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isco/sediment
Dear Dr. Brandstetter:
The problem of extracting water from a stream with mimimal impact to the streambed is of general interest. Based on my experience in using ISCO samplers and studying the jet dynamics of pure oxygen injected into reservoir with minimal disturbance of sediment and thermocline, I would like to make suggestions to your investigation here. Let me start with the theoretical consideration of this issue.
In using the ISCO water sampler, an intake tube is placed in the channel and the water is pumped up to the sample bottles through the tube. When the water is being extracting, a withdrawal zone is formed at the area immediately upstream of the intake tube. The hydraulic characteristics of the withdrawal zone depend upon flow rate, water depth, location of the tube, and the density distribution of the water. According to CE-QUAL-R1 and based on the results of laboratory experiments conducted by Bohan and Grace (1973), the upper and lower limits of the withdrawal zone can be found by solving the following equation:
Q - Z**2 * (Dr/r * g * Z)**0.5 = 0
where Q = flow rate through the tube, Z = distance from the tube center to the upper/lower withdrawal limit, Dr = density difference between the tube center and the upper/lower withdrawal limit, r = water density at the tube center, g = gravity.
Within the withdrawal limits, the vertical velocity profile is approximately parabolic. The location of the maximum velocity can be computed by:
Y1 = (Z1 + Z2) * [ sin(pi/2 * Z1/(Z1 + Z2) ]**2
Y2 = (Z1 + Z2) * [ sin(pi/2 * Z2/(Z1 + Z2) ]**2
where Y1 = distance from the lower withdrawal limit to the elevation of the maximum velocity, Y2 = distance from the upper withdrawal limit to the elevation of the maximum velocity, Z1 = distance from the lower withdrawal limit to the tube center, Z2 = distance from the upper withdrawal limit to the tube center.
When the water depth is larger than the withdrawal zone, the velocity profile is given by:
v = vm * [ 1 - (y * Dr)/(Y * Drm) ]**2
When a withdrawal limit coincides with the surface or the bottom, the velocity profile is given by:
v = vm * { 1 - [(y * Dr)/(Y * Drm)]**2 }
In the above equations, v = velocity, vm = maximum velocity, y = distance from the elevation of the velocity being computed to the elevation of the maximum velocity, Dr = density difference form the elevation of the velocity being computed to the elevation of the maximum velocity, Drm = density difference from the elevation of the maximum velocity to the elevation of the upper/lower limit, Y = distance from the elevation of the maximum velocity to the elevation of the upper/lower limit.
According the Karman and Prandtl's theories of tubulent flow, the velocity profile in a moderately narrow and shallow stream can be described by:
U/u' = (2.3/k) * log (c * y/ks)
where U= the time-averaged velocity, u' = the shear velocity at the boundary of laminar sublayer near the bed, k = the von Karman constant, c = a coefficient, y = the distance from the bed, ks = the effective grain roughness length for the particular conditions of flow.
The value of k ranges from 0.39 to 0.43 for clear water. It varies from 0.15 to 0.4 with the influence of flow and sediment characteristics of the water mixture. The value of c is 12.27 for clear water. It varies with sediment characteristics and generally decreases with the increase of the sediment concentration. For non- cohesive sediments, Keulegan (1938) defined the aove equation as
U/u' = 5.75 * log (30.2 * b * y/d)
where b = correction factor for the size of sediment grains and unity for the coarse grain, d = representative grain size of the sediment deposit at the bed.
For cohesive sediments, Krone (1956-59) gave the equation as
U/u' = (2.3/k) log (3.32 * R * u'/nu)
where R = hydraulic radius of the bed, nu = kinematic viscosity of the fluid.
The shear stress at the boundary of the laminar sublayer, tau, is defined as ru''**2. Sediment erosion occurs when tau is greater than the critical shear stress, tcr , of the bed. Many laboratory and field investigations have been carried out to determine the critical shear stress for as a function of sediment characteristics such as the grain diameter. However, the functional relationship established by the Shields' diagram is most commonly used.
Based on the above equations, one can determine whether the water extracting will cause the bed sediment to be scoured or not. The first step is to determine the major sediment characteristics including size distribution, representative diameter, and cohesiveness. The second step is to calculate the resultant velocity of the channel flow and the water extracting. The third step is to calculate the shear velocity and shear stress at the boundary of the laminar sublayer. Finally, compare the shear stress with the critical shear stress and determine if the sediment will be scoured according to the functional relationship representing the Shields' diagram.
Based on the above analysis, I suggest that you or your sponsoring agency measure the flow rate and temperature. There two major reasons. First, you can do the above anaysis to support your pumping design and to convince the regulatory agency that your pumping will have minimal impact to streambed. Second, your water quality data will be more meaningful and useful if the flow and temperature data are available.
If the above analysis is not feasible, I would suggest placing the intake tube one to two tube diameters below the water surface. Since the flow is episodic, you need a float to keep the tube at a constant submerged depth. You may tie the tube and the float to a rod with a length about one to two tube diameters.
Thus, a simple design to anchor the intake tube would be as follows:
(1) Stick a pole with smooth surfaces in the stream. In principle the pole should be as close to the center of the stream as possible.
(2) Link the intake tube to the pole with a ring that allows the tube to float up and down with the water. With a moderately large ring the tube may drift freely in the flow direction, which will reduce the resultant shear velocity and thus minimize the posibility of sediment scouring.
(3) Tie the terminal of the tube and a float to a rod with a length about one to two tube diameters.
If it is not necessary, it is better if the flow actuator is not put in the streambed. If it is possible, keep it on the land with the ISCO sampler.
Ching L. Chen
Systech Engineering, Inc.
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