0.5
Pa·s
500
cP
5
P
0.5
Pa·s
500
cP
5
P
The Viscosity Calculator determines the dynamic viscosity of a fluid from measured shear stress and velocity gradient using Newton's law of viscosity: $$\mu = \frac{\tau}{du/dy}$$ where $$\tau$$ is the shear stress in pascals, $$du/dy$$ is the velocity gradient (shear rate) in reciprocal seconds, and $$\mu$$ is the dynamic viscosity in pascal-seconds (Pa·s).
Dynamic viscosity is a fundamental fluid property that quantifies a fluid's internal resistance to flow. It plays a critical role in fluid mechanics, chemical engineering, lubrication science, and biomedical applications. Viscosity determines how fluids behave in pipes, channels, bearings, and biological systems, directly affecting pressure drops, flow rates, and energy dissipation.
Newton's law of viscosity defines the relationship between shear stress and the rate of deformation in a fluid. For a Newtonian fluid, the shear stress is linearly proportional to the velocity gradient:
$$\tau = \mu \frac{du}{dy}$$
Rearranging to solve for viscosity:
$$\mu = \frac{\tau}{du/dy}$$
Here, the velocity gradient $$du/dy$$ represents how quickly the fluid velocity changes across layers perpendicular to the flow direction. Imagine a fluid between two parallel plates — the bottom plate is stationary and the top plate moves at velocity U. The velocity gradient is $$du/dy = U/h$$ where h is the gap between the plates.
Key concepts in viscosity:
The SI unit of dynamic viscosity is the pascal-second (Pa·s). In the CGS system, the unit is the poise (P), where $$1\,\text{Pa·s} = 10\,\text{P} = 1000\,\text{cP}$$. Water at 20°C has a viscosity of approximately 1.002 cP (0.001002 Pa·s), which serves as a convenient reference point.
Viscosity is measured using viscometers and rheometers. Common instruments include capillary viscometers (measuring flow time through a tube), rotational viscometers (measuring torque at known angular velocity), and falling-ball viscometers (measuring terminal velocity of a sphere through the fluid).
The calculated dynamic viscosity tells you how resistant the fluid is to shearing motion. Compare your result with known fluids: water is about 0.001 Pa·s (1 cP), honey is roughly 2–10 Pa·s, motor oil (SAE 30) is about 0.2 Pa·s at 20°C, and glycerin is approximately 1.5 Pa·s. If your result falls outside the expected range for the fluid type, check that the shear stress and velocity gradient measurements are consistent and that the fluid is behaving in a Newtonian manner at the test conditions.
Inputs
Results
A shear stress of 0.5 Pa at a shear rate of 500 s⁻¹ gives μ = 0.001 Pa·s = 1 cP, consistent with water at 20°C.
Inputs
Results
A shear stress of 50 Pa at 200 s⁻¹ gives μ = 0.25 Pa·s = 250 cP, typical of a medium-weight lubricating oil.
Dynamic viscosity (μ) is a measure of a fluid's internal resistance to flow under shear stress. It is defined by Newton's law of viscosity: $$\mu = \frac{\tau}{du/dy}$$. A higher viscosity means the fluid resists deformation more strongly. The SI unit is Pa·s (pascal-second), and the common CGS unit is the centipoise (cP).
Dynamic viscosity (μ) measures resistance to shear flow and has units of Pa·s. Kinematic viscosity (ν) is the ratio of dynamic viscosity to density: $$\nu = \mu / \rho$$, with units of m²/s. Kinematic viscosity accounts for the fluid's inertia and is used in the Reynolds number calculation.
A Newtonian fluid has a constant viscosity regardless of the applied shear rate — the shear stress is linearly proportional to the velocity gradient. Water, air, light oils, and most gases are Newtonian. Non-Newtonian fluids (blood, paint, polymer solutions) have viscosity that varies with shear rate.
For liquids, viscosity decreases with increasing temperature because thermal energy weakens intermolecular bonds. The Arrhenius equation models this: $$\mu = A e^{E_a/(RT)}$$. For gases, viscosity increases with temperature due to greater molecular momentum transfer during collisions.
The SI unit is the pascal-second (Pa·s). The CGS unit is the poise (P), where 1 Pa·s = 10 P. Centipoise (cP) is commonly used: 1 cP = 0.001 Pa·s. Water at 20°C has a viscosity of approximately 1.002 cP, making the centipoise a convenient practical unit.
Common methods include: (1) capillary viscometers — timing fluid flow through a narrow tube using Poiseuille's law; (2) rotational viscometers — measuring torque on a spinning cylinder or cone in the fluid; (3) falling-ball viscometers — timing a sphere falling through the fluid using Stokes' law. Each method suits different viscosity ranges and fluid types.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
Density Calculator
Fluid Properties Calculators
Pressure Calculator
Fluid Properties Calculators
Hydrostatic Pressure Calculator
Fluid Properties Calculators
Buoyancy Calculator
Fluid Properties Calculators
Buoyant Force Calculator
Fluid Properties Calculators
Fluid Pressure Calculator
Fluid Properties Calculators
