Krikor Mardirossian February 2, 2004

Problem A protective linear exactly 12 m wide is available to line a channel for conveying water from a reservoir to downstream areas. If a trapezoidal-shaped channel (see figure 1.1) is constructed so that the linear will cover the surface completely, what is the flow area for x = 2 m and Ө = 45º? The geometry is defined such that 0 < x < 6 and 0 < Ө < 90°. Flow area multiplied be average flow velocity will yield volume rate of flow, an important parameter in the study of open-channel flows.

Diagram x x Ө 12 – 12x Figure 1.1

Solution The Flow Area Is Given by the Expression for the Area of a Trapezoid. Equation 1.1

Solution The variables in equation 1.1 represent:

Solution Plugging in the variables into the area equation 1.1, the equation will become: Equation 1.2

Solution It is given that x = 2 and Ө = 45º Inserting these values into equation 1.2, will give the flow area for theses variables. Equation 1.3

Computing equation 1.3 will give the answer to the problem.