Discharge.pdf

Measurement of Discharge/Streamflow

Measurement of Discharge by Velocity-Area Method

Outline 1. Measurement of Discharge by Velocity-Area Method

• Streamflow • Several basic methods to determine streamflow • Velocity-Area method • Determination of discharge • Determination of area • Determination of average water velocity • Current meter • Float method 2. Measurement of Discharge by Stage-Discharge Method

Streamflow • Water flow within a river channel, for example expressed in m3/s. A synonym for river discharge (IPCC, 2013) • Streamflow = overland flow + interflow + baseflow

Several basic methods of streamflow measurement • Bucket Method • Weir Method • Salt-dilution Method • Slope-area Method • Stage-discharge method • Velocity-area method

VELOCITY-AREA METHOD - reliable and applicable to a wide range of sites and discharges - can be used for larger streams - difficult to use with very shallow streams

Velocity-Area Method Determination of Discharge

w 𝑑1

Q = AV Where: Q = discharge, cms; A = area, sq.m; V = velocity, m/s

More accurate results may be determined through determining the discharge through partial areas (An)

𝑎1

𝑑2 𝑎2

𝑑3 𝑎3

𝑑4

𝑑5

𝑑6

𝑑7

𝑑8

𝑑9

𝑎4

𝑸 = 𝒂𝟏 𝒗𝟏 + 𝒂𝟐 𝒗𝟐 + 𝒂𝟑 𝒗𝟑 + ⋯ 𝒂𝒏 𝒗𝒏 Determining the area

𝒅𝟐 + 𝒅𝟑 𝒂𝟑 = 𝒘 𝟐 Where: a3 = partial area, sq.m, d2 & d3 =depth, m, w = width of partial area, m

Determination of area

𝒅𝟐 + 𝒅𝟑 𝒂𝟑 = 𝒘 𝟐

In the field, a surveying tape can be stretched along the stream

w 𝑑1 𝑎1

And a ruler or calibrated stick can be used to measure the DEPTH of water at appropriate point along the tape

Where: a3 = partial area, sq.m, d2 & d3 =depth, m, w = width of partial area, m

𝑑2 𝑎2

𝑑3 𝑎3

𝑑4 𝑎4

𝑑5

𝑑6

𝑑7

𝑑8

𝑑9

Determination of water velocity Current meter – the most common method for measuring velocities at any depth in larger streams and rivers which are not turbulent

A price current meter

The speed of rotation of cups being a function of the velocity of water Used to measure v in the range of 0.2 to 5 m/s with probable error of 2 %

Example A river with a total width of 8 meters was subdivided into 4 partial areas, using a digital price current meter, the average velocities were measured as 1.0, 1.2, 0.8 and 0.6 m/s respectively, the depths were measured as 1.0, 1.5 and 0.8 m. Determine the river discharge. Given: d1 = 1.0 m; d2 = 1.5 m ; d3 = 0.8 m; v1 = 1.0 m/s; v2 = 1.2 m/s; v3 = 0.8 m/s; v4 = 0.6 m/s ; w = 2 m

Find: Q Solution:

𝑄 = 𝑎1 𝑣1 + 𝑎2 𝑣2 + 𝑎3 𝑣3 + ⋯ 𝑎𝑛 𝑣𝑛 Q=

𝑑1 𝑑1 + 𝑑2 𝑑2 + 𝑑3 𝑤𝑣1 + 𝑤𝑣2 + 𝑤𝑣3 + 2 2 2

𝑑3 𝑤𝑣4 2

1 1 + 1.5 1.5 + 0.8 Q= 2(1) + 2(1.2) + 2(0.8) + 2 2 2

0.8 2(0.6) 2

Answer:

Q = 6.32 cms

Float Method – easiest method for determining velocities in a stream, requires no equipment, but cannot be used accurately for shallow streambed

Surface velocity

𝑫 𝒗𝒔 = 𝒕 Where: D = distance, m; t = time, s

Average velocity

𝐯 = 𝑪 𝒗𝒔 Where: C = correction factor When vs is measured at the center of stream (C= 0.6 for a stream with rocky bed, 0.85 for smooth bed)c When vs is measured over that partial area (c = 0.75 for shallow streams, c = 0.95 for deep streams)

Example The discharge in a stream with a smooth bed and the profile is to be determined. A float placed near the center of the stream takes 8.4 s to cover 10.0 m. Determine the discharge if the cross sectional area is 0.7 sq.m. Given:t = 8.4 s; D = 10.0 m; A =0.7 sq.m

Find: Q Solution: 𝐷 10.0 𝑚 𝑚 𝑣𝑠 = = = 1.2 𝑡 8.4 𝑠 𝑠

𝑣 = 𝐶 𝑣𝑠 = 0.85

𝑚 𝑚 1.2 = 1.0 𝑠 𝑠

𝑄 = 𝐴𝑉 = 0.7

𝑚2

𝑚 𝑚3 1.0 = 0.7 𝑠 𝑠 Answer:

Q = 0.7 cms

Measurement of Discharge by Stage-Discharge Method

Stage-discharge method involves development of a stage-discharge rating curve Rating curve is a graph of discharge versus stage for a given point on a stream, usually at gauging stations.

Wherein, numerous measurements of stream discharge (using a current meter or velocity area method) are made over a range of stream stages (or water level).

stage-discharge relationship 180 160

y = 27.074x1.1659

140 120 100

80 60 40 20 0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Stage 0.2 0.4 0.5 0.6 0.7 0.9 1.1 1.2 1.3 1.5

Q,cms 4.5998 8.0838 12.6405 15.0919 15.8476 23.8898 30.452 33.6004 37.9423 46.0942

Thank you! Presented by: MARY ANGELINE O. NAPAY BUCAF, Guinobatan, Albay