Falling Ball Viscometer
- Objective
The intent of this experiment is to find the dynamic viscosity of Glycerol by following falling ball viscometer method. Multiple steel spheres will be used to fall down the liquid and the time taken to fall a specific distance will be measured.
- Background
A body falling in a liquid is subjected to gravitational, buoyancy and drag forces which results in the achievement of a terminal velocity of the fall. According to Archimedes principle, we know that buoyant force is equal to weight of the displaced liquid. Implementing these principles, we get following equations, which result in calculation of viscosity of the liquid.
∑F = 0 = W - FD - Fb
W=Weight of the body
FD= Drag Force; Fb = Buoyancy Force
FD= C ρl U2A2 (2)
C= drag coefficient; ρl = density of liquid; U= terminal velocity of sphere
A= presented are of the sphere
Here, C= 24/Re (3)
Where Re is Reynolds number = U D ρlμl (4)
D= diameter of the sphere; µl= dynamic viscosity of the liquid
Archimedes principle: - Fb = γlV (5)
γl = Specific weight of the liquid
V= Volume of the sphere
Solving for µl in Equation 4 we get
μl=γs-γlD218U
- Apparatus
Graduated cylinder- 1000ml, Scale- 1 foot, Stop watch, Thermometer, Glycerol, Steel Spheres- 20 Nos, Tweezers or Nose pliers, Vernier Calipers or micrometer, Electronic Scale, Masking Tape and Ring Stand.
- Experimental Procedure
Using vernier calipers and electronic scale, measured the size and weight of the steel spheres. The cylinder was filled with glycerol. A piece of masking tape pasted 2 inches below the surface of glycerol and another piece 12 inches lower than the first piece. The thermometer was immersed in the glycerol using ring stand. Using a tweezer, a ball was immersed 1 inch below the surface of the liquid and released. The time taken by the ball to fall to the lower tape piece was noted. Last step was repeated with the rest of the balls keeping track of the temperature as well.
- Results and Calculation
The table gives us an average value of 1.09*103 centipoise. Possible errors could be from uneven surface of graduated cylinder, any impurities in glycerol, measurement errors in size of spheres, Cylinder side wall induce a retarding effect on the terminal velocity of the sphere which can result in inaccurate calculation of viscosity of the liquid. For more accuracy, use cylinders of larger radius thus reducing possible effect of walls on terminal velocity. Also use pure glycerol for more accurate observations. Try to avoid formation of bubbles in the liquid. Glycerol is a Newtonian fluid tending to exert same force all across the liquid.
