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

ID: 1819186 • Letter: C

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.

1. Reynolds number of the flow in a pipe (same diameter and fluid velocity for the two fluids)

Explanation / Answer

The Reynolds Number, the non-dimensional velocity, is defined by the ratio of

and can be expressed as

Re = ( u2) / ( u / L)

    = u L /

    = 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)

= dynamic viscosity (Ns/m2, lbm/s ft)

L = characteristic length (m, ft)

= kinematic viscosity (m2/s, ft2/s)

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 /

    = u dh /           (2)

where

dh = hydraulic diameter (m, ft)

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

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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