It should be understood that the study of open channel flow is complex. Flow is seldom uniform, the roughness of the channel may vary, turbulence is almost always present, and the cross- sectional area may not be constant.
Most flow measurements are estimations at best, and empirical methods (methods developed by real world experiences) are very common. Because of the length of this publication and the practicality to aquaculture, more in-depth discussion will be presented only for the velocity-area and the slope hydraulic radius methods.
How to use the velocity-area method:
The velocity-area method is a procedure that is simple and practical for channels of the size normally used in aquaculture.
The basic relationship is:
Q = VA, Where : Q = Flow in cubic feet per minute : V = Velocity in feet per minute : A = Cross-sectional area in feet 2
This is the basic equation of all flow. Therefore, to evaluate a channel to determine the amount of water flowing we need to measure the cross-sectional area (A) and the average velocity (V) across the cross-sectional area.
Area (A) is determined by measuring the width (W) (Figure 2) and taking measurements of the depth at equal distances across W and averaging them. Then W X D will give the cross-sectional area.
Measuring the velocity is the difficult part of this procedure since the velocity varies widely across the cross-section. There at least 8 procedures used to determine the mean velocity. The most common are the two-point method and the six-tenths-depth method.
The two-point method is used where the water depth is more than 2 feet. Here the velocity is measured at .2 and .8 of the depth and averaged. Accuracy of this method is high. The six-tenths depth method measures velocity at .6 the depth from the surface.
The accuracy is not as good as the two-point method, but adequate in shallow channels. With both methods a current meter is required. Velocity measurements are recorded at equal intervals across the channel and averaged.
The equation Q = AV is then applied to determine the flow (Q). Accuracies of ± 20 percent should result if care is taken with measurements. Devices used to measure velocity in open channels are known as current meters. A number of different types of current meters are available. Morris and Wiggert (1972) reviewed these devices. The more common are Doppler Ultrasonic meters, Turbine meters, rotating element meters, electromagnetic probe meters and Eddyshedding Vortex meters.
Improvements in electronics have enhanced the accuracy of these meters.
How to use the slope hydraulic radius method:
The Manning Equation in its various forms is the most used empirical method for estimating the flow in open channels. This equation can also be used to design open channels. The Manning Equation can be written as follows:
Q = A X V = 1.49 R : Q = Flow in cubic feet per second : R = Hydraulic Radius = A/P in ft. : A = Cross-sectional area of the channel in ft.2
P = Wetted perimeter of the channel in ft. : S = Slope of the channel - dimensionless : n = The roughness coefficient - dimensionless
If Q is desired in gal/min, the equation becomes
For the Manning formula to be applied the channel should be nearly uniform in slope, cross-section and roughness, and free of outside water sources, turns and rapids. The straight section should be at least 200 feet long (longer if possible).
It can be seen that the average velocity and flow vary inversely with the roughness of the channel (n). Therefore, the higher the n value the lower the flow, all other factors being equal. Table 1 gives n values for several channel types.
R is defined as the hydraulic radius, the cross-sectional area divided by the wetted perimeter. This is dependent on the slope and depth of water flowing.
Table 2 provides geometric elements for channels of 4 cross-sectional slopes. The most common shape for earthen open channels is the trapezoid. This shape allows for varying side slopes which can minimize erosion.
Table 3 shows permissible side slopes depending on soil types. This information is useful when designing an open channel.
The slope of the channel (S) is a measure of the channel bottom elevation difference at the ends of the uniform section divided by the length of the section.
As an example, suppose we want to know how much water is flowing in an open ditch with the following trapezoidal cross-sectional shape (Figure 3). The ditch bottom is known to drop 1 foot in 400 feet of nearly straight uniform cross-section.
The channel is vegetated and not well kept. This seems to be a large amount of water flowing. Is the velocity too high for the sandy loam soil?
Table 4 shows that the maximum allowable mean velocity to minimize erosion = 160 ft/min. The average velocity in our example channel is:
Therefore, the velocity will not cause excessive erosion.
From the discussion and the example it should be evident that in the design of an open channel that is to be nearly straight and uniform, the Manning Equation can be very useful.
By considering various cross-sectional shapes and depths of flow with known slopes, needed flow rates for aquacultural applications can be planned. Remember, the calculated values are only as good as the input values. Variances in the shape, slope and straightness will cause the procedure to be less accurate and less useful.
Authors:
J. David Bankston, Jr. and Fred Eugene Baker
