Fluid Mechanics · Flow kinematics and material derivatives
In a two-dimensional incompressible flow the stream function (m²/s) is ψ = 3x² y − y³
Problem
In a two-dimensional incompressible flow the stream function (m²/s) is ψ = 3x² y − y³. Compute the volume flow rate per unit depth between the streamlines ψ = 0 and ψ = 0.12 m²/s. Identify a geometric path connecting a point on ψ = 0 to a point on ψ = 0.12 across which that volume flux can be evaluated as a simple integral of the velocity, and carry out the integral as a check.
Hint
Volume flow per unit depth between two streamlines equals the difference of the stream-function values (with the sign convention used to define psi).
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