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1
Flow Measurement I
Hydromechanics VVR090
Need for Flow Measurements
Accurate record of discharge crucial in many applications.
Often required to estimate flow rate:
• to wastewater treatment plants
• to irrigation channels
• for water consumption in households/industry
• in rivers (evaluation of water resources, dilution potential)
• to hydropower plants (turbines; regulation of flow)
• to industrial processes
Purpose: to discuss a number of methodologies to measure the discharge in the field and laboratory.
2
Flow Measurements
• stream gaging (rating curve)
• tracers
• measurement flumes
• weirs
• sluice gates
• point velocity measurements in a cross section
• turbine meters
• orifices, nozzles
Discharge Measurement Stations: Stage Recording
Stage: elevation of the water surface relative to a datum
Measurement method: Derive a functional relationship between stage and discharge (through calibration). Perform accurate measurements of the discharge at a number of different stages.
Rating curve
3
Discharge Measurement Stations: Structures
Rectangular weirV-notch weir
Parshall flume Broad-crested weir
Criterion for Establishing Control Section for Discharge Measurement
Structure establishing the control section should:
• not create undesirable flow field disturbances
• have sufficient height to eliminate the effects of variable downstream conditions
• be designed so that small changes in discharge results in measurable change in the stage
• be stable and permanent (even under extreme conditions)
4
Method of Discharge Measurement
1. Divide cross section into a number of subsections (N).
2. Determine average velocity in each subsection .
3. Summarize product between subsection area and average velocity:
1
N
i ii
Q u A=
=∑
iu
iA
Velocity might be measured with a propeller meter, electromagnetic current meter, or acoustic doppler velocimeter (ADV).
Propeller Meter
• measure uni-directional current
• sensitive to sediment
• not disturbed by vertical currents
• easy to operate
Water velocity proportional to the propeller rotational speed (calibration needed).
5
Electromagnetic Current Meter
When the flowing water moves through a magnetic field a voltage is induced proportional to the velocity.
Acoustic Doppler Velocimeter (ADV)
A sound pulse is emitted and the doppler shift occurring when this pulse is reflected against particles in the water is related to the particle velocity (= water velocity).
6
Measurement Strategy
Cross section is divided into a number of vertical sections (no section should contain more than 10% of the flow). 20-30 vertical sections are typically required. The number of measurements in a cross section should be limited to allow coverage during constant flow conditions.
Velocity profile in a subsection:
*2.5 lno
yu uy
⎛ ⎞= ⎜ ⎟
⎝ ⎠
Average velocity is approximately obtained from:
(0.8 ) (0.2 )2
(0.4 )
u D u Du
u u D
+=
=
(see problem from tutorial)
7
Integration Method to Obtain Flow
Numerical integration technique:
1 1
1 2 2
Ni i i i
i ii
b b b bQ u y − +
=
− −⎛ ⎞= +⎜ ⎟⎝ ⎠
∑
Trapezoidal method:
1/ 2 1/ 2
1
1 1
2
2 2
Ni i
i ii
i i i ii
d dQ u w
b b b bw
− +
=
− +
+⎛ ⎞= ⎜ ⎟⎝ ⎠
− −= +
∑
Structures for Flow Measurements
Structures may be placed in a channel to measure the flow rate (in some cases existing structures may be used to estimate the flow rate).
Examples of structures used for flow measurements:
• weirs
• critical-depth flumes
• culverts
• bridge piers
• dams
8
Weirs
Types of weirs (classified according to shape):
• rectangular
• V-notch
• trapezoidal
• parabolic
• special type (e.g., Cipoletti, Sutro)
Distinguish between:
• Broad-crested
• Sharp-crested
Broad-Crested Weir
A structure with a horizontal crest above which the water pressure is considered hydrostatic.
Limits: 0.08 < H1/L < 0.50
(0.08 from limit for energy losses; 0.50 from curvature of the streamlines)
9
Broad-Crested Weir
Discharge Formula for Rectangular Broad-Crested Weir
Apply Bernoulli equation between upstream section and the control section (critical depth occurs here).
h1H1
10
Modified discharge formula for rectangular broad-crested weir (taking into account simplifying assumptions):
1/ 23/ 21
2 23 3D vQ C C g Th⎛ ⎞= ⎜ ⎟⎝ ⎠
Cv: velocity coefficient (correct for neglecting velocity head in the approach channel)
CD: discharge coefficient (correct for neglecting viscous effects, turbulence, non-uniform velocity distribution etc)
Velocity coefficient Cv is given by:
1
1v
HCh
φ⎛ ⎞
= ⎜ ⎟⎝ ⎠
f: power of the variable h in the discharge equation
H1 is normally not known => equation hard to use
Diagram over Cv
11
Rectangular Broad-Crested Weir
Typical layout
Weir block placed in a rectangular channel perpendicular to the flow direction
Discharge Coefficient
CD assumed constant if:
1 1
1
0.08 0.33 and 0.35h hL h p
≤ ≤ ≤+
CD = 0.848 (basic discharge coefficient)
Outside the limits CD should be multiplied with a correction coefficient F.
12
Triangular Broad-Crested Weir
Suitable for measuring a wide range of discharges.
Discharge formula for triangular broad-crested weir:
( )1/ 2
5/ 21
16 2 tan / 225 5D vQ C C g h⎛ ⎞= θ⎜ ⎟
⎝ ⎠
Discharge coefficient given by diagram:
(Cv from previous figure)
13
Sharp-Crested Weir
Weir is considered sharp-crested if H1/L > 15.
Sufficient air should be supplied behind the nappe.
Sharp-Crested Weir
14
Discharge formula for sharp-crested weir:
( )1
1/ 21
0
2 ( )h
eQ C g b z h z dz= −∫
Main assumptions in the derivation:
• height of water level above weir crest is h1
• velocity over the crest horizontal
• approach velocity can be neglected
Definition Sketch: Deriving Discharge Formula for Sharp-Crested Weirs
Derivation of discharge equation not based on the presence of critical section; integrate through the section at the weir crest. Employ Bernoulli equation to get velocity through this section.
h1
z
15
Correct for assumptions made by introducing a discharge coefficient Ce.
( )1
1/ 21
0
2 ( )h
Q g b z h z dz= −∫
( )12u g h z= −
Velocity in control section (from Bernoulli equation):
Total flow over the weir:
( )1/ 2 3/ 21
2 23 eQ C g bh=
Rectangular sharp-crested weir:
Three weir types:
• fully contracted
• partially contracted
• full width
16
Discharge coefficient:
1
1
1
1
/1 0.602 0.075 /0.8 0.597 0.045 /0.6 0.593 0.018 /0.4 0.591 0.0058 /
e
e
e
e
e
b T CC h pC h pC h pC h p
= +
= +
= += +
( ) ( )1/ 2 5/ 21
8 2 tan / 215 eQ C g h= θ
Triangular sharp-crested weir:
Two weir types:• fully contracted• partially contracted
Ce coefficient
17
Discharge Equations for Weirs I
Discharge Equations for Weirs II
18
Other Weirs
Trapezoidal control section.
Cipoletti weir
Sutro weir Discharge linearly proportional to total head (above some level)
Discharge formulas:
Cipoletti weir ( )1/ 2 3/ 21
2 23 D vQ C C g Th=
Sutro weir ( ) ( )1/ 212 / 2DQ C b ga h a= −
19
Example: Sharp-Crested Weir
Treating the upper edge of the pipe as a sharp weir crest, estimate the flow rate when the water depth in the basin is 0.75 m.