Question

Your boss tells you that water at 68 F is flowing in a cooling tower loop at a rate of 600 gpm, in an 8-inch inside diameter pipe. Your boss asks you whether this flow is the laminar or turbulent flow regime. Calculate the Reynolds number and state whether the flow is laminar or turbulent.

Answer 1

Explanation:

The volumetric flow rate of water will be as follows.

       q = $600 gpm \times \frac{0.000063 m^{3} s^{-1}}{1 gpm}$

         = 0.0378 $m^{3}/s$

    Diameter = $8 in \times \frac{0.0254 m}{1 in}$

                   = 0.2032 m

Relation between area and diameter is as follows.

           A = $\frac{\pi}{4} \times D^{2}$

               = $\frac{3.14}{4} \times (0.2032 m)^{2}$

               = 0.785 x 0.2032 x 0.2032

               = 0.0324 $m^{2}$

Also,     q = A × V

or,         V = $\frac{q}{A}$

                = $\frac{0.0378 m^{3}/s}{0.0324 m^{2}}$

                = 1.166 m/s

As, viscosity of water = 1 cP = $10^{-3}$ Pa-s

Density of water = 1000 $kg/m^{3}$

Therefore, we will calculate Reynolds number as follows.

 Reynolds number = $\frac{D \times V \times density}{viscosity}$

                                 = $\frac{0.2032 m \times 1.166 m/s \times 1000}{10^{-3}}$  

                                = 236931.2

Hence, the flow will be turbulent in nature.

Thus, we can conclude that the Reynolds number is 236931.2 and flow is turbulent.