# The Relationship Between Reynolds Number and Kinematic Viscosity

### Key Takeaways

• Reynolds number is a dimensionless measurement that describes the degree of laminar or turbulent fluid flow.

• Fluid viscosity can be measured as absolute or dynamic viscosity and kinematic viscosity.

•  As the kinematic viscosity increases, the Reynolds number decreases and vice versa. The range of Reynolds numbers indicate the degree of laminar or turbulent flow

In systems influenced by fluid flow, it is important to analyze the fluid dynamics in order to quantify their effect. The flow behavior of such systems can be analyzed using computational fluid dynamics (CFD) simulations. With these simulations, a clear understanding of the flow regime as well as its paths and velocities can be obtained.

To identify the flow type, engineers depend on a dimensionless quantity called the Reynolds number. The range of Reynolds numbers indicate the degree of laminar or turbulent flow. Reynolds number is dependent on several fluid properties such as density, velocity, and viscosity, and this number shares an inversely proportional relationship with the kinematic and dynamic viscosity. In this article, we will explore the relationship between the Reynolds number and the kinematic viscosity.

## What Is Reynolds Number?

Generally, the Reynolds number is a dimensionless measurement that describes the degree of laminar or turbulent fluid flow. Fluid can be gas or liquid, and the value of the Reynolds number determines whether the flow is laminar or turbulent. When the Reynolds number is between 2300 and 4000, the fluid flow is transitional. As the Reynolds number increases above 4000, the fluid flow becomes turbulent. Reynolds numbers with a value of less than 2300 indicate a laminar flow of the fluid.

Reynolds number is the ratio of inertial forces to viscous forces, and this number categorizes fluid systems. It can also be interpreted as the ratio of dynamic pressure to shearing stress. It reveals the effect of fluid viscosity in controlling the flow pattern or velocity of the fluid. Mathematically, the Reynolds number can be given by the following equation: Note that is the density of the fluid, is the velocity of the fluid, l is the characteristic length or hydraulic diameter of the fluid flow, is the dynamic or absolute viscosity of the fluid, and v is the kinematic viscosity of the fluid.

## Reynolds Number and the Viscosity of a Fluid

In fluid dependent systems, viscosity influences the fluid behavior and fluid motion. When a fluid is in motion, it experiences a resistance called shear resistance due to the inter-molecular friction between the layers of the fluid. Viscosity is the fluid’s resistance to flow, and expresses the measure of a fluid’s resistance to the slow deformation caused by shear or tensile stress.

Fluid viscosity can be measured as:

1. Absolute or dynamic viscosity - The absolute or dynamic viscosity measures the tangential force per unit area required to slide one horizontal layer with respect to another layer that is spaced at a unit distance in the fluid at a unit velocity. It is an indicator of a fluid’s internal resistance to flow.

2. Kinematic viscosity - The ratio of absolute or dynamic viscosity to density is called kinematic viscosity. The SI unit of kinematic viscosity is m2/s. Commonly used units of kinematic viscosity are  ft2/s and Stoke (St). In the above equation, it is shown that both absolute or dynamic viscosity and kinematic viscosity are involved in the calculation of the Reynolds number. When the density and absolute or dynamic viscosity is known, the first equation on the right hand side of the above equation can be used. When the kinematic viscosity value is known, the Reynolds number can be calculated using the equation in the middle.

There is a strong relationship between Reynolds number and kinematic viscosity, which we will examine next.

## Reynolds Number and Kinematic Viscosity

The kinematic viscosity is the normalized dynamic viscosity to density. It describes the momentum the fluid in motion can transfer per volume. Reynolds number is negatively influenced by kinematic viscosity. As the kinematic viscosity increases, the Reynolds number decreases and vice versa.

The higher the kinematic viscosity, the more efficient the fluid becomes at transporting momentum. The increase in momentum transport or momentum diffusion in fluids accounts for more laminar flow regimes. Highly viscous fluids and low-density liquids are good examples of high momentum diffusion with low Reynolds number values. Turbulent flow occurs at a relatively high value of Reynolds number, which means the kinematic viscosity of the turbulent fluid flow is less, and such fluids transport low momentum.

### Using the Navier-Stokes Equation to Solve Fluid Flow Problems

To resolve fluid flow problems, the Navier-Stokes equation can be utilized. However, the partial differential Navier-Stokes equations are usually scaled to form non-dimensionalized equations based on the Reynolds number. From the known values of fluid velocity, density, and viscosity, the Reynolds number of the fluid of interest can be calculated.

Understanding the relationship between Reynolds number and kinematic viscosity is critical, especially when solving complex fluid flow problems. You can characterize the flow regime in fluid problems using Cadence’s suite of CFD software. With these tools, it is easier to run CFD simulations in complex fluid-dependent systems that facilitate fluid flow modeling.