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Hydraulic Geometry, Recreation Values, and the Manning Equation <br />Suppose a river has opportunities for camping and boating and you want to know how flows affect these <br />recreation outputs or activities. Taking a simplified case, assume that on the low and you want to know the point at <br />which the flow is too low for a boat to pass through a riffle, and at the high end you want to know when the flow is <br />so high that beaches are inundated and camping is no longer possible. <br />One way to get the answers would be to measure flows in the field through the full range of flows. With <br />enough observations and the right timing, you would eventually be able to identify the required flows, but this work <br />would be both costly and time - consuming. <br />The alternative is to use hydraulic geometry relationships to estimate these flows, either based on existing <br />gage data or a single set of cross section data collected in the field. For the sake of simplicity, assume that the <br />critical boat passage riffle and camping beach are at the same location so the same "critical reach" can be used to <br />explore both issues. A cross section or transect would be established at this location resulting in the channel <br />diagram shown in Figure 14. <br />Rivers generally show predictable increases in width, depth, and velocity as flow increases (Leopold and <br />Maddock, 1953). These relationships, called "at -a- station hydraulic geometry," can be developed directly from <br />repeated stream gage measurements, or they can be estimated indirectly from a single set of cross section data <br />using a hydraulic formula such as the Manning Equation. The Manning Equation shows the relationship between <br />depth, flow, velocity, cross section area, and wetted perimeter. It is thus possible to specify a minimum depth for <br />boating (the depth when a boat can pass without grounding) and identify the flow when this depth occurs, or <br />choose the point on the profile (and its corresponding flow) above which the beach is too small for camping. <br />Figure 14. Simplified case where hydraulic geometry modeling can be used to <br />identify flows that provide minimum depths for boating or that would inundate <br />camping beaches. <br />21 <br />