Quick answer For a Newtonian fluid, the shear stress is τ=μ·γ̇ (μ = viscosity). For non-Newtonian fluids, τ=K·γ̇ⁿ (n<1 is shear-thinning/pseudoplastic, n>1 is dilatant). The Reynolds number Re=ρUL/μ=UL/ν distinguishes laminar from turbulent flow.
Calculate viscosity, shear stress, and Reynolds number for Newtonian and non-Newtonian fluids (power-law) in real time. Compare temperature dependence and fluid types on interactive graphs.
Fluid Selection
Dynamic Viscosity μ1.00 mPa·s
Density ρ
kg/m³
Flow Velocity U
m/s
Characteristic Length L
m
Power-Law Exponent n
While paused, move the sliders to update the result instantly.
Couette Flow: See the Shear & Velocity Gradient
Shear stress τ
1.00
Pa
Shear rate du/dy
1000
1/s
Dynamic viscosity μ
1.00e-3
Pa·s
Kinematic viscosity ν
1.00e-6
m²/s
τ = μ·(du/dy). In Couette flow the velocity profile is linear (du/dy = U/h). Higher viscosity, a faster plate, or a narrower gap all require more force (shear stress) to move the plate.
Ketchup often does not flow at first, but then suddenly runs after you tap or shake the bottle. Is that also a non-Newtonian fluid?
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Yes. Ketchup is a shear-thinning, or pseudoplastic, fluid: its apparent viscosity drops as shear rate increases. In a power-law model, that corresponds to n<1. Honey is close to a Newtonian fluid, so its viscosity stays nearly constant regardless of shear rate.
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When solving the Navier-Stokes equations in CAE, water is convenient because μ is constant. Are non-Newtonian fluids like blood much harder?
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Yes. If viscosity is constant, as in water, standard CFD can treat it as a steady incompressible Newtonian fluid. Blood often uses a Carreau-Yasuda model at low shear rates and approaches roughly 3.5 mPa·s at high shear rates. Non-Newtonian viscosity models like this are available in OpenFOAM, Fluent, and similar solvers.
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I learned that flow becomes turbulent when the Reynolds number exceeds 2300. What does that actually mean?
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Re=ρUL/μ is the ratio of inertial forces to viscous forces. A larger Re means inertia overwhelms viscous damping and the flow becomes unstable. In pipe flow, Re<2300 is usually laminar, 2300 to 4000 is transitional, and Re>4000 is turbulent. Turbulence improves heat transfer and mixing, but greatly increases flow resistance.
Frequently Asked Questions
Q. What is 1 centipoise (cP)?
A. cP (centipoise) is an older unit of viscosity, where 1 cP = 1 mPa·s = 0.001 Pa·s. Since water at 20°C is about 1 cP, it can be used intuitively as a relative value to water. Engine oil ranges from tens to hundreds of cP, while honey ranges from 2,000 to 10,000 cP.
Q. What types of viscometers are available?
A. Capillary viscometers (Ubbelohde type), falling-ball viscometers, rotational viscometers (Brookfield, etc.), and vibrational viscometers. Rotational viscometers (rheometers) are used to measure flow curves of non-Newtonian fluids. For CAE material data, rotational rheometer measurements over a range of shear rates are standard.
Q. Why is viscosity important in injection molding and extrusion?
A. Polymer melts are pseudoplastic fluids. Calculating flow velocity distribution and pressure drop in molds and extrusion dies requires temperature- and shear-rate-dependent viscosity models (e.g., Cross-WLF). In CAE filling analysis (Moldflow, Cadmould, etc.), this viscosity data is the most critical material property.
Q. What is the relationship between y+ and viscosity?
A. y+ = ρu_τy/μ (u_τ: friction velocity, y: distance from wall) is the dimensionless distance of near-wall mesh. It is used for turbulent wall function applicability (y+ > 30) and LES/DNS (y+ ≈ 1). Higher viscosity μ reduces y+ for the same mesh, making it easier to resolve the viscous sublayer for high-viscosity fluids.
What is Fluid Viscosity?
Fluid Viscosity is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
Physical Model & Key Equations
The simulator is based on the governing equations behind Fluid Viscosity & Non-Newtonian Flow Calculator. Understanding these equations is key to interpreting the results correctly.
Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.
Real-World Applications
Engineering Design: The concepts behind Fluid Viscosity & Non-Newtonian Flow Calculator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.
Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.
CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.
Common Misconceptions and Points of Caution
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.
Set dynamic viscosity (μ) using the mu-slider over a logarithmic range of 10⁻³–10³ Pa·s; water is about 0.001 Pa·s and oils 0.1–1 Pa·s at 20°C
Input fluid density (ρ) via rho-slider; use 1000 kg/m³ for water, 850 kg/m³ for mineral oil
Adjust flow velocity (u) with u-slider in m/s; typical pipe flow ranges 0.5–3 m/s
Select fluid model (Newtonian or power-law) to compute shear stress τ = μ(du/dy) and Reynolds number Re = ρud/μ
Read output Reynolds number to classify laminar (Re < 2300) or turbulent (Re > 4000) pipe flow regimes
Worked Example
SAE 10W-40 motor oil at 40°C: μ = 0.095 Pa·s, ρ = 870 kg/m³, flowing through 25 mm diameter pipe at u = 1.5 m/s. Wall shear rate (laminar pipe flow): γ̇ = 8u/D = 8×1.5/0.025 = 480 s⁻¹. Shear stress τ = 0.095 × 480 ≈ 45.6 Pa. Reynolds number Re = (870 × 1.5 × 0.025) / 0.095 = 343, confirming laminar flow. For non-Newtonian pseudoplastic (power index n = 0.8), apparent viscosity decreases with shear rate, reducing the effective wall shear stress below this Newtonian value.
Practical Notes
Temperature dramatically affects viscosity: SAE 10W-40 oil varies 10× between −10°C (800 cP) and 100°C (60 cP); recalibrate slider for seasonal changes in hydraulic systems
Non-Newtonian fluids (polymer solutions, ketchup, blood) show shear-thinning behavior; use power-law model with n < 1 for accurate pump sizing and pressure drop predictions
High Reynolds number transitions (> 10,000) in turbulent regime increase friction losses by 60–80%; critical for cooling loop design in automotive and aerospace applications
🎬 Watch it in motion
Pipe Flow | a parabolic profile, and radius rules everything #Shorts
