Stoke's law & Terminal Velocity

1. STOKES’ LAW & TERMINAL VELOCITY
ENGR. MD. SHAMIM AHMED
LECTURER
DEPT. OF CIVIL ENGINEERING
SOUTHERN UNIVERSITY BANGLADESH

2. STOKES’ LAW
The force that retards a sphere moving through a viscous fluid is directly proportional to
the velocity of the sphere, the radius of the sphere, and the viscosity of the fluid.
• FD is the drag force on the sphere falling through the fluid in newtons (N)
• η is the viscosity of the fluid in kilograms-per-meter-per-second (kg/m/s)
• r is the radius of the sphere in meters (m)
• vT is the terminal velocity of the sphere in meters-per-second (m/s)
This equation holds at low velocities, laminar flow which are free from turbulence.

3. Terminal velocity
Terminal velocity is maximum constant velocity a acquired by
the body which is falling freely in a viscous medium.
When a small spherical body falls freely through viscous medium
then 3 forces acts on it:-
1) Weight of body acting vertically downwards, FG
2) Up thrust due to buoyancy = weight of liquid displaced, FB
3) Viscous drag (FD) acting in the direction opposite to the
motion of body.

4. Terminal velocity …
As the body falls through a medium, its velocity goes on
increasing due to ‘gravity. Therefore, the opposing viscous
drag which acts upwards also goes on increasing. A stage
reaches when the true weight of the body is just equal to the
sum of the upward thrust due to buoyancy and the upward
viscous drag. At this stage, there is no net force to
accelerate the body. Hence it starts falling with a constant
velocity, which is called terminal velocity.

5. Terminal velocity …
Let p = Density of material, r = Radius of spherical body, po = Density of Medium. Therefore,
True weight of the body = w = volume x density x g
Therefore, terminal velocity varies directly as
the square of the radius of the body and
inversely as the coefficient of viscosity of the
medium. It also depends upon densities of the
body and the medium.

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