The Difference Between Dynamic and Kinematic Viscosity
When calculating the Reynolds number, the most critical, confusing, and highly variable parameter from fluid to fluid is viscosity. Viscosity can be roughly defined as a fluid's "internal resistance to flow" or its "thickness." The viscosity of honey is much higher than that of water. When computing the Reynolds number using our Reynolds Sayısı Hesaplama tool, you might encounter two different definitions of viscosity:
- Dynamic (Absolute) Viscosity ($\mu$ - Mu): Its unit is $Pa\cdot s$ or $kg/(m\cdot s)$. It represents the fluid's net resistance to shear stress. It is located in the denominator of the classic Reynolds formula ($Re = (\rho \cdot v \cdot D) / \mu$).
- Kinematic Viscosity ($\nu$ - Nu): Its unit is $m^2/s$ or $Stoke$. It is the ratio of dynamic viscosity to the fluid's density ($\nu = \mu / \rho$). Because kinematic viscosity directly reflects the ratio of inertial forces to friction forces, it sometimes offers a more practical use in the Reynolds formula ($Re = (v \cdot D) / \nu$). If you want to use kinematic viscosity in our calculator, you can enter 1 in the density ($\rho$) field and input the kinematic viscosity value in the viscosity field.
Now, to see the effect of these properties on the Reynolds number, let's compare three different fluids—water, air, and motor oil—under the same conditions (same pipe diameter and same velocity).
Case Study: Same Pipe, Same Velocity, Three Different Fluids
Scenario: A fluid is flowing through a pipe with an internal diameter of $0.1 m$ (10 cm) at an average velocity of $2 m/s$. The ambient temperature is assumed to be $20^\circ C$.
1. Water
- Density ($\rho$): $\approx 998 \text{ kg/m}^3$
- Dynamic Viscosity ($\mu$): $\approx 0.0010 \text{ Pa}\cdot\text{s}$ (or $1 \times 10^{-3}$)
- Calculation: $Re = (998 \cdot 2 \cdot 0.1) / 0.0010 = 199,600$
- Result: Since the critical Reynolds number for internal pipe flow is 4000, water is flowing in a highly turbulent regime. Because water has low viscosity and high density, even at a small velocity, inertial forces overcome friction forces, and the flow immediately turns turbulent. Almost all flows in water networks are turbulent.
2. Air
Although air feels much lighter and "less viscous" compared to water, the situation becomes interesting when we plug it into the calculation.
- Density ($\rho$): $\approx 1.2 \text{ kg/m}^3$ (About 830 times lighter than water)
- Dynamic Viscosity ($\mu$): $\approx 0.000018 \text{ Pa}\cdot\text{s}$ (or $1.8 \times 10^{-5}$) (About 55 times less viscous than water)
- Calculation: $Re = (1.2 \cdot 2 \cdot 0.1) / 0.000018 \approx 13,333$
- Result: Since air's Reynolds number is greater than 4000, air is also in a turbulent regime. However, note that air's Reynolds number is about 15 times lower than water's! This is because the density ($\rho$) of air drops at a much more dramatic rate than its viscosity ($\mu$). In other words, the kinematic viscosity ($\nu = \mu / \rho$) of air is higher than that of water.
3. Motor Oil (SAE 30)
Oil is one of the most viscous (syrupy) liquids we encounter in daily life.
- Density ($\rho$): $\approx 890 \text{ kg/m}^3$ (Slightly lighter than water)
- Dynamic Viscosity ($\mu$): $\approx 0.29 \text{ Pa}\cdot\text{s}$ (About 290 times more viscous than water)
- Calculation: $Re = (890 \cdot 2 \cdot 0.1) / 0.29 \approx 613$
- Result: Because the Reynolds number is less than 2300, motor oil flows in a laminar regime. The immense internal friction (viscosity) of the oil prevents the formation of irregularities even at a relatively fast flow of $2 m/s$, succeeding in keeping the flow in parallel layers.
Implications for Industrial Process Designers
These three examples clearly illustrate why different design criteria are used in different industrial sectors.
- Hydraulic and Pneumatic Systems: Hydraulic systems utilizing machine oils generally operate in laminar flow due to their very high viscosity. Therefore, hydraulic circuit designers work with the simpler laminar friction coefficient formula $f = 64/Re$, rather than the complex turbulence curves of the Moody chart. However, as the oil cools in winter, its viscosity increases further, causing pressure losses to spike to incredible levels.
- HVAC and Ventilation: Due to its low density, air produces a "relatively" low (but still turbulent) Reynolds number in ducts. To ensure air flows laminarly (quietly and efficiently), ventilation duct diameters are kept very large, and flow velocities ($v$) are set low. Increasing the velocity pulls the Reynolds number deeper into turbulence, which creates vibration and noise in the ducts.
- Water Plumbing: Water inevitably flows turbulently in plumbing systems. Engineers must overcome the pressure losses caused by this turbulent flow using pumps.
To quickly see how the flow regime will be affected when the fluid in your piping or system changes, you can use our Reynolds Sayısı Hesaplama tool to test your system by merely changing the density and viscosity while keeping the same velocity and diameter values.
