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Scaling variables work when the flow is fully turbulent and exact geometric similarity is maintained. When these two conditions are true, the effect of fluid viscosity is negligible. The flow field can be made dimensionless using a characteristic length scale and a characteristic velocity scale. Once fully developed turbulence is satisfied, dimensionless velocities scale exactly with
the characteristic velocity.
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(b) Fully turbulent flow. Scaling variables work when the flow is fully turbulent and exact geometric similarity is maintained. When these two conditions are true, the effect of fluid viscosity is negligible. The flow field can be made dimensionless using a characteristic length scale and a characteristic velocity scale. Once fully developed turbulence is satisfied, dimensionless velocities scale exactly with the characteristic velocity. In a stirred tank, this velocity is the tip speed of the impeller. Figure 2-16a shows the radial velocity profile in the discharge stream of a Rushton turbine, scaled with the tip speed of the impeller. The velocity profile is measured at three different rotational speeds and in three different fluids. All of the data collapse onto one line. In Figure 2-16b, the local dissipation, ¦Å, below an Lightnin A310 impeller is scaled in the same way. Note that the last place to attain this scaling in the impeller discharge is the velocity peak at the tip of the impeller blades.
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