Question

A patient recovering from surgery is being given fluid intravenously. The fluid has a density of `1030` `kg``/``m^3` and `9.5 * 10^-4``m^3` of it flows into the patient every six hours. What is the mass flow rate in `kg``/``s`?

Answer 1

The mass flow rate is `4.5 × 10^-5 color(white)(l)"kg/s"`

Explanation:

Let's calculate the mass flow first.

We can use the density as a conversion factor to convert the volume to mass.

`"Mass" = 9.5×10^(−4) color(red)(cancel(color(black)("m"^3))) × "1030 kg"/(1 color(red)(cancel(color(black)("m"^3)))) = "0.978 kg"`

Next, convert the time to seconds.

`6 color(red)(cancel(color(black)("h"))) × (60 color(red)(cancel(color(black)("min"))))/(1color(red)(cancel(color(black)("h")))) × "60 s"/(1color(red)(cancel(color(black)("min")))) = "21 600 s"`

Finally, we can calculate the mass flow rate.

`"Mass flow rate" = "kilograms"/"seconds" = "0.978 kg"/"21 600 s" = 4.5 × 10^-5 color(white)(l)"kg/s"`