Couette Flow

Calculus Level pending

The flow between two parallel plates, with the upper plate moving with constant velocity \( U \) and distance \( h \) between them, can be described by the differential equation below: \[ \frac{d^2 u}{dy^2} =0, \] where \( u \) is the flow velocity and \( y \) is the distance from the lower plate. Considering that the distance between the plates is \( h = 1 \) mm and that the upper plate is moving with constant speed \(U = 1 \) m/s, which is the expression for the flow velocity \( u(y) \) as a function of \( y \)?

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