viscosity and terminal velocity questions with solutions

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• Multi-correctmediumProperties of solid and fluidviscosity and terminal velocity

  Geometrically similar spheres of the same material fall terminally through the same viscous liquid and obey Stokes' law. Which scaling statements are correct?

  Select all that apply

  • Option A

    Terminal speed varies as r².

  • Option B

    Viscous drag at terminal speed varies as r³.

  • Option C

    Rate of heat production due to viscosity varies as r⁵.

  • Option D

    Heat produced while moving through a fixed distance varies as r³.

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• MCQeasyProperties of solid and fluidviscosity and terminal velocity

  A small rigid sphere of radius r moves with speed v through a viscous liquid in the creeping-flow regime where Stokes' law is valid. What is the magnitude of the viscous drag?

  Options

  • Option A

    6πηrv

  • Option B

    6πηr²v

  • Option C

    4πηrv²

  • Option D

    ηv/(6πr)

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• MCQmediumProperties of solid and fluidviscosity and terminal velocity

  A sphere of radius r and density ρₛ is already moving with terminal speed through a liquid of density ρₗ. It falls a further vertical distance H. Assuming Stokes' law and constant terminal speed, how much heat is generated by viscous dissipation during this distance?

  Options

  • Option A

    4πr³(ρₛ-ρₗ)gH/3

  • Option B

    8πr⁵(ρₛ-ρₗ)²g²H/(27η)

  • Option C

    6πηrvₜ²H

  • Option D

    2πr²SH

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• NumericmediumProperties of solid and fluidviscosity and terminal velocity

  A flat-bottomed body is driven by a constant horizontal force of 100 N. Its contact area is 10 m² and it moves over a fixed surface with a Newtonian liquid layer of effective thickness 10 m and viscosity 2 Pa·s between them. Assume a linear velocity profile and neglect all other resistance. If its limiting speed is N m/s, find N.

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• MCQmediumProperties of solid and fluidviscosity and terminal velocity

  N identical spherical drops, each of radius r, fall through the same viscous medium with terminal speed v. They coalesce completely into one spherical drop of the same material. Assuming Stokes' law remains valid, what is the terminal speed of the new drop?

  Options

  • Option A

    v∛N

  • Option B

    v(∛N)²

  • Option C

    Nv

  • Option D

    v/N

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• NumericeasyProperties of solid and fluidviscosity and terminal velocity

  A solid sphere of radius 1 mm and density 5500 kg/m³ falls through a liquid of density 1000 kg/m³ and viscosity 1 Pa·s. Take g = 10 m/s². If its terminal speed is N cm/s, find N.

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• NumericmediumProperties of solid and fluidviscosity and terminal velocity

  A spherical ball of radius 1 cm and density 5500 kg/m³ is released from rest at a height 1.25 m above the surface of a liquid of density 1000 kg/m³. Immediately after entering the liquid, it continues with constant speed. Take g = 10 m/s² and assume Stokes' law. If the liquid viscosity is N/10 Pa·s, find N.

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• Multi-correctmediumProperties of solid and fluidviscosity and terminal velocity

  Which statements are generally correct regarding viscosity and the validity of Stokes' law?

  Select all that apply

  • Option A

    The viscosity of most liquids decreases as temperature increases.

  • Option B

    The viscosity of gases generally increases as temperature increases.

  • Option C

    Stokes' law is appropriate at very low Reynolds number.

  • Option D

    Stokes' law is not intended for strongly turbulent wake-dominated motion.

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• NumericmediumProperties of solid and fluidviscosity and terminal velocity

  A circular disc of radius 0.20 m rotates at angular speed 20 rad/s above a fixed plate. A Newtonian liquid film of thickness 1 mm and viscosity 0.50 Pa·s lies between them. If the viscous torque is Nπ N·m, find N.

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• NumericmediumProperties of solid and fluidviscosity and terminal velocity

  Sixty-four identical spherical drops fall through a viscous gas with terminal speed 5 cm/s. They coalesce into one spherical drop of the same material. Assuming Stokes' law remains valid, the new terminal speed is N cm/s. Find N.

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