I have been toying around with the idea of a hydraulic KERS-system, probably way too heavy and clumsy for F1, but anyway.
When hydraulic power is pressure times flow, a 40 MPa (400 Bar or 6000 psi) system would require a flow of 1.5 liters per second to achieve the 60 kW, which means 10 liters for those 6.6 seconds.
This could be built very simple around water-hydraulics for minimum losses, with a pump/motor unit and an accumulator.
However, as pressure falls from 40 MPa to zero when empty the accumulator, twice the flow is needed for 400 kJ, or 20 liters.