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in this example were looking at a trapezoidal channel were told that the flow rate in the channel is eight point four meters cube per second were given the channel dimensions told the roughness or the Mannings n value of the channel is not point naught to the longitudinal slope is not point naught naught five and what were trying to do is find the flow depth for the discharge of eight point four meter cube per second so what we want to do is try to work out what the depth of the flow is going to be at this given discharge so the starting point for this type of example would be to think about the continuity equation so we know that the discharge is going to be the velocity of water in the channel times by the cross-sectional area of the channel and we know thats we can find the velocity for your Mannings equation so the velocity given by my names equation is the hydraulic radius to 2 over 3 times the square root of the slope of the channel over the roughness and have work out t