The Time it Takes to Fill

Water is being continually poured into a container with a volume of 30 cubic meters at a constant rate. We measured the mass flow rate at 10 kilograms per second. How many seconds will it take for the water to fill up the container from when it began?

Details and Assumptions:

The mass flow rate, for this purpose, is given by this formula:

\(\dot { m } =\rho \cdot Q\)

where \(\dot { m }\) is the mass flow rate (in \(\text{kg/s}\)), \(\rho\) is density, and \(Q\) is the volume flow rate (in \({ \text{m} }^{ 3 }\text{/s}\)).

Take the density of water to be 1000 kilograms per cubic meter.

Write your answer without a measurement symbol.


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