The discussion centers on the velocity field in two-dimensional flow represented as \(\vec u = \langle u(y), v(y), 0 \rangle\). It is established that for incompressible fluids, the continuity equation necessitates that the velocity component \(v\) must remain constant across the flow. This conclusion is derived from the requirement that the divergence of the velocity field must equal zero, which directly influences the behavior of fluid properties in two-dimensional flow scenarios.
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glebovg said:If the velocity in a two-dimensional flow is given as \vec u = \left\langle {u(y),v(y),0} \right\rangle. Why must v be constant? I am not sure where to start. Can anyone help?