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  1. Problems
  2. /A flat plate of area 0.15 m² slides at a steady 0.60 m/s over a fixed surface, on a film of oil 1.2…
EasyPhysicsHigh School (11–12)Mechanics › Fluid Flow, Bernoulli's Principle and ViscosityNumericalBoard Exam

A flat plate of area 0.15 m² slides at a steady 0.60 m/s over a fixed surface, on a film of oil 1.2…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A flat plate of area 0.15 m20.15\ \text{m}^20.15 m2 slides at a steady 0.60 m/s0.60\ \text{m/s}0.60 m/s over a fixed surface, on a film of oil 1.2 mm1.2\ \text{mm}1.2 mm thick. A force of 15 N15\ \text{N}15 N keeps it moving. Find the viscosity of the oil.

Check your answer

Work it out on paper, then type your number. The answer itself stays hidden.

Pa s
Need a reminder? The key ideaShowHide

Viscosity: the force to slide a plate of area AAA at speed vvv over a film of thickness ddd is F=ηAvdF = \eta A\dfrac{v}{d}F=ηAdv​. Stokes' law: a small sphere feels 6πηrv6\pi\eta rv6πηrv, so it falls at a terminal speed vt=2r2(ρ−σ)g9ηv_t = \dfrac{2r^2(\rho - \sigma)g}{9\eta}vt​=9η2r2(ρ−σ)g​.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. η=15 N×1.2×10−3 m0.15 m2×0.60 m/s=0.20 Pa s\eta = \dfrac{15\ \text{N} \times 1.2 \times 10^{-3}\ \text{m}}{0.15\ \text{m}^2 \times 0.60\ \text{m/s}} = 0.20\ \text{Pa s}η=0.15 m2×0.60 m/s15 N×1.2×10−3 m​=0.20 Pa s.

Answer: 0.20 Pa s0.20\ \text{Pa s}0.20 Pa s, about the viscosity of a light machine oil.

Check. 0.20 Pa s×0.15 m2×0.60 m/s0.0012 m=15 N0.20\ \text{Pa s} \times 0.15\ \text{m}^2 \times \dfrac{0.60\ \text{m/s}}{0.0012\ \text{m}} = 15\ \text{N}0.20 Pa s×0.15 m2×0.0012 m0.60 m/s​=15 N.

Watch out. 1.2 mm=1.2×10−3 m1.2\ \text{mm} = 1.2 \times 10^{-3}\ \text{m}1.2 mm=1.2×10−3 m.

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