A viscous fluid flows steadily (no time dependence) in the z direction, with the flow confined between

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A viscous fluid flows steadily (no time dependence) in the z direction, with the flow confined between two plates that are parallel to the x-z plane and are separated by a distance 2a. Show that the flow’s velocity field is


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and the mass flow rate (the discharge) per unit width of the plates is


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Here dP/dz (which is negative) is the pressure gradient along the direction of flow. 

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