Falling Sphere Viscometer: It consists of a long container of constant area filled with a liquid whose viscosity has to be measured. Since the viscosity depends strongly with the temperature, so this container is kept in a constant temperature bath as shown in Fig. 7.1.2.
Fig. 7.1.2: Schematic diagram of a falling sphere viscometer.
A perfectly smooth spherical ball is allowed to fall vertically through the liquid by virtue of its own weight (W). The ball will accelerate inside the liquid, until the net downward force is zero i.e. the submerged weight of the ball 
is equal to the resisting force 
given by Stokes' law . After this point, the ball will move at steady velocity which is known as terminal velocity . The equation of motion may be written as below;
 |
(7.1.3) |
where, 
are the specific weights of the liquid and the ball, respectively. If the spherical ball has the diameter D that moves at constant fall velocity V in a fluid having viscosity 
, then using Stokes' law, one can write the expression for resisting force 
.
 |
(7.1.4) |
Substituting Eq. (7.1.4) in Eq. (7.1.3) and solving for 
,
 |
(7.1.5) |
The constant fall velocity can be calculated by measuring the time 
taken by the ball to fall through a distance 
. It should be noted here that the falling sphere viscometer is applicable for the Reynolds number below 0.1 so that wall will not have any effect on the fall velocity.
Capillary Tube Viscometer : This type of viscometer is based on laminar flow through a circular pipe. It has a circular tube attached horizontally to a vessel filled with a liquid whose viscosity has to be measured. Suitable head 
is provided to the liquid so that it can flow freely through the capillary tube of certain length (L) into a collection tank as shown in Fig. 7.1.3. The flow rate 
of the liquid having specific weight wl can be measured through the volume flow rate in the tank. The Hagen-Poiseuille equation for laminar flow can be applied to calculate the viscosity 
of the liquid.
 |
(7.1.6) |
Fig. 7.1.3: Schematic diagram of a capillary tube viscometer.