The flow will be laminar if Reynold's number[tex] N_{R} [/tex] is less than 2000.
Use the Reynold's formula and rearrange to calculate velocity of water in the pipe.
[tex] N_{R} = \frac{v D}{\nu} [/tex]
Where, [tex] v [/tex] is velocity of the fluid, [tex] D [/tex] is the diameter of pipe, and [tex] \nu [/tex] is the kinematic viscosity i.e. [tex] 1.12 \times 10^{-6} m^2/s [/tex] for water at 288.7 K from Appendix.
So, velocity is:
[tex] v = \frac{N_{R} \nu}{D} [/tex]
The flow rate Q:
[tex] Q = vA=v\pi D^2/4=\frac{\frac{N_R \nu}{D} \pi D^2}{4} =[tex] t = \frac{V}{\frac{N_R \nu \pi D}{4}} = \frac{4V}{N_R \nu \pi D} =\frac{4 \times 190 L\frac{10^{-3} m^3}{L}}{2000 \times 1.12\times 10^{-6} m^2/s \pi 15.24 cm\frac{1 m}{100 cm}} = 2226.3 s \frac{1 min}{60 s}= 37.1 min [/tex] [/tex]
Where A is the area of cross section of pipe.
The time taken to fill is:
[tex] t = Q/V [/tex]
Where V is the capacity of the tank.
