Data collection

The power consumption $P$ is given by $\Omega T$, where $\Omega=2 \pi N$ is the angular velocity ($s^{-1}$), $N$ is the angular velocity in RPS and $T$ is the torque. The torque is proportional to the strain measured by the strain gauge. Thus, the power can be calculated as

$$P=\Omega T=2 \pi N k \phi$$ (1)

where, $\phi$ is the electric output in $mV$, proportional to the torque $T$ through the constant $k$. The corresponding power number, $Ne$, is calculated as:

$$Ne=\frac{P}{\rho N^3 d^5}$$ (2)

where $\rho$ is the liquid density. The impeller Reynolds number is defined as

$$Re=\frac{\rho N d^3}{\mu}$$ (3)

The data acquisition system receives the gauge signals, $\phi$, from the strain gauge conditioner and the agitation speed signal, $N$, from the tachometer and calculates, on line, the values of $T$, $P$, $Ne$ and $Re$ for each experiment. The sampling frequency of the data acquisition system is $0.1~kHz$, the number of experimental points recorded was 10000 for each acquisition data, and each experimental data of power number is the average of 6 acquisition data.

Figure 2.1: Torospherical-bottom vessel used in present work.