The discharge per meter of width of the channel is 7.2 cubic meters per second, calculated using the cross-sectional area of 0.6 m² (from the 60 cm depth) and the given constant velocity of 12 m/s.
To calculate the discharge per meter of width for water flowing in a channel, we need to apply the formula for the flow rate, which is the product of the cross-sectional area A of the flow and the velocity v of the water:
Flow rate Q = A × v
Since the depth h of the channel is given, and the flow is perpendicular to this depth, we assume the width of the channel as 1 meter for the per-meter calculation. Therefore, the cross-sectional area A is simply the depth h times the width, which in this case is 1 meter, as we are calculating discharge per meter of width. The depth is given as 60 cm, which we convert to meters:
h = 60 cm = 0.6 m
A = h × width
A = 0.6 m × 1 m = 0.6 m²
The given velocity v is 12 m/s, so:
Q = A × v = 0.6 m² × 12 m/s = 7.2 m³/s
The discharge per meter of width of the channel is 7.2 cubic meters per second (m³/s).