Viscosity is the internal friction which exists between layers of the molecules of a fluid (liquid or gas) in motion. The viscosity of a fluid can also be defined as the measure of how resistive the fluid is to flow. It is a vector quantity & measured in pascal-seconds(pa.s). It can be defined mathematically as the ratio of the shearing stress to the velocity gradient in a fluid

Viscosity (ŋ) =           Force

Area x Velocity gradient  ……………………………………….1.

Velocity gradient = velocity

Length   …………………………………………………2


W = U +  V

W – U- V = 0        ……………………………………………………………3.

V = W – U (apparent or effective weight) where V-viscous force, W- weight, U- upthrust

NB : Substances with low viscosity include water, kerosene, petrol, ethanol. Those with high viscosity are glue, syrup, grease, glycerine etc


Experiment to Determine the Terminal Velocity of a Steel Ball Falling Through a Fluid

Aim: To determine the terminal velocity of a steel ball falling in through a jar of glycerin

Apparatus: steel ball, cylindrical calibrated jar, glycerine

Observation: It will be observed that the ball is accelerating in the liquid. Also the time taken for the ball to move from A-B will be different from B-C and so on. A time will be reached when the ball will be moving at a constant speed or velocity. It is that point that terminal velocity is experience.

Graph :


Conclusion: Terminal velocity is attained when W = V + U. At a point when the ball is moving at a constant speed through the glycerine.

Precaution: 1. The steel ball should be dropped gently on the liquid 2. Experiment should be done under constant temperature 3. Avoid error of measurement when taken the reading.

NB: Terminal velocity is the maximum velocity of an object when the viscous force due to motion of the object equals the apparent (effective) weight of the object in the fluid where there is no longer net force on the object.

Drag force is the force that keeps the object continuously moving after the terminal velocity has been attained.

Stokes’ Law state that at the terminal velocity, the upward frictional force (F) = 6Π ŋrV

Where F- Frictional/Drag force, ŋ- viscosity, r- radius of sphere, Vt–  Terminal velocity



  1. Derive the dimension of viscosity.
  2. Describe an experiment to determine the terminal velocity of a steel ball falling in a fluid.


Factors Affecting Viscosity

  1. Viscosity varies with material (viscosity is a property of material)
  2. The viscosity of simple liquids (a) decreases with increasing temperature (b) increases under very high pressure
  3. The viscosity of gases (a) increases with increasing temperature (b) is independent of pressure & density


Effect of Viscosity

  • Viscosity is responsible for different rate of fluid flow.
  • Viscosity affect motion of body in fluid.


Application of Viscosity

  • It is use as a lubricant.
  • The knowledge of viscous drag/drag force is applied in the design of ship & aircraft.
  • Use to estimate the enlarge size of particles.



  1. State two effects of viscosity.
  2. State two applications of viscosity.



  1. What is viscosity?
  2.  What is terminal velocity?
  3. State two(2) substances with high viscosity.
  4. State Stoke’s law.
  5. What is a viscostatic substance?



  1. Viscosity opposes motion of an object in (a) solid (b) liquid only(c) gas only (d) liquid & gas
  2. The SI unit of velocity gradient is (a) m/s (b) s-1 (c) m/s2 (d) ms
  3. Terminal velocity is attained when (a) w + v = u (b) w = v – u (c) w + u = v (d) w = v + u
  4. The following are vector quantities except (a) friction (b) viscosity (c) upthrust (d) pressure
  5. Friction and viscosity are similar but not the same. True/False



  1. Explain viscosity.
  2. Describe an experiment to determine the terminal velocity of a steel ball falling in a fluid.

NB: A liquid is said to be VISCOSTATIC if its viscosity does not change (appreciably) with change in temperature.

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