A 1-in-wide space between two horizontal plane surfaces is filled with SAE 30 Western lubricating oil at 80^{\circ} \mathrm{F} . What force is required to drag a very thin plate of 4-\mathrm{ft}^2 area through the oil at a velocity of 20 \mathrm{ft} / \mathrm{min} if the plate is 0.33 in from one surface?

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Fig. A.1: \quad \mu=0.0063 \mathrm{lb} \cdot \mathrm{sec} / \mathrm{ft}^2

Eq. (2.9): \quad \tau_1=0.0063 \times(20 / 60) /(0.33 / 12)=0.0764 \mathrm{lb} / \mathrm{ft}^2

Eq. (2.9): \quad \tau_2=0.0063 \times(20 / 60) /(0.67 / 12)=0.0394 \mathrm{lb} / \mathrm{ft}^2

From Eq. (2.9): \quad F_1=\tau_1 A=0.0764 \times 4=0.305 \mathrm{lb}

From Eq. (2.9): \quad F_2=\tau_2 A=0.0394 \times 4=0.158 \mathrm{lb}

Force =F_1+F_2=0.463 \mathrm{lb} \quad

\tau=\frac{F}{A}=\mu \frac{U}{Y}=\mu \frac{d u}{d y} (2.9 )

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