The diameters of a large and a small vessel are $1.62$ m and $16.2$ cm. ,respectively. The vessels are geometrically similar and operated under similar volumetric agitated power input. The mixing time in the small vessel was found to be $15$ s. Determine the mixing tune (in seconds) in the large vessel.

1. $15$
2. $30$
3. $61$
4. $122$