Enter measurement data
Formula used
For a smooth sphere falling at terminal speed, weight equals buoyancy plus viscous drag.
Here, η is dynamic viscosity, r is sphere radius, v is terminal velocity, and ρ values are densities.
When selected, the optional tube estimate uses ηcorrected = ηapparent / K and K = 1 + 2.4(d/D).
How to use this calculator
- Measure a smooth sphere’s diameter and identify its density.
- Measure the fluid density at the test temperature.
- Choose direct terminal speed or measured distance and time.
- Use a stable section of travel after the sphere stops accelerating.
- Enter tube diameter only when applying the optional wall estimate.
- Calculate, then review viscosity, forces, and Reynolds number.
- Repeat several trials and compare averaged values for better confidence.
Example data
| Sphere diameter | Sphere density | Fluid density | Terminal velocity | Estimated viscosity |
|---|---|---|---|---|
| 2.00 mm | 7850 kg/m³ | 1260 kg/m³ | 0.01244 m/s | 1.20 Pa·s |
Understanding Force Balance Viscosity
Viscosity describes a fluid’s resistance to flow. Thick liquids resist motion more strongly than thin liquids. A falling sphere method estimates this resistance from measurable forces. The sphere moves downward through a liquid. Gravity pulls it down. Buoyancy pushes it upward. Fluid drag also resists the motion. At terminal speed, these forces balance. The balance reveals the liquid’s dynamic viscosity.
Why Terminal Velocity Matters
The calculation requires terminal velocity, not initial speed. A released sphere first accelerates. Its drag force increases as speed rises. Eventually, drag plus buoyancy equals the sphere’s weight. Acceleration then becomes nearly zero. The sphere travels at a constant speed. Measure distance only within this stable travel region. A long, straight section improves the timing result. Repeating the measurement reduces random timing errors.
Using Density and Sphere Size
Sphere density must exceed fluid density for downward motion. The density difference creates the net driving force. Larger spheres create greater driving force. Their radius has a squared effect on the result. Measure diameter carefully. Convert millimetres into metres before calculating. A small diameter error can noticeably change viscosity. Use a smooth, uniform sphere. Avoid damaged surfaces, trapped bubbles, and porous materials. Enter densities in kilograms per cubic metre for direct SI results.
Checking Flow Conditions
Stokes’ law works best during slow, laminar flow. The Reynolds number helps assess that condition. Very small values support the simplest drag model. Values below 0.1 are ideal. Values below 1 can still be useful with care. Higher values can require more advanced drag corrections. The sphere should remain far from tube walls. Nearby walls slow the sphere. This makes apparent viscosity too large. The optional wall adjustment provides a limited low-speed estimate. Use a wider container whenever possible.
Reading the Results
The calculator returns dynamic viscosity in pascal seconds, millipascal seconds, and centipoise. Water near room temperature is close to one millipascal second. Kinematic viscosity divides dynamic viscosity by fluid density. It is commonly shown in square metres per second and centistokes. The force values help verify the physical balance. At terminal motion, drag should match the difference between weight and buoyancy. A negative driving force indicates unsuitable density values. A warning also appears when the assumptions are weak.
Improving Measurement Quality
Keep the fluid temperature steady. Viscosity often changes sharply with temperature. Remove bubbles before testing. Place the tube vertically. Release the sphere gently without spinning it. Start timing after the sphere reaches stable speed. Measure several runs. Use the average travel time. Record the sphere diameter, densities, temperature, and tube diameter. Clean equipment prevents contamination. For high precision work, compare results with a certified reference fluid. Treat this calculator as a transparent estimation tool, not a replacement for validated laboratory procedures. Document every result with its measurement units and test date. This supports comparisons across samples, operators, and future repeat trials. For improved confidence.
Frequently asked questions
1. What does force balance mean here?
At terminal speed, the downward sphere weight equals upward buoyancy plus upward viscous drag. The zero net force means acceleration has stopped. That balance lets the drag equation be rearranged for viscosity.
2. Which viscosity does this calculator report?
The main result is dynamic viscosity in pascal seconds, millipascal seconds, and centipoise. It also reports kinematic viscosity, which is dynamic viscosity divided by fluid density.
3. Can I calculate speed from distance and time?
Yes. Select the distance and time method. Measure a stable travel distance after the sphere reaches terminal speed. The calculator divides distance by time before applying the force balance.
4. Why must I use terminal velocity?
The simple balance only applies when acceleration is nearly zero. During early motion, forces do not yet balance. Using that changing speed can produce a misleading viscosity value.
5. Why must the sphere be denser than the fluid?
This page models a falling sphere. A denser sphere has a downward net driving force. When the fluid is denser, the sphere rises and requires a different setup and interpretation.
6. What Reynolds number should I aim for?
Values below 0.1 are best for the basic Stokes model. Values below 1 may still be usable carefully. Higher values indicate inertial effects that need more advanced drag corrections.
7. When should I apply the wall correction?
Use it only when tube diameter is known and the motion is slow. It gives a limited estimate for wall effects. A wide tube is usually a better experimental solution.
8. Does temperature affect the result?
Yes. Many fluids change viscosity significantly with temperature. Measure fluid density and terminal speed at the same controlled temperature. Record that temperature with every result.
9. Why are force values shown?
Weight, buoyancy, and drag provide a physical check. At terminal motion, observed drag should equal weight minus buoyancy. These values help identify implausible entries or unit mistakes.
10. Can this test non-Newtonian fluids?
Use caution. Non-Newtonian fluids change apparent viscosity with shear conditions. This method can provide an apparent value, but it does not fully describe the fluid’s rheological behavior.
11. What causes an unrealistic result?
Common causes include timing before terminal speed, incorrect density values, diameter errors, bubbles, tube wall effects, temperature drift, or Reynolds numbers that are too high for Stokes’ law.