Oil (SAE 30) at \(15.6{ }^{\circ} \mathrm{C}\) flows steadily between fixed, horizontal, parallel plates. The pressure drop per unit length along the channel is \(30 \mathrm{kPa} / \mathrm{m}\), and the distance between the plates is \(4 \mathrm{~mm}\). 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, 

(c) the velocity along the centerline of the channel.