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PRACTICE / Viscosity

Weight the speed by area

A fully developed laminar flow in a circular tube of internal radius 2.0 mm has centre speed 0.12 m/s. The liquid is incompressible and Newtonian, with a stationary no-slip wall.

What is the volume flow rate?

Organize the givens & assumptions
  • R = 2.0 mm
  • Centre speed = 0.12 m/s
  • Parabolic laminar profile

Steady or explicitly quasi-steady incompressible Newtonian flow; constant viscosity; long straight rigid circular tubes, stationary no-slip walls and fully developed laminar profiles. Neglect entrance, exit and connector losses unless stated. Verify the stated fixed-flow or fixed-pressure condition.

  1. A0.24π mL/s0.24\pi\ \mathrm{mL/s}
  2. B0.48π mL/s0.48\pi\ \mathrm{mL/s}
  3. C0.12π mL/s0.12\pi\ \mathrm{mL/s}
  4. D0.96π mL/s0.96\pi\ \mathrm{mL/s}

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