The World Meteorological Organization stream flow estimation.docx

Water engineering notes for civil engineering students

1. The World Meteorological Organization (WMO) provides several methodologies for estimating
streamflow, depending on the available data, hydrological conditions, and measurement methods.
Three of the common approaches outlined by the WMO are the Volumetric Method, the Velocity-Area
Method, and Hydraulic Methods. Each method uses different principles and data sources to estimate
streamflow or discharge.
1. Volumetric Method
The Volumetric Method is used when you have data on the volume of water that flows through a cross-
section of a river over a given period. This method is most appropriate for large-scale water resource
studies where flow is measured over extended periods, such as reservoir operations or catchment
hydrology.
Formula:
Q=VTQ = \frac{V}{T}
Where:
QQ = Streamflow or discharge (m³/s)
VV = Total volume of water (m³)
TT = Time period over which the volume was measured (seconds)
Steps:
1.Determine the Volume of Water (VV): Measure or estimate the total volume of water passing
through a specific cross-section of the stream over a defined period. This might be done using
flow gauging stations or reservoirs' volume data.
2.Time Period (TT): Identify the time period over which this volume of water passed through (e.g.,
one day, one hour, etc.).
3.Calculate Streamflow: Divide the volume of water by the time period to calculate the average
streamflow rate.
2. Velocity-Area Method
The Velocity-Area Method is the most common method used for measuring streamflow directly at a
specific cross-section of a river or stream. It requires measuring the velocity of the stream and the cross-
sectional area of flow. The method assumes that the flow is steady and that the velocity is relatively
uniform across the cross-section.
Formula:
Q=A×VQ = A \times V
Where:
QQ = Streamflow or discharge (m³/s)
AA = Cross-sectional area of the flow (m²)

2. VV = Average velocity of the stream at the cross-section (m/s)
Steps:
1.Measure the Cross-sectional Area (AA): Divide the stream's cross-section into smaller segments
(usually with a grid), and measure the depth of the water at each segment. Multiply the depth
by the width for each segment, then sum the areas of all segments to get the total cross-
sectional area.
2.Measure the Velocity (VV): Measure the velocity of the stream at different points across the
cross-section. This can be done using flow meters or a float method where you measure the
time it takes for a floating object to travel a known distance. The velocity is typically highest at
the surface and in the center of the stream, so measurements should account for variations in
velocity.
3.Calculate the Streamflow (QQ): Multiply the average velocity by the cross-sectional area to
estimate the streamflow. In practice, you may take velocity measurements at multiple depths to
calculate a weighted average velocity for the entire cross-section.
3. Hydraulic Methods
The Hydraulic Methods for determining streamflow are more complex and rely on the principles of
hydraulics to estimate the flow rate. They often involve the use of empirical relationships between flow,
water stage (height), and channel geometry. The most common hydraulic method is based on the
Manning’s equation for open channel flow.
Formula (Manning’s Equation):
Q=1nAR2/3S1/2Q = \frac{1}{n} A R^{2/3} S^{1/2}
Where:
QQ = Streamflow or discharge (m³/s)
nn = Manning's roughness coefficient (dimensionless)
AA = Cross-sectional area of flow (m²)
RR = Hydraulic radius (m) = AP\frac{A}{P}, where PP is the wetted perimeter (m)
SS = Channel slope (dimensionless), the slope of the flow direction
Steps:
1.Calculate the Cross-sectional Area (AA): Measure the cross-sectional area of the flow, similar to
the Velocity-Area Method.
2.Calculate the Wetted Perimeter (PP): This is the total length of the channel that is in contact
with the water, including the bottom and sides of the channel.
3.Determine the Hydraulic Radius (RR): The hydraulic radius is the ratio of the cross-sectional area
of flow to the wetted perimeter.

3. 4.Measure the Channel Slope (SS): The slope is the difference in water stage (height) over a
specific length of the channel. It can be measured as the change in elevation divided by the
horizontal distance.
5.Determine the Manning’s Roughness Coefficient (nn): This coefficient depends on the
characteristics of the channel bed and banks (e.g., smooth rock, vegetation, gravel, etc.).
Standard values for nn are available for different types of channels.
6.Calculate Streamflow (QQ): Finally, use the Manning’s equation to compute the streamflow.
Summary of Methods:
Method Formula/Concept Key Data Required Application
Volumetric
Method
Q=VTQ = \frac{V}{T}
Total volume of water (V),
time period (T)
Suitable for large-scale
flow measurements (e.g.,
reservoirs)
Velocity-Area
Method
Q=A×VQ = A \times V
Cross-sectional area (A),
average velocity (V)
Common for direct field
measurements at stream
cross-sections
Hydraulic
Methods
Manning’s equation:
Q=1nAR2/3S1/2Q = \frac{1}{n}
A R^{2/3} S^{1/2}
Cross-sectional area (A),
wetted perimeter (P), slope
(S), hydraulic radius (R),
Manning's nn
Suitable for natural
streams and channels
Choosing the Right Method:
Volumetric Method: Best when you have data on water volume over a period but not real-time
velocity or depth data.
Velocity-Area Method: Suitable for real-time streamflow estimation, especially when velocity
and cross-sectional area are directly measurable.
Hydraulic Methods: Ideal for estimating flow in natural or engineered channels where channel
geometry and hydraulic properties are well understood.
By selecting the appropriate method based on available data and conditions, you can accurately estimate
streamflow according to the WMO guidelines. Let me know if you'd like help applying any of these
methods to specific data!

4. Certainly! Below are solved examples for each method—Volumetric Method, Velocity-Area Method,
and Hydraulic Methods (Manning's equation). These examples illustrate how to use the formulas and
the necessary data for streamflow calculation.
1. Volumetric Method
Example:
Suppose you have data for a river, and you know that the total volume of water passing through a cross-
section over a 24-hour period is 150,000 cubic meters (m³). We need to calculate the streamflow.
Total volume (V) = 150,000 m³
Time period (T) = 24 hours = 24 × 60 × 60 = 86,400 seconds
Formula:
Q=VTQ = \frac{V}{T}
Calculation:
Q=150,000 m386,400 seconds=1.73 m3/sQ = \frac{150,000 \, \text{m}^3}{86,400 \, \text{seconds}} =
1.73 \, \text{m}^3/\text{s}
So, the streamflow is 1.73 m³/s.
2. Velocity-Area Method
Example:

5. Let’s say you're measuring the flow in a stream, and you’ve divided the cross-section into smaller
segments. Here are the measurements:
Width of the stream = 10 meters
Depth at 5 points across the width: 0.5 m, 1 m, 1.5 m, 1 m, 0.5 m
Velocity at each point: 0.3 m/s, 0.5 m/s, 0.7 m/s, 0.5 m/s, 0.3 m/s
We need to calculate the streamflow.
Steps:
1.Calculate the Cross-sectional Area (A):
oFirst, calculate the area of each section by multiplying the width of each segment by the
average depth for that segment. In this case, we will use the average of adjacent points.
Segment Areas:
oArea=0.5 m×0.5 m=0.25 m2\text{Area} = 0.5 \, \text{m} \times 0.5 \, \text{m} = 0.25 \, \
text{m}^2
oArea=1.0 m×1.0 m=1.0 m2\text{Area} = 1.0 \, \text{m} \times 1.0 \, \text{m} = 1.0 \, \
text{m}^2
oArea=1.5 m×1.5 m=2.25 m2\text{Area} = 1.5 \, \text{m} \times 1.5 \, \text{m} = 2.25 \, \
text{m}^2
oArea=1.0 m×1.0 m=1.0 m2\text{Area} = 1.0 \, \text{m} \times 1.0 \, \text{m} = 1.0 \, \
text{m}^2
oArea=0.5 m×0.5 m=0.25 m2\text{Area} = 0.5 \, \text{m} \times 0.5 \, \text{m} = 0.25 \, \
text{m}^2
Total Area (A):
A=0.25+1.0+2.25+1.0+0.25=4.75 m2A = 0.25 + 1.0 + 2.25 + 1.0 + 0.25 = 4.75 \, \text{m}^2
2.Calculate the Average Velocity (V): Average velocity can be calculated by averaging the velocities
at the five points.
V=0.3+0.5+0.7+0.5+0.35=0.46 m/sV = \frac{0.3 + 0.5 + 0.7 + 0.5 + 0.3}{5} = 0.46 \, \text{m/s}
3.Calculate the Streamflow (Q):
Q=A×V=4.75 m2×0.46 m/s=2.19 m3/sQ = A \times V = 4.75 \, \text{m}^2 \times 0.46 \, \text{m/s} =
2.19 \, \text{m}^3/\text{s}
So, the streamflow is 2.19 m³/s.
3. Hydraulic Methods (Manning’s Equation)

6. Example:
Let’s assume you’re working with a natural stream, and you have the following measurements:
Cross-sectional area (A) = 20 m²
Wetted perimeter (P) = 10 m
Slope (S) = 0.005 (dimensionless)
Manning’s roughness coefficient (n) = 0.035 (for a smooth gravel bed)
We need to calculate the streamflow using Manning’s equation.
Formula:
Q=1nAR2/3S1/2Q = \frac{1}{n} A R^{2/3} S^{1/2}
Where:
AA = Cross-sectional area (m²)
RR = Hydraulic radius = AP\frac{A}{P}
SS = Channel slope (dimensionless)
nn = Manning’s roughness coefficient
Steps:
1.Calculate the Hydraulic Radius (R):
R=AP=2010=2 mR = \frac{A}{P} = \frac{20}{10} = 2 \, \text{m}
2.Apply Manning’s Equation:
Q=10.035×20×(2)2/3×(0.005)1/2Q = \frac{1}{0.035} \times 20 \times (2)^{2/3} \times (0.005)^{1/2}
First, calculate the values for R2/3R^{2/3} and S1/2S^{1/2}:
(2)2/3≈1.587and(0.005)1/2≈0.0707(2)^{2/3} \approx 1.587 \quad \text{and} \quad (0.005)^{1/2} \
approx 0.0707
3.Plug in all values:
Q=10.035×20×1.587×0.0707Q = \frac{1}{0.035} \times 20 \times 1.587 \times 0.0707
Q=28.57×20×0.1125=64.3 m3/sQ = 28.57 \times 20 \times 0.1125 = 64.3 \, \text{m}^3/\text{s}
So, the streamflow is 64.3 m³/s.
Summary of Results:

7. Method Streamflow (Q)
Volumetric Method1.73 m³/s
Velocity-Area Method2.19 m³/s
Hydraulic Method64.3 m³/s
Each method gives a different result depending on the available data and the approach used. The
Volumetric Method is more suitable for large-scale water measurements (like reservoirs), the Velocity-
Area Method is more commonly used in field surveys of rivers and streams, and the Hydraulic Method
(Manning's) is ideal for more complex flow scenarios, particularly in natural channels where geometry
and roughness factors are important.
Let me know if you need further clarification or have additional questions!