Analyze falling objects across fluids with practical inputs. Compare drag, buoyancy, and stability in seconds. See terminal trends clearly with fast results and visuals.
The graph compares drag force with the net downward force. Terminal speed appears where both become equal.
| Case | Model | Key Inputs | Terminal Speed (m/s) | Terminal Speed (km/h) |
|---|---|---|---|---|
| Baseball in air | Quadratic | m=0.35, A=0.018, Cd=0.47, ρ=1.225 | 25.726 | 92.6135 |
| Skydiver spread posture | Quadratic | m=80, A=0.70, Cd=1.10, ρ=1.225 | 40.7688 | 146.7678 |
| Small grain in water | Stokes | r=0.0015, ρp=2650, ρf=1000, μ=0.001 | 8.0933 | 29.1357 |
Terminal speed:
vt = √[2(mg − ρfVg) / (ρfCdA)]
Use this when drag grows with velocity squared. It suits larger objects and faster motion through air.
Terminal speed:
vt = 2r²g(ρp − ρf) / 9μ
Use this for small particles in laminar flow, where viscous drag changes linearly with velocity.
Symbol guide: m = mass, A = projected area, Cd = drag coefficient, ρ = density, V = object volume, r = particle radius, μ = dynamic viscosity.
Physics meaning: terminal speed occurs when downward effective weight equals upward drag force, so acceleration becomes zero.
Terminal speed is the constant speed reached during a fall when drag and buoyancy fully balance the object’s effective weight. Acceleration then becomes zero, so the speed stops increasing.
Different flow regimes need different drag laws. Larger or faster objects often follow quadratic drag. Very small particles moving slowly through viscous fluids often follow Stokes flow.
Use the quadratic model for balls, people, droplets, and other objects moving fast enough that inertial drag dominates. It is common for air resistance problems and many engineering estimates.
Use the Stokes model for small particles in slow, smooth, laminar flow. It is especially useful in liquids, sedimentation studies, and particle settling estimates with low Reynolds numbers.
Fluid density affects both drag and buoyancy. A denser fluid pushes upward more strongly and also increases resistance. That usually lowers terminal speed compared with the same object falling in a lighter fluid.
The drag coefficient summarizes how shape, orientation, and surface behavior influence resistance. Streamlined objects have lower values, while bluff shapes usually have higher values.
Yes. Enter the correct fluid density and viscosity for air, water, oil, or another fluid. Then choose the model that best matches the expected flow regime.
Invalid results usually come from negative inputs, zero areas, zero viscosity, or a density combination that makes the object effectively float instead of settle downward.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.