Question 1.9: A 50 × 50 mm plate is moving on a 0.2 mm thick fluid layer w......
A 50 × 50 mm plate is moving on a 0.2 mm thick fluid layer with a velocity of 20 mm/s (Figure 1.9). Determine the force and power required to maintain the constant velocity if the viscosity of the fluid film is 1 poise.
Given,
\text { Thickness of fluid film }=0.2 mm =0.2 \times 10^{-3} m
\text { Velocity of upper plate, } u=20 mm / s =20 \times 10^{-3} m / s
Viscosity of fluid, μ = 1 poise = 0.1 Ns/m²
Assuming the linear velocity distribution, from Newton’s law of viscosity,
\begin{aligned} \tau & =\mu \frac{d u}{d t} \\ \tau & =0.1 \times \frac{20 \times 10^{-3}}{0.2 \times 10^{-3}} \\ \tau & =10 N / m ^2 \end{aligned}
So, the force required to maintain constant velocity
\begin{aligned} F & =\tau \times A=10 \times(50 \times 50) \times 10^{-6} \\ & =0.025 N \end{aligned}
Therefore, Power = Force × Velocity
\begin{aligned} & =0.025 \times 20 \times 10 \times 10^{-3} \\ & =5 \times 10^{-4} W \end{aligned}