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Viscosity Calculator

Calculate dynamic and kinematic viscosity of fluids using shear stress and velocity gradient relationships

Parameters

Paⓘ
s⁻¹ⓘ
kg/m³ⓘ
°Cⓘ
Show Trail

Controls

xⓘ

Calculated Values

Dynamic Viscosity:
0.10;Pa⋅s0.10;Pa·s
Kinematic Viscosity:
0.00;m2/s0.00;m²/s
Reynolds Number:
100.00;100.00;
Viscosity Index:
2.00;2.00;

Examples

Example 1: Water at 20°C

Water flowing between parallel plates with shear stress.

  • Dynamic Viscosity: 0.100.10
  • Kinematic Viscosity: 0.000.00
  • Reynolds Number: 100.00100.00

Example 2: Oil Flow

Engine oil with higher viscosity.

  • Dynamic Viscosity: 5.005.00
  • Kinematic Viscosity: 0.010.01
  • Reynolds Number: 1.701.70

Example 3: Air Flow

Air with low viscosity at room temperature.

  • Dynamic Viscosity: 0.000.00
  • Kinematic Viscosity: 0.000.00
  • Reynolds Number: 122.50122.50

Visualization

Viscosity

Viscosity is a measure of a fluid's resistance to flow and deformation. It describes the internal friction between fluid layers moving at different velocities. Viscosity is crucial in understanding fluid behavior, from simple pipe flow to complex industrial processes.

Dynamic viscosity (μ) is defined as the ratio of shear stress (τ) to velocity gradient (du/dy): μ = τ/(du/dy). It has units of Pa·s (Pascal-seconds) or N·s/m². Dynamic viscosity measures the fluid's resistance to shear deformation.

Kinematic viscosity (ν) is the ratio of dynamic viscosity to fluid density: ν = μ/ρ. It has units of m²/s. Kinematic viscosity is often more useful in fluid dynamics as it combines the effects of viscosity and density.

Newtonian fluids have constant viscosity regardless of shear rate, while non-Newtonian fluids have viscosity that changes with shear rate. Most common fluids like water, air, and oils are approximately Newtonian at moderate conditions.

Viscosity typically decreases with increasing temperature for liquids and increases with temperature for gases. This temperature dependence is crucial for many engineering applications and is often described by empirical relationships.

Key Concepts

  • Dynamic Viscosity: μ = τ/(du/dy) [Pa·s]
  • Kinematic Viscosity: ν = μ/ρ [m²/s]
  • Shear Stress: τ = F/A [Pa]
  • Velocity Gradient: du/dy [s⁻¹]
  • Newtonian Fluid: Constant viscosity
  • Temperature Dependence: Viscosity changes with temperature

Real-World Applications

  • Pipe Flow: Pressure drop calculations
  • Lubrication: Oil viscosity selection
  • Coating: Paint and ink flow
  • Food Processing: Rheology control
  • Blood Flow: Cardiovascular analysis

Explore Further

More fluid mechanics tools

Physics Equations

Dynamic Viscosity:
μ=τdudy\mu = \frac{\tau}{\frac{du}{dy}}
Kinematic Viscosity:
ν=μρ\nu = \frac{\mu}{\rho}
Shear Stress:
τ=μdudy\tau = \mu \frac{du}{dy}
Reynolds Number:
Re=ρvLμRe = \frac{\rho v L}{\mu}
Temperature Correction (Water):
μ=μ0e−0.024(T−T0)\mu = \mu_0 e^{-0.024(T-T_0)}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Identify Parameters

First, we identify the parameters needed for viscosity calculation:

Equation:

μ=τdudy\mu = \frac{\tau}{\frac{du}{dy}}

Calculation:

τ=10 Pa,dudy=100 s−1,ρ=1000 kg/m3,T=20°C\tau = 10 \text{ Pa}, \frac{du}{dy} = 100 \text{ s}^{-1}, \rho = 1000 \text{ kg/m}^3, T = 20 \text{°C}

Explanation:

These are the shear stress, velocity gradient, fluid density, and temperature.

2

Step 2: Calculate Dynamic Viscosity

Using the definition of dynamic viscosity:

Equation:

μ=τdudy\mu = \frac{\tau}{\frac{du}{dy}}

Calculation:

μ=10100=0.1000 Pa\cdotps\mu = \frac{10}{100} = 0.1000 \text{ Pa·s}

Explanation:

Dynamic viscosity is the ratio of shear stress to velocity gradient.

3

Step 3: Calculate Kinematic Viscosity

Kinematic viscosity is dynamic viscosity divided by density:

Equation:

ν=μρ\nu = \frac{\mu}{\rho}

Calculation:

ν=0.10001000=0.000100 m2/s\nu = \frac{0.1000}{1000} = 0.000100 \text{ m}^2/\text{s}

Explanation:

Kinematic viscosity combines the effects of viscosity and density.

4

Step 4: Calculate Reynolds Number (Example)

Reynolds number indicates flow regime (example: v=1 m/s, L=0.01 m):

Equation:

Re=ρvLμRe = \frac{\rho v L}{\mu}

Calculation:

Re=1000×1×0.010.1000=100.0Re = \frac{1000 \times 1 \times 0.01}{0.1000} = 100.0

Explanation:

Assuming typical velocity v=1 m/s and length L=0.01 m for this example.

5

Step 5: Interpret Results

Analyze the calculated values:

Calculation:

Dynamic viscosity: 0.1000 Pa\cdotpsKinematic viscosity: 0.000100 m2/sReynolds number: 100.0\text{Dynamic viscosity: } 0.1000 \text{ Pa·s} \\ \text{Kinematic viscosity: } 0.000100 \text{ m}^2/\text{s} \\ \text{Reynolds number: } 100.0

Explanation:

Compare with known values: water ≈ 0.001 Pa·s, oil ≈ 0.1-1 Pa·s, air ≈ 0.000018 Pa·s at room temperature.

Frequently Asked Questions (FAQ)

What is the difference between dynamic and kinematic viscosity?

Dynamic viscosity (μ) measures resistance to shear deformation and has units Pa·s. Kinematic viscosity (ν) is μ/ρ and has units m²/s. Kinematic viscosity is often more useful in fluid dynamics.

How does temperature affect viscosity?

For liquids, viscosity typically decreases with increasing temperature. For gases, viscosity increases with temperature. This is due to changes in molecular interactions and thermal energy.

What is a Newtonian fluid?

A Newtonian fluid has constant viscosity regardless of shear rate. Most common fluids like water, air, and oils are approximately Newtonian under normal conditions.

What is the Reynolds number?

The Reynolds number (Re = ρvL/μ) indicates the relative importance of inertial to viscous forces. It determines whether flow is laminar (Re < 2300) or turbulent (Re > 4000).

How is viscosity measured?

Viscosity is measured using viscometers that apply known shear stress and measure resulting velocity gradient, or by measuring flow through capillary tubes under controlled conditions.

Practice MCQs

  1. Dynamic viscosity is defined as:
  2. Kinematic viscosity has units of:
  3. For a Newtonian fluid:
  4. As temperature increases, liquid viscosity typically:
  5. The Reynolds number indicates:

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