Terminal Velocity in Fluids
Aims of the Experiment
The terminal velocity of a ball bearing in a viscous fluid can be determined experimentally using a cylinder filled with a viscous liquid. The aim of this experiment is to calculate the terminal velocity of the mass as it falls through a viscous fluid.
Variables
- Independent variable = Distance between markers (m)
- Dependent variable = Time to travel between markers (s)
- Control variables
- Use the same viscous fluid
- Use the same ball bearing
Equipment List
- Resolution of measuring equipment:
- Metre ruler = 1 mm
- Stopwatch = 0.01 s
Method
Experimental set up for investigating terminal velocity in a fluid
- Set up the equipment as shown in the diagram
- Wrap elastic bands, or draw marks using a marker pen, around the tube of viscous liquid at set intervals measured by the ruler
- Hold a ball bearing directly above the surface of the liquid, and then release it from rest
- Record the time it reaches each elastic band or marker line by using the lap feature on the stopwatch
- Calculate the time taken to travel between consecutive bands and calculate the average speed at each time
- Repeat the procedure several times over a wide range of readings
- An example table might look like this:
Analysis of Results
- When the ball bearing reaches terminal velocity, the distance it has travelled between each time interval will be the same, and so its velocity can be determined
- Use the equation speed = distance / time to find the average velocity of the ball bearing between each set of bands or markers
- Plot a graph of velocity against time and draw a line of best fit
- The maximum velocity is where the graph plateaus and has zero gradient
- This is the terminal velocity
- An example graph of results might look like this:
Evaluating the Experiment
Systematic Errors:
- Use a more viscous fluid to slow the ball more
- Using a denser fluid makes the object fall slower and therefore makes determining speeds easier
- Use a tube that is as tall as possible
- This allows the ball bearing to travel at its terminal velocity for longer
- Use larger intervals for the bands
- This reduces the percentage uncertainty in both the distance and time between the bands
Random Errors:
- Repeat at least four times to reduce the effect of random errors
- Instead of using a stopwatch, attach the ball to some ticker tape
- This punches holes at a set time interval so the distance between the dots can be used to find the velocities