Question

Water at 288.7 k flows through a 15.24-cm. diameter horizontal pipe into a 190-l drum. determine the minimum time it will take to fill the drum if the flow remains laminar.

Answer 1

The flow will be laminar if Reynold's number$N_{R}$ is less than 2000.

Use the Reynold's formula and rearrange to calculate velocity of water in the pipe.

$N_{R} = \frac{v D}{\nu}$

Where, $v$ is velocity of the fluid, $D$ is the diameter of pipe, and $\nu$ is the kinematic viscosity i.e. $1.12 \times 10^{-6} m^2/s$ for water at 288.7 K from Appendix.

So, velocity is:

$v = \frac{N_{R} \nu}{D}$

The flow rate Q:

$Q = vA=v\pi D^2/4=\frac{\frac{N_R \nu}{D} \pi D^2}{4} =[tex] t = \frac{V}{\frac{N_R \nu \pi D}{4}} = \frac{4V}{N_R \nu \pi D} =\frac{4 \times 190 L\frac{10^{-3} m^3}{L}}{2000 \times 1.12\times 10^{-6} m^2/s \pi 15.24 cm\frac{1 m}{100 cm}} = 2226.3 s \frac{1 min}{60 s}= 37.1 min$ [/tex]

Where A is the area of cross section of pipe.

The time taken to fill is:

$t = Q/V$

Where V is the capacity of the tank.