The figure plots streamlines of a steady two-dimensional flow in a 0.2 m high channel, with stream function Ψ in m²/s. Find volume flow rate per unit depth.
In two-dimensional incompressible flow, discharge per unit depth between streamlines equals their stream-function difference. The walls have Ψ = −1 and Ψ = +1 m²/s. Thus $q=1-(-1)=2$ m²/s, B. The channel height need not be multiplied again because Ψ already encodes the integrated velocity.
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