Question

Water is used to simulate the flow characteristics of oil in an industrial pipeline. The diameter of the test pipeline is 1/10th of that of the industrial pipeline. The viscosities of water and oil are 3.0 x10-4 and 2.9 x 10-2 N.s/m2 while their densities are 1000 and 1720 kg/m3 respectively. If the water velocity in the test pipeline is 10m/s, what is the corresponding oil velocity in the industrial pipeline? 

Answer 1

Since viscosity is directly proportional to elocity,

$\mu \ \alpha\ \rho v \\ \mu = kv\rho \\ \mu_{oil} v_{water}\rho_{water} = \mu_{water}v_{oil}\rho_{oil}\\ 2.9×10^{-2} ×10× 1000= 3.0×10^{-4} × v_{oil}× 1720\\ v_{oil} = 562.02\ m/s$

velocity is inversely proportional to area, since the flow rate is constant

$\therefore v = \dfrac{562.02}{10} = 56.2\ m/s$