Fluids of viscosities (mu_{1}=0.1 mathrm{~N} cdot mathrm{s} / mathrm{m}^{2}) and (mu_{2}=0.15 mathrm{~N} cdot mathrm{s} / mathrm{m}^{2}) are

Question:

Fluids of viscosities $\mu_{1}=0.1 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}$ and $\mu_{2}=0.15 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}$ are contained between two plates (each plate is $1 \mathrm{~m}^{2}$ in area). The thicknesses are $h_{1}=0.5 \mathrm{~mm}$ and $h_{2}=0.3 \mathrm{~mm}$, respectively. Find the force $F$ to make the upper plate move at a speed of $1 \mathrm{~m} / \mathrm{s}$. What is the fluid velocity at the interface between the two fluids?

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