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

Step-by-step 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)^{(1)/(4)}}`

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

= 0.03590453

Similarly, for laminar flow:

`F_(laminar) = (64)/(RC) = (64)/(6000)`

= 0.0107

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

Head loss =
`(Flv^(2))/(2gd)`

It is known that head loss is proportional to F.

Hence,

`(Head loss_(laminar))/(Head loss_(turbulent)) = (F_(lam))/(F_(tur))`

=
`(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%.