Discharge Measurement

The discharge mostly is not measured directly, but is computed over the measured depth of water, since this is a function of depth of water.
Small discharges as at springs can be measured also directly, e.g. with a bucket and a stop watch.
For discharges which cannot be measured with the above mentioned method, since they are too large, there are standardized profiles, which are built into the stretch of waters or channel. The most well-known is the Thompson weir, where the discharge depends only on the opening angle and the overflow height. Since the opening angle is constant, the discharge depends finally only on the overflow height.
Discharges in large irregular and eventually structured cross sections are computed over the depth of water. The depth of water is read from staff gauges, pressure gauges and float gauge indicators. The last two gauges record the water level continuously on graph paper. They are therefore suitable for remote areas where daily reading is not possible. Staff gauges must be read daily.
In order to be able to compute the discharge in these cross sections from the depth of water, the geometry of the cross section must be measured vertical to the direction of flow. According to the formula of Manning-Strickler the discharge (Q) can be computed as follows:

Q = v × A in m³/s

v = k_ST × r_hy^2/3 × I^0.5 in m/s

k_ST = coefficient of subgrade in m^1/3/s
r_hy = hydraulic radius in m^2/3
I = hydraulic gradient (as a rule parallel to the slope of bottom) in m/1000 m bzw. ‰
A = cross section vertical to direction of flow in m²

Current Meter

Also in irregular cross sections the discharges can be measured. For it the current meter is used. Depending upon depth of water and current in stretches of water one places himself into water, carries out the measurement of the boat or of the bridge or uses a rope crane installation. For it the width of the stretch of water and the position of the vertical is measured with a measuring tape.

Method of point of two

With that Method of point of two the velocity of flow is measured in 20 % and in 80 % of the depth of water of the measuring vertical. In addition the number of revolutions n of the current meter in a certain time (e.g. 100 s) counted. From the current meter own calibration formula (e.g. v = 0.1028 x n + 0.015) by using the revolutions n per second the velocity of flow at this point is computed. One receives the medium speed vm of a measuring vertical by averaging of the two measured speeds in 20 % and 80 % depth. If one plots the speed vertical to the measuring vertical, one receives the velocity profile of the measuring vertical.

velocity profile

The half width b between the two neighbouring measuring verticals, multiplied by the depth t and the medium speed vm results in the discharge ΔQ at the measuring vertical. By summing ΔQ one receives the total discharge Q.

By computational procedures, like e.g. those Simpsonformula or by polynomials of third degree, which are adapted between the neighbouring measuring verticals, velocity profile for the cross section can be computed.

cross section

Example of a discharge measurement according to the Method of point of two in 0,8 und 0,2 d
Stat.	d in m	w in m	A=w×d in m²	Measurements in						v_m in m/s	ΔQ in m³/s
				0,8 d			0,2 d
				R in 100 s	0,8 d in m	v0,8 in m/s	R in 100 s	0,2 d in m	v0,2 in m/s
10,40	0,30
10,60	0,38	0,18	0,0665	154	0,34	0,17	84	0,08	0,10	0,14	0,009
10,75	0,41	0,15	0,0615	186	0,33	0,21	118	0,08	0,14	0,18	0,011
10,90	0,40	0,23	0,0900	224	0,32	0,25	140	0,08	0,16	0,21	0,018
11,20	0,35	0,40	0,1400	268	0,28	0,29	210	0,07	0,23	0,26	0,036
11,70	0,31	0,50	0,1550	292	0,25	0,32	214	0,06	0,23	0,28	0,043
12,20	0,31	0,50	0,1550	328	0,25	0,35	198	0,06	0,22	0,29	0,044
12,70	0,30	0,50	0,1550	324	0,24	0,35	226	0,06	0,25	0,30	0,047
13,20	0,27	0,50	0,1350	362	0,22	0,39	224	0,05	0,25	0,32	0,043
13,70	0,26	0,50	0,1300	381	0,21	0,41	264	0,05	0,29	0,35	0,046
14,20	0,29	0,40	0,1160	320	0,23	0,34	236	0,06	0,26	0,30	0,035
14,50	0,30	0,23	0,0675	258	0,24	0,28	192	0,06	0,21	0,25	0,017
14,65	0,31	0,13	0,0388	220	0,25	0,24	198	0,06	0,22	0,23	0,009
14,75	0,28	0,13	0,0350	156	0,22	0,18	118	0,06	0,14	0,16	0,006
14,90	0,21

		ΣA	1,3453							ΣQ	0,364

w = 4,50 m
d_m = A / w = 1,3453 / 4,50 = 0,30 m
d_max = 0,41 m
v = Q / A = 0,364 / 1,3453 = 0,27 m/s
v_o = 0,41 m / s
v / v_o = 0,27 / 0,41 = 0,658 ≈ 2/3

Method of point of many

With that Method of point of many is proceeded as with the method of point of two. The only difference is that one is not limited to two measurements in a measuring vertical, but into same depth sections partitions. For each section the current meter revolutions in 100 seconds are counted. The appropriate v-values are computed by using each the current meter own calibration formula. The computed v-values are plotted over the depth d and the velocity profile fv according to the addition method is computed. From this the average speed vm = fv / d is computed.

Units

l/s; m³/h; m³/d; m³/a;
l/(s × ha);
mm

Analysis

NQ, MQ, HQ in m³/s
NNQ, MNQ, MHQ in m/s
Nq, Mq, Hq, NNq, MNq, MHq in l / (s × ha)