Estimating Flow in Streams
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Dana O. Porter
West Virginia University
Extension - Agricultural Engineering Specialist

In evaluating the capacity of a surface water resource to support livestock, aquaculture or other activities, it is important to estimate the volume, quality, and reliability of the water supply.

Methods for determining flow in open channels range from very detailed and precise to "quick and dirty." This article briefly describes some of these methods.

Fundamentals of Open Channel Flow

The flow of water in an open channel is expressed in units of volume per time. Common units are gallons per minute (gpm), cubic feet per second (cfs), liters per second (l/s), or cubic meters per second (m3/s). In flow measurement, flow is often estimated by determining the velocity at which water flows through a given cross-sectional area.

Flow = velocity X cross-sectional area or simply Q = VA

Alternately, the flow can be routed through a measurement device and measured directly, or it may be determined indirectly through use of appropriate measurements and mathematical models.

Current Meters

Current meters measure the energy (expressed as a pressure, rotational velocity, etc.) of moving water and translate it into a flow velocity. For instance, impeller meters relate the velocity of stream flow to the speed at which a submerged impeller rotates in the current. Current meters can measure velocity very accurately, provided that they are used correctly.

Velocity of water flowing in an open channel is not constant throughout a given cross-section. Roughness of the channel sides and bottom affects resistance to flow. The resulting distribution of the flow velocity may be generalized by the following sketch as:

 

In order to determine the "average" flow in the channel, one must estimate the cross-sectional area and an "average" current velocity in the channel. In practice, this is accomplished by subdividing the cross-section of the channel, determining the "average" flow for each subdivision, and summing the subdivision flows into a total flow for the channel. In a deep stream subsection, the average velocity is estimated by the average of velocities measured 20% depth (0.2D) and 80% depth (0.8D). In a shallow stream subsection where measurement at two depths is difficult, the average velocity is determined by measuring velocity at 60% of the depth (0.6D). This is shown schematically below:

The flow for each subdivision is determined by multiplying the cross-sectional area of the subdivision by the average flow velocity within the subdivision. The volume flow through this channel, for instance, would be:

Flow = (AaHVa) + (AbHVb) + (AcHVc) + (AdHVd) + (AeHVe) + (AfHVf) + (AgHVg) +(AhHVh)

where Aa,, Ab, ...Ah = cross-sectional areas of subdivisions a, b, ...h
Va,, Vb, ...Vh = average flow velocities of subdivisions a, b, ...h

The number and widths of the subdivisions depend upon accuracy desired.

Weirs

Weirs are structures which are inserted in the channel to measure flow. As water flows over the weir, the depth or "head" of the water is measured. The water head is entered into a discharge formula specific to the geometry of the weir. Some common weirs and their discharge formulae are:

90 degree V-notch weir:

 

Q = 2.49 (h) 2.48 (Cuenca, 1989)

 

where Q = flow in cubic feet per second
h = head (depth of flow) above the notch invert (lowest point) in feet

rectangular, sharp-crested weir:

Q = CwLh3/2

where: Q = flow
h = head (depth of flow) above the weir crest
L = length of weir crest
Cw = weir coefficient

Flumes

Flumes include various specially shaped and stabilized channel sections that are used to measure flow. Use of flumes is similar to use of weirs in that flow is related to flow depths at specific points along the flume.

Float

The float method is a very simple and inexpensive method for estimating flow in open channels.

Velocity can be estimated by using partially filled plastic bottles or other floating objects and noting the time required for the objects to travel a measured distance.

Velocity = distance traveled
time of travel

Volume rate of flow is then determined by multiplying the average flow velocity by the average cross-sectional area of the stream (Q = VA). An important drawback of this method is that the cross-sectional area may be difficult to determine, especially when the stream bank is not uniform. Further, since the flow velocity varies depending upon stream cross-section and position within the cross-section (see Fundamentals of Open Channel Flow, above), velocity estimates may be subject to errors. An average of several velocity measurements may improve accuracy of the estimated value.

Manning Equation

If the channel cross-section, slope, and roughness are known, flow can be estimated in some circumstances by the Manning Equation:

V =

R2/3 s1/2
_______
n


and Q = VA

 

Where: V = flow velocity
R = cross-sectional area divided by the wetted perimeter
s = hydraulic gradient (slope of the channel)
n = roughness coefficient of the channel
Q = volumetric flow
A = cross-sectional area

Estimating Cross-Sectional Area and Wetted Perimeter

Cross-sectional areas and wetted perimeters of some common channel sections can be determined by the following formulae (after Cuenca, 1989).

Reliability of Flow

A given water resource may or may not provide a reliable, sufficient amount of water for a particular purpose. A producer should consider whether possible seasonal variations in the water volume are a concern. Generally the production level of a particular operation should be limited to that which can be adequately supported by the water resource, unless alternative or supplemental water supplies are available. For instance, a producer planning to install a flow-through aquaculture system on a spring-fed stream should determine the minimum reliable flow from the spring. This low flow may limit the number of fish to be produced, unless the producer can supplement the flow with other water resources or recirculate a portion of the water. Either alternative may require significant additional capital and operational expenses.

Unfortunately, since many streams are not gaged, accurate estimates of low flows may be unavailable. A landowner may not have historical perspective to estimate the stream flow.

Under these circumstances, the producer should be conservative in estimating the capacity of the water resource.

For More Information

Cuenca, Richard H. 1989. Irrigation System Design: An Engineering Approach. Prentice Hall, Englewood Cliffs, New Jersey.

WVU Extension Service Aquaculture Web Page
http://www.wvu.edu/~agexten/aquaculture/index.htm

USGS. 1995. Stream-Gaging Program of the U.S. Geological Survey. U.S. GEOLOGICAL SURVEY CIRCULAR 1123. Reston, Virginia, 1995 http://h2o.usgs.gov/public/pubs/circ1123/index.html

Colorado State University Water Resources Web Page. "Streamflow Measurement."
http://www.cnr.colostate.edu/CWK/flowmeas.htm