Question

b) The terminal velocity of a steel sphere falling in a liquid is 0.03 m/s. The sphere is 1 mm diameter and the density of the steel is 7830 kg/m². The density of the liquid is 800 kg/m . Calculate the dynamic and kinematic viscosity of the liquid ​

Answer 1

the dynamic viscosity of the liquid = 0.1195 kg/m.s

the kinematic viscosity of the liquid = 1.49 x 10^ -4 kg/m².s

Given:

Terminal velocity v = 0.03 m/s

diameter of sphere d = 1mm

the density of the steel ρb  = 7830 kg/m³

the density of the liquid ρl = 800 kg/m³

To find:

Calculate the dynamic and kinematic viscosity of the liquid ​

Solution:

• terminal velocity: maximum velocity or speed attainable by an object as it falls through a fluid.
• S.I unit is m/s.
• the kinematic viscosity : the absolute viscosity of a liquid divided by its density at the same temperature.
• the S.I unit is m²/s.

Terminal velocity V = 1/18 (ρb - ρl)gd²/μ

where g is the gravitational acceleration.

μ is the dynamic viscosity.

0.03 = 1/18 *( [7.830 kg/m³ - 800 kg/m³]* 9.18 * (1 mm)²)/μ

μ = 1/18 * 7030 kg/m³ * 9.18 * (1 x10^-3 m)²/0.03

μ = 0.1195 kg/m³

Kinematic viscosity v = μ/ρ

v = 0.1195/800

v = 0.000149 m²/s

v = 1.49 x 10^-4 m²/s

So, the dynamic viscosity of the liquid = 0.1195 kg/m.s

So, the kinematic viscosity of the liquid = 1.49 x 10^ -4 kg/m².s

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