Question #225840

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?

Expert's answer

Since viscosity is directly proportional to elocity,

"\\mu \\ \\alpha\\ \\rho v \\\\\n\\mu = kv\\rho \\\\\n\\mu_{oil} v_{water}\\rho_{water} = \\mu_{water}v_{oil}\\rho_{oil}\\\\\n2.9\u00d710^{-2} \u00d710\u00d7 1000= 3.0\u00d710^{-4} \u00d7 v_{oil}\u00d7 1720\\\\\nv_{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"

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Black18.08.21, 00:47Thank you for this

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