Hydrobiologia 222: 109-114, 1991. © 1991 Kluwer Academic Publishers. Printed in Belgium.
109
Head tube: a simple device for estimating velocity in running water Jan J.H. Ciborowski Department of Biological Sciences, University of Windsor, Windsor, Ontario, N9B 3P4, Canada Received 9 August 1990; accepted 20 September 1990
Key words: water velocity, stream, flow, meter, measurement, hydrodynamics
Abstract Construction and operation of a head tube are described. A head tube is an inexpensive, easily-built alternative to a current meter for measuring water velocity in streams and rivers. When water flowing in a channel is obstructed by an object, its depth increases at the point of zero velocity (stagnation zone). The difference between the flowing-water depth and depth in the stagnation zone is the head (h). A head tube consists of a clear, hollow, 2.5 cm diameter acrylic tube and a sliding sleeve made of clear plastic. The tube is placed vertically on the river bottom. The difference (head) between water level inside the tube and the height of water against the tube's upstream face is measured against a scale (cm s - ) drawn on the sleeve, which provides a direct reading of velocity. Graduations of the scale are calculated from a hydrodynamic equation relating mean velocity (U) to head (h): U = (2 gh)°0 5, where g is acceleration due to gravity. When tested in a laboratory flume, the head tube gave very precise estimates of velocity (R 2 of relationship = 0.98), although the original calibration scale overestimated current meter-measured velocity by 22 percent. The relationship between head tube and current meter estimates of mean velocity determined in a river with stony substrate was less precise than the correspondence observed in the laboratory (R 2 = 0.81). However, estimates of discharge based on head tube measurements were within 8 percent of estimates based on current meter readings.
Introduction Current meters can accurately measure water velocity in rivers, but they are expensive, delicate and time-consuming to use. Hynes (1970) and John (1978) reviewed various methods of measuring flow rates in running waters. A velocity head rod (Wilm & Storey, 1944) is one of several simple, alternative instruments that exchange the precision of metered readings for ease of use and simplicity of construction. A head rod measures mean velocity at a point in a shallow stream by locally obstructing flow. The obstruction transforms flowing water's
kinetic energy (momentum) to potential energy, which is manifested as a rise in depth at the upstream face of the rod (Newbury, 1983). For example, a metre stick is commonly used as a head rod. When the stick faces the water flow edge-on, there is minimal obstruction of the water, and the depth can be measured. However, if the stick is turned to expose its broad face to the current, water rises against the upstream face. This rise in water level is the head (h, cm), which can be related to mean velocity (U, cm s - ') by the equation
U = (2 gh)°0.5,
(1)
110 where g is acceleration due to gravity (980 cm s-2) (Vogel, 1981). Simple head rods tend to bend and slip on the substrate when turned. This produces inaccurate readings. Drost (1963) and Chapman & McIntyre (1964) modified Wilm & Storey's (1944) design by adding a swivelling foot plate to the base. However, even this instrument is large (1 m long x 13 cm wide), and requires use of a calculator to convert head measurements into velocity estimates. I developed a head tube as a more portable alternative. This instrument is a directreading equivalent to a velocity head rod that need not be rotated to provide measurements.
For example, the 20 cm s - graduation is determined by substituting '20' into equation (2) and calculating h ( = 0.204 cm). The 20 cm s- 1 line should thus be drawn 2.04 mm above the baseline. The acetate sheet is then rolled up (ink side inward) and glued to form a sleeve 25.4 cm long that slides over the tube. Chloroform or trichloroethane acts as an excellent adhesive. A small amount applied from the tip of a hypodermic needle beneath the outer edge of the rolled acetate sheet temporarily dissolves and then seals the acetate sheet to itself without causing loss of transparency.
Operation Materials and methods Construction I made the instrument from a transparent, 60 cm long x 2.5 cm diameter hollow acrylic tube and a 20.3 x 25.4 cm sheet of acetate overhead projector transparency. I found a tube of these dimensions to be convenient for general use. However, in principle, neither the diameter nor the tube length used should influence operation of the instrument. The tube itself serves to obstruct the water flow and generate head. The magnitude of h can be estimated by comparing this external (upstream) water level with the baseline level of water inside the tube. A gasket of weatherstripping glued to bottom of the tube can help maintain contact with uneven substrates. The sheet of acetate is used to form a sleeve that is graduated to provide direct readings of velocity from the amount of head generated. Rearranging the energy equation (1) permits one to calculate changes in depth (cm) that correspond to specific velocity readings: h = U 2 /2g
= 0.00051
2.2
(2)
A baseline is drawn with a marking pen at the bottom of the acetate sheet, and reference lines are drawn distances h (cm) above the baseline.
In use, the tube rests upright on stream bottom (Fig. 1A). Water rises up the centre and provides a measure of depth. The sleeve is slid along the tube to align the baseline with the water level inside the tube. The height of water against the upstream face of the tube can be seen through the side of the tube. Velocity is read directly by matching upstream water level to the scale lines on the sleeve (Fig. 1B). A typical measurement takes 10-20 s. The tube must be kept vertical to minimize misreadings. The head (h) increases exponentially with velocity; thus, readings at very slow flows are difficult to distinguish. Flow rates < 20 cm s often do not register. Similarly, water surges at high velocity can reduce precision. Chapman & McIntyre (1964) cautioned that velocities < 30 cm s - ' were below the sensitivity of their head rod. They reported greatest precision of readings with their rod at high velocities. I was unable to find locations at which to take readings with velocities greater than 80 cm s -' (see below). However, John (1978) reported that velocity head rods have a useful operating range of up to 250 cm s -'. The maximum operating velocity of the head tube should be similar, provided that flow is not supercritical (i.e., Froude number < 1.0). Two factors can reduce tube and sleeve clarity and make readings difficult. Condensation can
111
A
B
VELOCITY GRADUATION G
j, Tube
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-
LE$VEL
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INTERN WATI LEVEL ______
BASEUNE
SLEEVE
TUBE
Fig. 1. A. Velocity head tube. B. Detail of tube showing baseline of sleeve adjusted to internal water level. Velocity is read by matching level of upstream wave against nearest graduation on sleeve.
form on the inner surface of the tube when air and water temperatures differ greatly. Suspended sediments trapped between the sleeve and tube eventually scuff the surfaces and necessitate occasional replacement of the acetate sleeve. These problems were not encountered during the testing procedures outlined below.
Laboratory testing Laboratory estimates of accuracy and precision of the head tube were generated from measurements taken at two points in a large (10 m long x 0.42-2.0 m wide, 15-20 cm deep) laboratory flume that circulated water at accurately metered rates. One series of head tube readings was taken at a rectangular portion of the channel. Actual mean water velocity at this point was calculated by dividing total flume discharge by the cross-sectional area of the channel. There was almost perfect correspondence between mean water velocity calculated from discharge and readings taken here with an Ott C-2 current meter (R 2 = 0.998). A second series of head tube
readings was taken where the channel bed was a shallow, truncated V. These latter readings were compared with mean velocity estimated with an Ott C-2 current meter (50-s measurements recorded at 0.6 x depth). Comparisons were made for mean velocities over the range 20-85 cm s- '. Linear regression analysis was used to evaluate the relationship between mean velocity estimated from the head tube and mean velocity determined from discharge and/or the current meter.
River testing Head tube reliability under natural conditions was evaluated by comparing velocity head tube readings with measurements of mean velocity taken with an Ott C-2 current meter. Readings were taken across three transects located 10 m apart in a shallow, rocky riffle in the Ausable River, southwestern Ontario, Canada. Here, maximum depth of the river was 40 cm. For each transect, readings were taken one m apart across the 12-14 m width of the river. At each point, I measured depth (metre stick), metered mean velo-
112 city (current meter - one 30-s reading at 0.6 x depth if depth was < 30 cm; the mean of readings at 0.2 x and 0.8 x if depth was > 30 cm), and estimated mean velocity (head tube). Velocities recorded with the current meter ranged from 3-66 cm s-1 ' . The data from river measurements were interpreted in two ways. Linear regression analysis was performed to determine the precision of the relationship between single values of mean velocity estimated with the current meter and mean velocity measured with the head tube. Additionally, river discharge at each transect was calculated from the current meter readings and from the head tube readings. Mean discharge determined by the two methods was compared using a paired-comparison t-test.
LABORATORY FLUME
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In the laboratory, the instrument produced precise estimates of mean velocity (Fig. 2). Linear regression of mean velocity estimated from the head tube against mean velocity calculated from flume discharge or current meter produced a coefficient of determination (R 2 ) of 0.984. The intercept of the regression equation did not differ from zero (intercept = -0.81 + 1.28, t = 0.63, p > 0.50). However, the slope of the relationship (0.818 + 0.020) was significantly less than 1.0 (t = 8.83,p < 0.001). Thus, the head tube consistently overestimated the true mean velocity by a factor of approximately 22 percent. River data were more variable than were laboratory readings (R2 of this relationship = 0.812; Fig. 3). This reduced precision was the result of local obstruction of flow by rocks, which made velocity measurements taken with both the head tube and the current meter more subject to error. Although the relationship between current meterestimated velocity and head tube estimates of velocity was linear, the slope of this relationship was substantially but not significantly different than 1.0 (slope = 0.855 + 0.082, t = 1.76, 0.05
p > 0.05)). Dashed line represents 1: I correspondence.
Table 1. Discharge (m3 s along 3 transects using Ott Percent excess represents estimate exceeded current
') of Ausable River estimated C-2 current meter and head tube. percentage by which head tube meter estimate.
Transect
Current meter
Head tube
% Excess
1 2 3 Mean + S.E.
0.427 0.367 0.475 0.423 _+0.031
0.447 0.436 0.489 0.457 + 0.163
4.7 18.8 2.9 8.0
Discussion There was a strong relationship between mean velocity estimated by the head tube and velocity estimated by more standard methods. However, the head tube apparently overestimated readings by approximately 22 percent. The difference between water levels inside and upstream of the
tube was greater than that predicted by hydrodynamic theory. The most likely explanation for the discrepancy is that the tube tends to overrepresent the contribution of surface velocity rather than providing a true estimate of the depth-averaged velocity (J.A. McCorquodale, University of Windsor, personal communication); surface velocity is generally greater than mean velocity. The head tube lost precision when it was used to estimate velocity in areas with uneven substrates. This problem was noted by Heede (1974) for head rods used in boulder-strewn mountain streams. Despite the increased variability of measurements that accompanied field use of the instrument, my estimates of stream discharge calculated from head tube readings were reasonably close (8 percent) to those determined using a current meter. Because the laboratory tests indicated that the tube overestimates readings, especially at high velocities, the correspondence may have been a function of the relatively low velocities encountered at many points in the Ausable River. Evidently, underestimated readings taken at very low velocity in the Ausable River (
