Raise the width of the channel at its base to the power of 2.5. If the base width is 10 feet, for example, 10^2.5 = 316.2.
Multiply the result by the square root of g, the acceleration due to gravity. The square root equals 5.7 for English units or 3.1 for metric units. For example, multiply 316.2 by 5.7 to get 1802.34.
Raise the slope of the sides of the channel to the power of 1.5. The slope is expressed as m:1 where m is the horizontal component and 1 is the vertical component. If m = 2, for example, calculate 2^1.5 to get 2.8.
Multiply the result by the volumetric flow through the channel. If the flow rate is 100 cubic feet per second, for example, multiply by 2.8 to get 2,800.
Divide this result by the result of the calculations using g and the channel width. For example, divide 2,800 by 1802.34 to get 1.55.
Pinpoint this number on the x-axis of a critical depth chart for trapezoidal channels. Move up from that point on the x-axis to the diagonal line on the chart. Move left from this point to the y-axis. The value at this point on the y-axis is y', a dimensionless variable related to critical depth. If the original number is 1.55, y' = 1.
Multiply y' by the base width of the channel. If y' is 1 and the base width is 10 feet, 1x10 = 10 feet.
Divide the result by m, the channel slope. If m = 2, for example, divide 10 feet by 2 to get 5 feet. This is the critical depth.