A dashpot resists relative motion and dissipates mechanical energy. In an ideal linear viscous model, damping force opposes velocity and has magnitude c|v|. A fluid-filled piston and restricted passage illustrate this behavior; real devices can have nonlinear force-speed characteristics.
Dashpot Interactive Calculator
Inspect a double-ended linear viscous dashpot. Enter a damping coefficient, maintained piston speed, stroke and comparison mass. The animation demonstrates two externally driven constant-speed strokes.
Equation Used
- Linear viscous behavior with a constant nonnegative coefficient.
- Constant speed over each one-way stroke; instantaneous idealized reversals.
- No spring, end-stop impact, temperature, cavitation or fluid-compressibility model.
- Force/mass is an instantaneous comparison, not a prediction of the prescribed motion.
The speed is prescribed, not solved from the mass. End reversals are idealized; their inertia is excluded. The flow arrows show direction, not a computed fluid velocity.
Fluid crosses the piston as the rod moves
The cutaway shows a fixed cylinder and a piston on a double-ended rod. As the piston moves right, fluid passes from its right-hand chamber to its left-hand chamber through the restricted passage. Both directions reverse on the return stroke. Equal rod diameters leave equal effective swept areas on the two sides.
The blue arrows show flow direction. The orange force arrow always opposes piston motion. The passage is schematic: its diameter and the fluid viscosity are not calculated from the damping coefficient.
Compare force, power and stroke energy
Use a measured or specified linear damping coefficient to compare operation at different maintained speeds. Increasing speed increases the resisting force linearly and dissipated power quadratically. A longer stroke increases energy dissipated when speed remains the same.
In the illustrated double-ended layout, equal rod diameters give equal swept volumes on both sides of the piston. Commercial dampers may instead use single-ended rods, accumulators, bypass passages or directional valves.
Linear viscous damping
For signed piston velocity v, the force exerted by the damper on the moving rod is −cv. The positive rate of energy dissipation is cv². Over a constant-speed one-way distance S, dissipated energy is c|v|S. The entered stroke is converted from millimetres to metres.
The fourth result is force magnitude divided by the entered mass. It would be the instantaneous acceleration magnitude due to this damper force alone. It is not the actual acceleration of the externally maintained constant-speed animation.
A maintained 0.08 m/s stroke
With c=250 N·s/m, force magnitude is 20 N. Dissipated power is 1.6 W. Traversing an 80 mm stroke takes 1 second at this speed and dissipates 1.6 J. For a 5 kg comparison mass, force divided by mass is 4 m/s².
A freely coasting 5 kg mass starting at 0.08 m/s contains only 0.016 J of kinetic energy. It cannot dissipate 1.6 J without added work. Maintaining the specified speed supplies that work; this is why a constant-speed stroke is different from a free stopping calculation.
Ideal model and real damper behavior
A real restriction can produce nonlinear resistance; force is not always proportional to velocity. Temperature, seals, pressure, aeration and valve behavior can affect performance. The damping coefficient alone does not determine manufacturing tolerances, service life or operating temperature.
Instantaneous direction changes in the display simplify repeated strokes. They do not represent a physically achievable acceleration profile or calculate reversal loads.
Dashpot questions
Why does the fluid arrow oppose piston travel?
The shrinking chamber pushes fluid through the piston into the expanding chamber.
Why use rods at both ends?
Equal rods keep swept volumes equal in this simplified closed-fluid illustration.
Why does changing mass not alter the animation?
The velocity is prescribed. Mass changes only the force/mass comparison.
Does a stationary piston resist a static load in this model?
No. Ideal linear viscous force is zero when velocity is zero. This is not a locking or holding mechanism.
References
Texas A&M Rotorlab, Planar Kinetics of Lumped Mass Systems, lecture 7, viscous damping and energy-dissipation models. William L. Hallauer Jr., Introduction to Linear Time-Invariant Dynamic Systems, Appendix B, mechanical work, energy and power: viscous force opposes velocity and dissipated power is cv².
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