$5.$ Water flows steadily between fixed, horizontal, parallel plates. The pressure drop per unit length along the channel is $5$ kPa$/$m$,$ and the distance between the plates is $4$ mm$.$ The flow is laminar. Determine: $($a$)$ the volume rate of flow $($per meter of width$),($b$)$the magnitude and direction of the shearing stress acting on the bottom plate, and $($c$)$the velocity along the centerline of the channel.