Chemicals Inc claims to have invented a new fluid called PDR, that has all of th

Question

Chemicals Inc claims to have invented a new fluid called PDR, that has all of the same properties as water except that its dynamic viscosity (µ) is half that of water. In particular, the density (?) of water and PDR are the same. State wheter each of the following would increase decrease or remain the same, and if there is a change, would the change be a factor of more than, less than, or exactly a factor of 2.

Drag force on a sphere at very low Re ( same sphere diameter and same velocity for the two fluids)

Explanation / Answer

The Reynolds Number, the non-dimensional velocity, is defined by the ratio of dynamic pressure (? u2) and shearing stress (µ u / L) and can be expressed as Re = (? u2) / (µ u / L) = ? u L / µ = u L / ? (1) where Re = Reynolds Number (non-dimensional) ? = density (kg/m3, lbm/ft3 ) u = velocity based on the actual cross section area of the duct or pipe (m/s, ft/s) µ = dynamic viscosity (Ns/m2, lbm/s ft) L = characteristic length (m, ft) ? = kinematic viscosity (m2/s, ft2/s) Reynolds Number for a Pipe or Duct For a pipe or duct the characteristic length is the hydraulic diameter. The Reynolds Number for a duct or pipe can be expressed as Re = ? u dh / µ = u dh / ? (2) where dh = hydraulic diameter (m, ft) Reynolds Number for a Pipe or Duct in common Imperial Units The Reynolds number for a pipe or duct can also be expressed in common Imperial units like Re = 7745.8 u dh / ? (2a) where Re = Reynolds Number (non dimensional) u = velocity (ft/s) dh = hydraulic diameter (in) ? = kinematic viscosity (cSt) (1 cSt = 10-6 m2/s ) The Reynolds Number can be used to determine if flow is laminar, transient or turbulent. The flow is laminar when Re < 2300 transient when 2300 4000 Example - Calculating Reynolds Number A Newtonian fluid with a dynamic or absolute viscosity of 0.38 Ns/m2 and a specific gravity of 0.91 flows through a 25 mm diameter pipe with a velocity of 2.6 m/s. The density can be calculated using the specific gravity like ? = 0.91 (1000 kg/m3) = 910 kg/m3 The Reynolds Number can then be calculated using equation (1) like Re = (910 kg/m3) (2.6 m/s) (25 mm) (10-3 m/mm) / (0.38 Ns/m2) = 156 (kg m / s2)/N = 156 ~ Laminar flow (1 N = 1 kg m / s2)

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