Question

Water flows in a tube that has a diameter of D= 0.1 m. Determine the Reynolds number if the average velocity is 10 diameters per second. (b) Repeat the calculations if the tube is a nanoscale tube with a dimeter of D= 100 nm.

Answer 1

a)
`Re_(D) = 111896.745`, b)
`Re_(D) = 1.119* 10^(-7)`

Step-by-step explanation:

a) The Reynolds number for the water flowing in a circular tube is:

`Re_(D) = (\rho\cdot v\cdot D)/(\mu)`

Let assume that density and dynamic viscosity at 25 °C are
`997\,(kg)/(m^(3))`
`0.891* 10^(-3)\,(kg)/(m\cdot s)`, respectively. Then:

`Re_(D)=((997\,(kg)/(m^(3)) )\cdot (1\,(m)/(s) )\cdot (0.1\,m))/(0.891* 10^(-3)\,(kg)/(m\cdot s) )`

`Re_(D) = 111896.745`

b) The result is:

`Re_(D)=((997\,(kg)/(m^(3)) )\cdot (10^(-6)\,(m)/(s) )\cdot (10^(-7)\,m))/(0.891* 10^(-3)\,(kg)/(m\cdot s) )`

`Re_(D) = 1.119* 10^(-7)`