Viscosity Calculator
Calculate shear force using Newton's law of viscosity τ = η·A·(dv/dy).
η (Pa·s): Water 20°C=0.001, Air 20°C=1.81e-5, Blood=0.003, Olive oil=0.084, Honey≈10, Pitch≈10⁸
What Is Viscosity Calculator?
Calculate shear force using Newton's law of viscosity τ = η·A·(dv/dy). — one of the key formulas in its field, derived from fundamental physics principles.
The relationship connects physical quantities in a measurable, predictable way. Understanding when and how it applies is as important as the calculation itself.
Real-world applications span many fields: engineering design, scientific research, industrial processes, and everyday phenomena all rely on this formula.
Always verify that inputs are in consistent SI units. The calculator converts common units automatically where indicated, but mixed units are a frequent source of errors.
Formula Reference Table
| Solve For | Formula | Notes |
|---|---|---|
| Shear stress | τ = η · (dv/dy) | Pa; τ = F/A |
| Shear force | F = η · A · (dv/dy) | N |
| Viscosity | η = F/(A·dv/dy) = τ/(dv/dy) | Pa·s |
| Kinematic viscosity | ν = η/ρ | m²/s |
| Reynolds number | Re = ρvL/η | Laminar < 2300 |
| Poiseuille flow | Q = πr⁴ΔP/(8ηL) | Laminar pipe flow |
3 Worked Examples
Plate 0.5 m², v gradient 10 s⁻¹, η=0.001 Pa·s.
- F = η×A×(dv/dy) = 0.001×0.5×10 = 0.005 N = 5 mN
Blood in tube: shear stress τ = 5 Pa at gradient 1667 s⁻¹.
- η = τ/(dv/dy) = 5/1667 = 0.003 Pa·s
- Agrees with blood η ≈ 0.003 Pa·s
Engine bearing oil film: η=0.1 Pa·s, A=0.01 m², gap=0.1 mm, shaft v=5 m/s.
- dv/dy = 5/0.0001 = 50,000 s⁻¹
- F = 0.1×0.01×50,000 = 50 N shear force in bearing
Real-World Applications
Common Mistakes to Avoid
Use SI units.
Apply correct version of formula.
Formula assumes ideal conditions.
Check positive/negative.
Check formula exponents carefully.
Frequently Asked Questions
Related Physics Calculators
Formula Explorer connections
Interpretation: This relationship connects pressure, velocity, density, viscosity, geometry or transport in a fluid system. Assumption: Check whether flow is steady, incompressible, laminar, fully developed or one-dimensional. Reynolds and Mach regimes determine whether simplified formulas are valid.