1.46 m³/s.

The following data is observed on a stream using current meter. The rating equation of current meter is $V = (0.05 + 0.3N)$ m/s, where N is rev/sec was used to measure the velocity at 0.6 d depth. Calculate the discharge of the stream.

Distance from bank (m)	0.8	1.6	2.4	3.0	3.6	4.2	5.0	5.8	6.6
Depth (m)	0.5	1.0	1.6	2.0	2.0	1.8	1.2	0.6	0.0
No. of rev.	12	23	27	33	32	28	24	14	-
Time (sec)	48	52	54	58	58	53	50	45	-

Mid-section method with $v = 0.05 + 0.3N$ at 0.6 d ( $N$ in rev/s). The first listed vertical is 0.8 m from the bank; the bank itself (0 m, depth 0) is taken as the starting end, and the last vertical at 6.6 m (depth 0) is the opposite bank.

q_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 $w\,d$ (m $^2$ )	$q = v\,w\,d$ (m $^3$ /s)
0.8	0.5	12/48 = 0.250	0.125	0.8	0.400	0.050
1.6	1	23/52 = 0.442	0.183	0.8	0.800	0.146
2.4	1.6	27/54 = 0.500	0.200	0.7	1.120	0.224
3	2	33/58 = 0.569	0.221	0.6	1.200	0.265
3.6	2	32/58 = 0.552	0.216	0.6	1.200	0.259
4.2	1.8	28/53 = 0.528	0.208	0.7	1.260	0.263
5	1.2	24/50 = 0.480	0.194	0.8	0.960	0.186
5.8	0.6	14/45 = 0.311	0.143	0.8	0.480	0.069
Total					7.420	1.461

Total area $= 7.42$ m $^2$ ; mean velocity $= 0.197$ m/s.

Answer: Discharge $Q \approx 1.46\ \text{m}^3/\text{s}$ .

✓ Answer checked by Claude Sonnet 5.5

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