The sphere can be a small marble or steel ball. Make sure its diameter is no greater than half the diameter of the graduate cylinder so it can easily be dropped into the cylinder. A graduated cylinder is a plastic container that has graded markings on the side that allow you to measure volume. You can use a watch instead of a stopwatch, but your measurements will be more accurate with a stopwatch. The liquid must be clear enough to see the marble as it’s dropped through the liquid. Try testing many different liquids with different flow rates to see how their viscosities differ. Some common liquids you could try including water, honey, corn syrup, cooking oil, and milk.
Measure the mass by placing the sphere on a balance. Record the mass in grams (g). Determine the volume of a sphere using the formula V= (4/3) x π x r3, where V is volume, π is the constant 3. 14, and r is the radius of the sphere. You can find the radius by measuring around the center of the sphere to get its circumference and then dividing the circumference by 2π. You can also find volume by measuring the displacement of water in a graduated cylinder. Record the initial water level, place the sphere in the water, and record the new water level. Subtract the initial from the new water level. This number equals the volume of your sphere in milliliters (mL). Calculate density with the formula d=m/v{\displaystyle d=m/v}. The unit for density is g/mL.
Measure the mass of the liquid by first weighing the empty graduated cylinder. Pour your liquid into the graduated cylinder and then weigh it again. Subtract the mass of the empty cylinder from that of the cylinder with the liquid in it to obtain the mass of the liquid in grams (g). To find the volume of the liquid, simply determine the amount of liquid you poured into the graduated cylinder by using the graded markings on the side of the cylinder. Record the volume in milliliters (mL). Use the formula d=m/v{\displaystyle d=m/v} and your measurements to calculate the density of the liquid in g/mL.
Draw a mark at the top of the cylinder about 2. 5 centimeter (1 in) (1 in) from the top of the liquid. Draw a second mark about 2. 5 centimeter (1 in) (1 in) from the bottom of the graduated cylinder. Measure the distance between the top and bottom marks. Place the bottom of the ruler at the bottom mark and record the distance to the top mark.
Liquids with low viscosities are going to be more difficult to measure with this method because it will be harder to accurately start and stop the stopwatch. Repeat this step at least three times (the more times you repeat, the more accurate your measurement will be) and average the three times together. To find the average, add up the times for each trial and divide by the number of trials you performed. This works best if the ball is small enough that the flow around the ball is truly viscous and far from turbulent. The ball must also be much smaller than the container so the ball can be dropped at least 10 ball-radii from the side walls.
Using your measurements, plug them into the equation v=d/t{\displaystyle v=d/t} to find the velocity of the sphere.
For example, let’s say the density of your fluid is 1. 4 g/mL, the density of your sphere is 5 g/mL, the radius of the sphere is 0. 002 m, and the velocity of the sphere is 0. 05 m/s. Plugging into the equation: viscosity = [2(5 – 1. 4)(9. 8)(0. 002)^2]/(9 x 0. 05) = 0. 00062784 Pa s
