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An agitated cylinder vessel is fitted with baffles and flat blade impellers. The power number for this system is given by $N_{p}=\frac{P}{\rho n^{3}D^{5}}$ where $P$ is the power consumed for the mixing, $\rho$ is the density of the fluid, $n$ is the speed of the impeller and $D$ is the diameter of impeller. The diameter of the impeller is $1/3^{th}$ the diameter f the tank and the height of liquid level is equal to the tank diameter. The impeller speed to achieve the desired degree of mixing is $4\:rpm$. In a scaled up design, the linear dimensions of the equipment are to be doubled, holding the power input per unit volume constant. Assuming the liquid to be Newtonian and $N_{p}$ to be independent of Reynolds number, what is the impeller speed (in $rpm$) to achieve the same degree of mixing in the scaled up vessel?

  1. $0.13$
  2. $1.26$
  3. $2.52$
  4. $3.82$
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