Calculate dynamic and kinematic viscosity of water at any temperature using μ = A × 10^(B/(T - C)). Free online fluid mechanics calculator for physics and engineering with temperature-dependent viscosity calculations.
Calculate dynamic and kinematic viscosity of water based on temperature
Formulas:
μ = A × 10^(B/(T - C))
ν = μ / ρ
Where: μ = dynamic viscosity, ν = kinematic viscosity, T = temperature (K), ρ = density, A = 2.414×10⁻⁵, B = 247.8 K, C = 140 K
Copy the code below to embed this calculator on your website
Viscosity is one of the most important properties in fluid mechanics, describing a fluid's resistance to flow. For water, viscosity changes significantly with temperature, making it crucial for engineers, physicists, and scientists working with fluid systems. Our Water Viscosity Calculator makes it easy to determine both dynamic and kinematic viscosity of water at any temperature using the empirical correlation: μ = A × 10^(B/(T - C)), where A = 2.414×10⁻⁵ Pa·s, B = 247.8 K, C = 140 K, and T is temperature in Kelvin.
Understanding water viscosity is essential for designing hydraulic systems, predicting flow behavior, calculating Reynolds numbers, and optimizing engineering applications ranging from plumbing to chemical processing. As temperature increases, water viscosity decreases, which significantly affects flow characteristics in pipes, channels, and industrial processes.
Our Water Viscosity Calculator is designed for accuracy and ease of use. Follow these steps:
The calculator uses the empirical formula: μ = 2.414×10⁻⁵ × 10^(247.8/(T - 140)) for dynamic viscosity, where T is temperature in Kelvin. Kinematic viscosity is calculated as ν = μ / ρ, where ρ is the temperature-dependent density of water.
Water viscosity is calculated using empirical correlations based on experimental data:
μ = A × 10^(B/(T - C))
Where: μ = dynamic viscosity (Pa·s), A = 2.414×10⁻⁵ Pa·s, B = 247.8 K, C = 140 K, T = temperature (Kelvin)
This formula accurately predicts water viscosity over a wide temperature range, accounting for the exponential decrease in viscosity as temperature increases.
ν = μ / ρ
Where: ν = kinematic viscosity (m²/s), μ = dynamic viscosity, ρ = density (kg/m³)
Kinematic viscosity relates dynamic viscosity to fluid density, providing a measure of viscous forces relative to inertial forces in the fluid.
Temperature has a profound effect on water viscosity, with viscosity decreasing as temperature increases:
This temperature dependence is critical for understanding flow behavior, as higher temperatures lead to lower viscosity, which affects flow rates, pressure drops, and mixing characteristics.
Water viscosity calculations are essential in numerous engineering and scientific applications:
Calculate the dynamic and kinematic viscosity of water at 20°C.
T = 20°C = 293.15 K
μ = 2.414×10⁻⁵ × 10^(247.8/(293.15 - 140)) = 0.001002 Pa·s = 1.002 mPa·s
ρ ≈ 998.2 kg/m³
ν = μ / ρ = 0.001002 / 998.2 = 1.004×10⁻⁶ m²/s = 1.004 cSt
Result: Dynamic viscosity = 1.002 mPa·s, Kinematic viscosity = 1.004 cSt
Calculate the viscosity of water at 80°C for a heating system design.
T = 80°C = 353.15 K
μ = 2.414×10⁻⁵ × 10^(247.8/(353.15 - 140)) = 0.000355 Pa·s = 0.355 mPa·s
ν = 0.000355 / 971.8 = 0.365×10⁻⁶ m²/s = 0.365 cSt
Result: Viscosity is significantly lower at higher temperatures, affecting flow rates and pressure drops.
Calculate viscosity for cold water applications.
T = 5°C = 278.15 K
μ = 2.414×10⁻⁵ × 10^(247.8/(278.15 - 140)) = 0.001519 Pa·s = 1.519 mPa·s
Result: Cold water has higher viscosity, requiring more pump power for the same flow rate.
Understanding the difference between dynamic and kinematic viscosity is crucial:
For water, kinematic viscosity is typically used in flow calculations because it naturally incorporates density effects, making it more convenient for engineering applications.
While temperature is the primary factor, several other conditions affect water viscosity:
For most engineering applications, temperature is the dominant factor, and our calculator focuses on this primary dependency.
Viscosity plays a critical role in engineering design:
Water viscosity is a measure of water's resistance to flow. It matters because it affects flow rates, pressure drops, pump power requirements, heat transfer, and mixing characteristics. As temperature increases, water viscosity decreases, significantly impacting fluid system performance.
Water viscosity decreases exponentially as temperature increases. At 0°C, viscosity is about 1.792 mPa·s, while at 100°C it drops to about 0.282 mPa·s - a reduction of over 84%. This temperature dependence is crucial for designing systems that operate at different temperatures.
Dynamic viscosity (μ) measures a fluid's internal resistance to flow and is independent of density. Kinematic viscosity (ν) is dynamic viscosity divided by density (ν = μ/ρ) and accounts for both viscous and inertial effects. Dynamic viscosity is used in force calculations, while kinematic viscosity is commonly used in flow regime analysis and Reynolds number calculations.
At 20°C (68°F), water has a dynamic viscosity of approximately 1.002 mPa·s (0.001002 Pa·s) and a kinematic viscosity of about 1.004×10⁻⁶ m²/s (1.004 cSt). These values are commonly used as reference points in engineering calculations.
The formula μ = A × 10^(B/(T - C)) is accurate to within about 1-2% for temperatures between 0°C and 100°C, which covers most engineering applications. For extremely accurate calculations or temperatures outside this range, more complex correlations or experimental data may be needed.
No, this calculator is specifically designed for pure water. Other fluids have different viscosity-temperature relationships and require different formulas. For example, oils have much higher viscosities, and their temperature dependence follows different correlations.
Viscosity is a key component of the Reynolds number formula: Re = (ρ × v × D) / μ. Reynolds number determines whether flow is laminar, transitional, or turbulent. Since water viscosity changes with temperature, the same flow conditions can result in different Reynolds numbers and flow regimes at different temperatures.
Dynamic viscosity is commonly expressed in mPa·s (millipascal-seconds) or cP (centipoise), where 1 mPa·s = 1 cP. Kinematic viscosity is often given in cSt (centistokes) or m²/s. Our calculator supports multiple units for convenience in different engineering applications.
Understanding water viscosity and its temperature dependence is fundamental to fluid mechanics, hydraulic engineering, and many practical applications. Our Water Viscosity Calculator simplifies these calculations, making it easy to determine both dynamic and kinematic viscosity at any temperature.
Whether you're designing hydraulic systems, calculating Reynolds numbers, optimizing heat transfer processes, or analyzing fluid flow, accurate viscosity values are essential. Ready to explore more fluid mechanics concepts? Check out our other calculators like the Reynolds Number Calculator for flow regime analysis, the Flow Rate Calculator for flow rate calculations, or the Friction Loss Calculator for pipe flow analysis - all of which use viscosity in their calculations.
Get instant results with our optimized calculation engine
Precise calculations you can trust for any project
Works perfectly on all devices and screen sizes