The Time it Takes to Fill

Classical Mechanics Level 2

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.

The answer is 3000.

2 solutions

Lukas Leibfried
Aug 22, 2015

We know that $\dot { m } =\rho \cdot Q$ , so we must transform this equation to find $\rho$ . By doing this, we get the equivalent equation $\rho =\frac { \dot { m } }{ Q }$ . Substituting in $30\frac { {m}^{3} }{ s }$ for $\dot{m}$ and $1000\frac { kg }{ {m}^{3} }$ for $\rho$ , we must perform the following calculation: $Q=\frac { 10 { kg }/{ s } }{ 1000 kg/{ m }^{ 3 } }$ $Q=0.01\frac { { m }^{ 3 } }{ s }$ Now, we must find the time it takes for the container to be filled. We must divide the target volume by the volume flow rate to do this. $\frac { 30{ m }^{ 3 } }{ 0.01{ m }^{ 3 }/s } =3000\quad s$ The answer, therefore, is 3000 seconds.

Jecko Augustine
May 17, 2015

Ans=3000 sec since m=p.Q, Q=.01 cubic meter per sec. so,tot sec=30/.01 =3000 sec.

The Time it Takes to Fill

The answer is 3000.

2 solutions

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