Surface Water Hydrology
Professor. Rajib Maity
Department of Civil Engineering
Indian Institute of Technology, Kharagpur
Lecture 18
Area-Velocity and Moving-Boat Methods
Today’s lecture will cover two very important measuring methods one is the Area-Velocity
method and the Moving-Boat method.
(Refer Slide Time: 00:29)
There are many methods are available for measuring the streamflow, they are as follows
Area-Velocity Method Ultrasonic Method
Moving-Boat Method Hydraulic Structures
Dilution Technique Slope-Area Method
Electromagnetic Method
Today’s lecture will cover two methods first one is the area-velocity method, and the second one
is the moving-boat method. So, before starting these methods, we will just go for a basic
introduction to the streamflow measurement also.
(Refer Slide Time: 01:09)
The outline of this lecture goes like this, the first will give a brief introduction to the streamflow
measurement, and then we will take off the area of velocity method with its introduction, its
mathematical formulation, and some example problem. Then we take up the moving boat
method, again the same thing introduction, mathematical formulation, and example problem will
take before concluding with the summary for these two methods.
(Refer Slide Time: 01:34)
Streamflow Measurement
Introduction
Streamflow is measured as the amount of water passing through a specific section of a river or
stream over a fixed period of time. It is measured in the unit of discharge, i.e., volume per unit
time (e.g., m3/s, also known as cumec, ft3/s, also known as cusec). The measurement of discharge
forms an important branch of Hydrometry, the science and practice of water management.
(Refer Slide Time: 02:18)
Broad Categories of Streamflow Measurement Techniques
There are two major measurement techniques are there, we can categorize into two parts one is
the direct method and the other one is the indirect method. In the direct method, these are
generally time-consuming and these are costly also and it depends on the site condition where we
can apply it and it particularly depends on the site condition for its applicability, there are other
that in the indirect method, it utilizes the relationship between the discharge and the depth at a
specific location.
And the depth at a specific location is specifically designed to know where we know the
relationship between the height above some level and then with respect to its discharge. So, this
kind of through when it goes to some control structure, we call it as indirect method and
otherwise, we go for the direct method.
(Refer Slide Time: 03:08)
The area velocity method, moving boat method, dilution technique, an electromagnetic method,
and ultrasonic method these are these come under the direct method. The hydraulic structures
and the slope area method come under the indirect method.
(Refer Slide Time: 03:55)
Area-Velocity Method
In this method, the cross-sectional area of the river and velocity of the flow is measured at a
selected section it is referred to as its gauging site. So, wherever measured the stream flow that
one called as a gauging site. Now, the selection of the gauging site depends on different
condition.
The stream should have a well-defined cross-section with no seasonal variation.
The site should be easily accessible throughout the year.
The site should be in a straight and stable stretch.
The site should be free from the backwater effect.
These factors ensure that the stage discharged relationship remains constant over a long period of
time. So, that is why these are the conditions that ensure the applicability of the area velocity
method for a particular gauging location.
(Refer Slide Time: 05:13)
To evaluate the discharge, the cross-section along a vertical section is divided into a large
number of subsections by vertical.
The segment width should not be greater than 1/15 to 1/20 of the width of the
river. The number of segments should be optimized to increase the accuracy of
the discharge measurement and reduce time and cost.
The discharge in each segment should be less than 10% of the total discharge.
The difference of velocities in the adjacent segments should not be more than
20%.
The average velocity in these subsections are measured by the current meters or the floats and we
take generally there are different techniques are there we go to the boat and at this location we
stop and we measured the depth and the velocity using different instruments.
For calculation of the discharge for the entire cross-section, the following formula is used
Δ𝑄𝑖 = Discharge in the ith section
(Refer Slide Time: 07:39)
Discharge in the ith section can be written as,
𝑣𝑖= Average velocity at the ith vertical
For the i = 2 to n-2
For the first (i = 1) and the last (i = n-1) section considering these sections as triangular areas
(Refer Slide Time: 09:18)
Example
The following data were collected at a gauging site. Estimate the discharge in the stream.
(Refer Slide Time: 10:29)
Solution
The average width for the different sections can be evaluated as follows,
For the first and last sections,
For the rest of the sections,
Given that the velocity is measured at 0.2 and 0.8 depths, the average velocity at that vertical is
the average of the two velocities measured.
(Refer Slide Time: 10:58)
Solution
The discharge is calculated as follows,
So, the total discharge in the stream is this 13.29-meter cube per second
(Refer Slide Time: 12:10)
Example
The following data is available at a gauging site. Estimate the discharge in the stream.
Consider the rating equation of the current meter as follows,
(Refer Slide Time: 13:38)
Solution
The average width for the different sections can be evaluated as follows,
For the first and last sections,
For the rest of the sections,
Given that the velocity is measured at 0.6 depth, thereby the measured velocity is the average
velocity at that particular depth.
(Refer Slide Time: 14:00)
Solution
The discharge is calculated using the mid-section method as follows,
(Refer Slide Time: 14:57)
Moving-Boat Method
Discharge measurement of large alluvial rivers is very time-consuming by the standard current
meter even when the flow is low or moderate. During high flow, it is impossible to use the
standard current meter technique as it is difficult to keep the boat stationary.
In such cases, the moving-boat method may be extremely effective.
A special current meter is towed in a boat at a specific velocity, right angle to streamflow.
An echo-depth recorder is used to measure the depth at various points where velocity is
measured.
(Refer Slide Time: 16:56)
In this method, the velocity over the width of a segment is measured using the following
mathematical formulations,
The flow in the sub-area between two verticals is,
𝑦𝑖, 𝑦𝑖+1, vR, 𝜃 are the variables measured at the site.
Summation of all the segmental discharges over the whole width gives the stream discharge
(Refer Slide Time: 19:41)
To apply this method at the field,
An adequate stretch of river with no shoals, islands, bars, etc. needs to be selected.
The cross-sectional line should be defined by permanent structures so that the boat can be
aligned with the line.
Evaluation of the Average Velocity
A special current meter of the propeller type is used in which the velocity and inclination
of the meter to the boat direction in the horizontal plane can be measured.
The current meter is generally immersed at a depth of 0.5 m from the water surface to
record the surface velocities.
The surface velocities (𝑣𝑠) are converted to average velocities (v̅) across the vertical by
applying the following equation.
The reduction factor K lies between 0.85 to 0.95.
(Refer Slide Time: 21:09)
Example
In the moving boat method of discharge measurement, the magnitude of the recorded velocity
(vR) and direction (θ) of the velocity is measured. Estimate the discharge in the river. Assume
mean velocity in a vertical to be 0.95 times the surface velocity measured by the instrument. The
various sections are spaced at a constant distance of 3 m apart.
(Refer Slide Time: 22:05)
Solution
Given that all the sections are equally spaced (3 m apart), the average width for the different
sections can be evaluated as follows,
For the first and last sections,
For the rest of the sections,
The average velocity at a vertical is evaluated using the following equation,
(Refer Slide Time: 22:45)
Solution
(Refer Slide Time: 23:55)
Summary
In summary, we learned the following points from this lecture:
Different direct and indirect methods are used for streamflow measurement.
Two commonly used techniques namely Area-Velocity Method and Moving-Boat
Method are discussed in this lecture.
Both the methods include evaluation of the cross-sectional area of the river and the
average velocity at a particular section to finally estimate the total discharge at that
vertical section.
During high flow, it is impossible to use the standard techniques for streamflow
measurement as it is difficult to keep the boat stationary, in such cases the Moving-Boat
Method is used.
The following lecture discusses other direct streamflow measurement techniques like
dilution technique, an electromagnetic method, an ultrasonic method.
