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

Jan 8, 2016

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.

$\text{Mass" = 9.5×10^(−4) color(red)(cancel(color(black)("m"^3))) × "1030 kg"/(1 color(red)(cancel(color(black)("m"^3)))) = "0.978 kg}$

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.

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