Discharge of Nakhu Khola from current meter data

Short answer

Mean velocity at each vertical was (v0.2 + v0.8)/2. Using mid-section method, segment discharge v_mean·depth·width summed to Q ≈ 6.62 m^3/s.

Discharge measured at Nakhu Khola using current meter has the following data. Calculate the total discharge of river.

Distance from left bank (m)	Depth (m)	Velocity at 0.2d (m/s)	Velocity at 0.8d (m/s)
0	-	-	-
1.5	1.3	0.6	0.4
3.0	2.5	0.9	0.6
5.0	1.7	0.7	0.5
6.0	1.0	0.6	0.4
7.5	0.4	0.4	0.3
9.0	-	-	-

Mid-section method. Two velocities are given at each vertical, so the mean velocity is

v_m=\frac{v_{0.2}+v_{0.8}}{2},\qquad q_i=v_m\,d\,\frac{b_{i+1}-b_{i-1}}{2}

The two banks (0 m and 9 m) have zero depth.

x (m)	d (m)	$v_{0.2}$	$v_{0.8}$	$v_m$ (m/s)	w (m)	Area (m $^2$ )	q (m $^3$ /s)
1.5	1.3	0.6	0.4	0.500	1.5	1.950	0.975
3	2.5	0.9	0.6	0.750	1.75	4.375	3.281
5	1.7	0.7	0.5	0.600	1.5	2.550	1.530
6	1	0.6	0.4	0.500	1.25	1.250	0.625
7.5	0.4	0.4	0.3	0.350	1.5	0.600	0.210
Total						10.725	6.621

Mean velocity $= 0.617$ m/s.

Answer: Total discharge $Q \approx 6.62\ \text{m}^3/\text{s}$ .

✓ Answer checked by Claude Sonnet 5.5

Distance from left bank (m)	Depth (m)	Velocity at 0.2d (m/s)	Velocity at 0.8d (m/s)
0	-	-	-
1.5	1.3	0.6	0.4
3.0	2.5	0.9	0.6
5.0	1.7	0.7	0.5
6.0	1.0	0.6	0.4
7.5	0.4	0.4	0.3
9.0	-	-	-

Distance from left bank (m)	Depth (m)	Velocity at 0.2d (m/s)	Velocity at 0.8d (m/s)
0	-	-	-
1.5	1.3	0.6	0.4
3.0	2.5	0.9	0.6
5.0	1.7	0.7	0.5
6.0	1.0	0.6	0.4
7.5	0.4	0.4	0.3
9.0	-	-	-

Related questions

Distance from left bank (m)	Depth (m)	Velocity at 0.2d (m/s)	Velocity at 0.8d (m/s)
0	-	-	-
1.5	1.3	0.6	0.4
3.0	2.5	0.9	0.6
5.0	1.7	0.7	0.5
6.0	1.0	0.6	0.4
7.5	0.4	0.4	0.3
9.0	-	-	-