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#?

Question

Naomi Aronson · Accepted Answer

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

First, let's compute the mass flow.

To convert the volume to mass, we can apply the density as a conversion factor.

#"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"#

Afterwards, change 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"#

We can now compute the mass flow rate.

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

Peyton Adams · Answer

undefined To calculate the mass flow rate, use the formula:

$$ \text{Mass flow rate} = \text{Density} \times \text{Volume flow rate} $$

Given:
Density ($ \rho $) = 1030 kg/m³
Volume flow rate ($ \dot{V} $) = 9.5 * 10^-4 m³ every six hours

Substitute the given values into the formula and convert the time to seconds:

$$ \text{Volume flow rate} = \frac{9.5 \times 10^{-4} \, \text{m}^3}{6 \times 60 \times 60 \, \text{s}} $$

$$ \text{Mass flow rate} = 1030 \, \text{kg/m}^3 \times \left( \frac{9.5 \times 10^{-4}}{6 \times 60 \times 60} \right) \, \text{m}^3/\text{s} $$

Calculate the mass flow rate.