Asst. Lec. Ali Abdul-Hussein Abed

Fourth year

HYDROLOGY Stream flow

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Stream Flow and Its Measurement Methods

The most satisfactory determination of the runoff from a catchment is by measuring

the discharge of the stream draining it, which is termed as stream gauging. A gauging

station is the place or section on a stream where discharge measurements are made.

1- Water stage or Evaluation of water (L) Is the elevation above some arbitrary zero datum of the water surface at a

station. The datum is sometimes taken as mean sea level

There are three types of water level gages:-

a- Non- recording (manual) gages.

b- Recording gages.

c- Crest stages gages.

a- Manual Gages.

a) Simple stuff gages: it is a simplest method to measure the water stage.

b) Inclined gages.

c) Suspended weight gages.

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b- Recording gages.

These gages can represent the water stage with time.

In Continuous-chart record motion of float moves a pen across a long strip

chart.

c - Crest stages gages.

It used to readings maximum water level.

Measurement Approaches

𝑄 = 𝑉 ∗ 𝐴

First: - Direct methods (stream gaging) (a):- Current-meter method

(b):- Ultrasonic method (ADCP)

(c):- Pitot tube

(d):- Venture meter

(e):- Orifice meter

(f):- Floats

Second: - Hydraulic Devices (a):- Weirs and notches

(b):- Orifices

(c):- Flumes

Third: - Indirect Techniques (a):- Slope-area method

(b):- Rating Curve

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a) Current meters:

Current-Meter measurements:

A discharge measurement requires determination of sufficient point velocities to

permit computation of an average velocity in the stream. Cross-sectional area

multiplied by the average velocity gives the total discharge.

Practical method to find the discharge of rivers:

The practical procedure involves dividing the stream into a number of vertical

sections. No section should include more than about 10% of the total flow; thus 20

to 30 vertical sections are typical, depending on the width of stream.

The equation below can be used to calculate the velocity from a Current-

Meter:

V=a +b*N

Where V = flow velocity;

a = starting velocity to overcome mechanical friction;

b = equipment calibration constant;

N = revolutions/sec.

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Velocity distribution can be shown as below:-

Velocity equations:

𝑉𝑠 = 1.2 𝑉𝑎𝑣 = 0.9 𝑉𝑚𝑎𝑥

𝑉𝑎𝑣 =𝑉0.2𝑑 + 𝑉0.8𝑑

2

At river approaches (less than 0.6 m) the average velocity can be calculated at

0.6 of the depth.

𝑉𝑎𝑣 = 𝑉0.6𝑑

The total discharge can be calculated from the summation of discharges of the

section

𝑄𝑡𝑜𝑡𝑎𝑙 = ∑ 𝑞𝑖

𝑛

𝑖=1

𝑄𝑡𝑜𝑡𝑎𝑙 = ∑ 𝑉𝑎𝑣𝑖 ∗ 𝐴𝑖

𝑛

𝑖=1

Example: find the discharge of the river has the data below where a = 0.1, b = 2.2 for

velocity in ft. /s

Distance depth Meter

depth

Time

(sec) revolutions

N

(revoluti

on/sec)

V

ft./s

𝑉𝑎𝑣

ft./s

Area

ft2

𝑞𝑖

cfs

2 1 0.6 50 10 10/50

4 3.5 0.8 55 22

0.2 52 35

6 5.2 0.8 53 28

0.2 58 40

9 6.3 0.8 58 32

0.2 60 45

11 4.4 0.8 45 28

0.2 46 33

13 2.8 0.6 50 22

15 0.8 0.6 49 12

17 0 0 - -

𝑄𝑡𝑜𝑡𝑎𝑙 =

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B) Acoustic Doppler Current Profiler

The ADCP uses the Doppler Effect to determine water velocity by sending a sound

pulse into the water and measuring the change in frequency of that sound pulse

reflected back to the ADCP by sediment or other particulates being transported in the

water. The change in frequency, or Doppler Shift, that is measured by the ADCP is

translated into water velocity.

(c):- Pitot tube

𝑄 = 𝑐𝑑 ∗ 𝐴 ∗ √2𝑔 (ℎ2 − ℎ1)

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(d):- Venture meter

2

1

2

212

)(1

)(2

a

a

hhgaCQ dP

dC = discharge coefficient (0.92-0.99)

(e):- Orifice meter

1)(

)(2

2

E

F

FEEdP

a

a

hhgaCQ

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(f):- Floats

Inexpensive and simple Measures surface velocity mean velocity obtained using a

correction factor Basic idea: measure the time that it takes an object to float a

specified distance downstream.

Surface velocity = distance / time,

Average velocity = (0.85*surface velocity)

Second: - Hydraulic Devices

(a):- Weirs and notches

2

3

*23

2HbgQP

Where:

Q = discharge (m3/s) , b = average width of approach channel, m

H = head measured above the weir crest, m

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2

5

*tan215

8HgCQ dP

Where:

/s,3= discharge over weir in m Q

= angle of v-notch,

Free overflow weir

2

3

LHCQ dP

Submerged weir

2

3

)( v

v

ddP LH

H

HCQ

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(b):- Orifices

Free fall through large openings

)( 2

3

12

3

2 HHLCQ dP

Over flow under pressure

Submerge opening

HgACQ dP *2

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(c):- Flumes

Parshall flume

2

3

)( v

v

ddP LH

H

HCQ

Third: - Indirect Techniques a) Slope-area method

Manning's eq. method

ASP

A

nQP

2

1

3

2

)(1

543210 *)( mnnnnnn

Hv

Hd

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(b):- Rating Curve

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b/ Jet

𝑉𝑎 = 𝑥 ∗ (𝑔

2𝑦)1/2

Q=Va * A

𝐴 =𝜋

4𝐷2

c) Stage-discharge relation. Periodic meter measurements of flow and simultaneous stage observations provide

data for calibration curve called a rating curve or stage-discharge relation.

Stage-discharge measures 10-15 time every year to the river to get the relation

between stage and discharge of the river.

𝑄 = 𝑘 ∗ (𝑔 − 𝑏)𝑎

𝑄 = Discharge,

𝑘, 𝑏, 𝑎𝑛𝑑 𝑎 = Station constant, and

𝑔 = Stage.

Constant b can be found from the equation below but a and k can be found from using

least-square method.

𝑎 = 𝑁( ∑ 𝑋𝑌) − (∑ 𝑋)(∑ 𝑌)

𝑁 (∑ 𝑋2) − (∑ 𝑋)2

Drive the equation of b:

𝐿𝑜𝑔 (𝐾) =∑ 𝑌 − 𝑎 (∑ 𝑥)

𝑁

Example: given data below of stage-discharge find:

The relation of stage-discharge where

𝑞 = 𝑘 ∗ (𝑔 + 0.103)𝑎,

What is the discharge when the stage of water 20 m, and

What is the stage of water if the discharge 500𝑚3

𝑠𝑒𝑐?

Stage (m) Discharge (

𝐦𝟑

𝐬𝐞𝐜)

5 20

6 45

7 80

9 180

10 254

12 405

15 720

17 920

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Solution:

H.W/ The recorded discharges and water levels are shown below estimate the

following relation and find Q when g = 13 m

𝑄 = 𝑘 ∗ (𝑔 − 3)𝑎

Q (m3 s⁄ ) 1 2 4 10

g (m) 6 8 10 11

Q1- - Given canal section what is the hydraulic radius?

Q2- The following table representing the relation between the recorded discharge (Q)

with the water levels (W.L.) .Estimate the following relation and find Q5?

𝑄 = 𝑏 [𝑊. 𝐿. −2]𝑑

Q (m3/s) 10 20 40 100 Q5

W.L. (m) 5 7 9 10 14

Q3- Rectangular channel bed width 1 m, slope of channel 1% and normal depth 2 m .

Compute the discharge if the material for river bed is earth , and have a smooth

of irregularity , there is small gradual variation in the river cross section , no

vegetation, minor meandering .

30 m

5 m