Question

A fluid flows in a smooth pipe with a Reynolds number of 6000. By what percent would the head loss be reduced if the flow could be maintained as laminar flow rather than the expected turbulent flow

Answer 1

Explanation:

It is given that Reynolds number is 6000 (turbulent flow). Formula to calculate friction factor for turbulent flow is as follows.

          $F_{turbulent} = \frac{0.316}{(RC)^{\frac{1}{4}}}$

                     = $\frac{0.316}{(6000)^{\frac{1}{4}}}$

                     = 0.03590453

Similarly, for laminar flow:

                  $F_{laminar} = \frac{64}{RC} = \frac{64}{6000}$

                                 = 0.0107

Now, formula to calculate the head loss is as follows.

              Head loss = $\frac{Flv^{2}}{2gd}$

It is known that head loss is proportional to F.

Hence,

   $\frac{Head loss_{laminar}}{Head loss_{turbulent}} = \frac{F_{lam}}{F_{tur}}$

                = $\frac{0.0107}{0.03590}$

                =  0.2980

So,   $\frac{h_{L_{turb}} - h_{L_{lam}}}{h_{L}} = 1 - \frac{h_{l_{lam}}}{h_{L_{turb}}}$

                      = 1 - 0.2980

                      = 0.702

                      = 70.2%

Therefore, head loss can be reduced by 70.2%.