The cylindrical container in figure has a radius of 1 m and contains motor oil with a density of 730 kg m^-3.Oil is seen to flow out of the 20-cm long,2-cm diameter tube at the bottom of the container.If 3.80 *10^-3 m³ of oil flows out of the tube in 29 seconds,what is the viscosity of the oil? Assume the change in the level of the oil in the reservoir over the time period is negligible. A)0.30 Pa s B)0.29 Pa s C)0.54 Pa s D)0.68 Pa s E)0.47 Pa s

Question

Quizplus · Accepted Answer

We can use Poiseuille's law to relate the flow rate to the viscosity of the oil:
Q = (πr^4/8η)LΔP
where Q is the flow rate, r is the radius of the tube, η is the viscosity of the oil, L is the length of the tube, and ΔP is the pressure difference across the tube.

We can rearrange this equation to solve for η:
η = (πr^4/8Q)LΔP

Substituting in the given values, we get:
η = (π(0.01 m)^4/8(3.80 x 10^-10 m^3/s))(0.20 m)(0.730 x 9.81 m/s^2)
η ≈ 0.54 Pa s

Therefore, the answer is C: 0.54 Pa s.

The Cylindrical Container in Figure Has a Radius of 1