Reynolds Number Calculation for Cooling Tower Water Flow

To determine the flow characteristics in the cooling tower pipe, we need to calculate the Reynolds number ($Re$). The Reynolds number helps distinguish between laminar, transitional, and turbulent flow regimes. The formula is:

$ Re = \frac{\rho v D}{\mu} $

Where:

• $ \rho $ = Density of the fluid (1000 kg m$^{-3}$)
• $ v $ = Velocity of the fluid (0.1 m s$^{-1}$)
• $ D $ = Inner diameter of the pipe (0.2 m)
• $ \mu $ = Dynamic viscosity of the fluid ($8 \times 10^{-3}$ N s m$^{-2}$)

Step-by-Step Calculation

1. Substitute values: Plug the given values into the Reynolds number formula.

   $ Re = \frac{(1000 \text{ kg m}^{-3}) \times (0.1 \text{ m s}^{-1}) \times (0.2 \text{ m})}{8 \times 10^{-3} \text{ N s m}^{-2}} $

2. Calculate the numerator:

   Numerator = $ 1000 \times 0.1 \times 0.2 = 20 $ kg m s$^{-1}$

3. Calculate the Reynolds number:

   $ Re = \frac{20}{8 \times 10^{-3}} = \frac{20}{0.008} $

   $ Re = 2500 $

Flow Regime Determination

The calculated Reynolds number is $ Re = 2500 $. We compare this value to the standard ranges for flow regimes:

• Laminar flow: $ Re < 2300 $
• Transitional flow: $ 2300 < Re < 4000 $
• Turbulent flow: $ Re > 4000 $

Since $ Re = 2500 $ falls between 2300 and 4000, the flow is characterized as critical/transitional flow.