Motor oil, with a viscosity of $0.25 \mathrm {~N} \cdot \mathrm { s } / \mathrm { m } ^ { 2 }$ is flowing through a tube that has a radius of 5.0 mm and is 25 cm long. The drop in pressure is 300 kPa. What is the volume of oil flowing through the tube per second?

Question

Motor oil, with a viscosity of $0.25 \mathrm {~N} \cdot \mathrm { s } / \mathrm { m } ^ { 2 }$ is flowing through a tube that has a radius of  5.0 mm and is  25 cm long. The drop in pressure is  300 kPa. What is the volume of oil flowing through the tube per second?

Quizplus · Accepted Answer

The volume flow rate can be calculated using Poiseuille's law: $ Q = \frac{\pi r^4 \Delta P}{8 \eta L} $. Substituting the given values: $ r = 0.005 \, \text{m} $, $ \Delta P = 300,000 \, \text{Pa} $, $ \eta = 0.25 \, \text{N} \cdot \text{s/m}^2 $, and $ L = 0.25 \, \text{m} $, we find $ Q \approx 0.0012 \, \text{m}^3/\text{s} $.

Motor Oil, with a Viscosity Of 0.25 N⋅s/m20.25 \mathrm {~N} \cdot \mathrm { s } / \mathrm { m } ^ { 2 }0.25 N⋅s/m2

Motor Oil, with a Viscosity Of $0.25 \mathrm {~N} \cdot \mathrm { s } / \mathrm { m } ^ { 2 }$