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236 <br />Student t-tests to determine if there was a signifi- <br />cant difference between the control and treatment <br />casts. In addition, we used casts of two species <br />lacking humps, but closely related to each of the <br />treatment fishes, to compare drag and force <br />direction of nuchal humped and non-humped <br />casts. The more streamlined catostomid was the <br />flannehnouth sucker, C. latipinnis, and the more <br />streamlined cyprinid was the roundtail chub, Gila <br />robusta, 439 and 403 nun TL, respectively. We also <br />determined drag coefficients of two well-known <br />objects, a 324 mm TL rainbow trout, Oncorhyn- <br />chus mykiss, and a 57.17 mm diameter sphere for <br />comparison with other studies. <br />We compared humped vs. non-humped mor- <br />photypes by analysis of drag coefficients, which are <br />widely used for comparing the hydrodynamic drag <br />among fishes. The drag coefficient (CD) is defined <br />as <br />CD = 2DIPSU2 <br />where D is the drag force, p is the fluid density, S is <br />the reference area, and U is the velocity (Denny <br />1988, Alexander 1990, Vogel 1994). The drag <br />coefficient is a dimensionless function of the Rey- <br />nolds number that can be used to compare the <br />effects of hydrodynamic drag on objects of differ- <br />ent morphologies, including fishes (Webb 1975, <br />Denny 1988, Alexander 1990). We compared drag <br />coefficients of our fish casts with nuchal humps to <br />those of more streamlined fishes and the casts with <br />the nuchal humps removed to help evaluate the <br />hydrodynamic role of nuchal humps of the Colo- <br />rado River fishes. Such hydrodynamic compari- <br />sons have often been made between species, which <br />may make it difficult to separate effects from other <br />interspecific differences (Pettersson & Bronmark <br />1999). Hence, we tested both models of conge- <br />nerics and models with humps removed. <br />We used two different methods for determining <br />the surface area in this study: frontal area (the <br />maximum projection of the body onto a plane <br />normal to the direction of flow) and wetted area <br />(the total surface exposed). We used the frontal <br />area to calculate the drag coefficient of the sphere, <br />and the wetted area to determine the drag coeffi- <br />cients of the fish casts. We calculated the reference <br />area measurement in this manner to keep to con- <br />vention and produce quantities that could be <br />compared to values previously reported in the lit- <br />erature. Frontal surface area is considered easier <br />to measure accurately, while wetted surface area is <br />difficult to measure in complex shapes. <br />We tested drag and lift components of fish casts <br />in an 18.3 in x 0.9 in x 0.6 in flow tank at the U.S. <br />Bureau of Reclamation Hydraulics Laboratory in <br />Lakewood, Colorado (Figure 2). Two 100 hp <br />centrifugal pumps delivered water into a 950 000 1 <br />reservoir and then into the tank baffle through a <br />30 cm diameter pipe. A stone baffle within a screen <br />helped to control the flow of water at the filling <br />point, and 4.6 in below the baffle water also passed <br />through an array of flow-straighteners consisting <br />of 200 galvanized pipes (5.1 cm diameter and <br />51 cm long) stacked upon one another to fill the <br />channel. We used a Sontek Adv-4 Doppler veloc- <br />ity probe to measure the flow rates, which reached <br />1.0 in s-1 in the flume. <br />We tested effects of lower velocities (i.e., <br />0.3 in s-1) on the fish casts in a smaller flow tank <br />at the University of Colorado at Boulder. Water <br />flow was generated by a 0.5 hp electric motor <br />which operated a propeller in a 15 cm PVC recir- <br />culating pipe. The water entered the flow tank <br />through a pipe baffle to disperse flow into a larger <br />upper end (0.3 in x 0.3 in x 0.64 m), which nar- <br />rowed to a 0.3 in x 0.23 in x 0.64 in working sec- <br />tion. The water entered the working section <br />through a flow-straightener constructed of <br />approximately 2000 drinking straws of 0.48 cm <br />',,.,Drag <br />Figure 2. Experimental flume at the U.S. Bureau of Reclama- <br />tion Hydraulics Laboratory in Lakewood, Colorado illustrating <br />experimental design, including mounting and orientation of the <br />fish casts along with various flow components.