This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

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- Nutrition Labels
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- Intravenous (IV) Administration
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Fluids can be given to a patient slowly, over a period of time, through a vein (*intravenous*). The rate at which these fluids flow (*flow rate*) into the patient is important and must be controlled precisely.

The **flow rate **of an infusion is the volume of fluid that enters the patient over a period of time. For example, \(25\, mL/h\) and \(15\, gtt/min\) are flow rates. The flow rate in relation to volume and time can be expressed as:

\[Flow\,Rate=\frac{Volume}{Time}\]

The formula can be arranged to solve for the time and volume.

\[Time=\frac{Volume}{Flow\,Rate}\]

\[Volume=Flow\,Rate\times Time\]

**Examples: **

**1. An order of Lactated Ringer's at 167 mL/h IV for 6 hours. How many millilitres will the patient receive in 6 hours?**

mL is a measure of volume, so we are looking for the volume given the flow rate of 167 mL/h and time of 6 hours.

\[Volume = \frac{167\,mL}{h} \times \frac{6\,h}{1} = 1002\,mL\]

The patient will receive 1002 mL of Lactated Ringer's intravenously for 6 hours.

**2. A physician orders \(\frac{1}{2}\) NS 1000 mL IV at 50 mL/h. If the IV starts at 12 pm on Monday, at what time will it finish?**

We are looking for the time given the volume of 1000 mL and the flow rate of 50 mL/h.

\begin{align}Time&=\frac{Volume}{Flow\,Rate}\\&=\frac{1000\,mL}{50\,mL/h}\\&=\frac{1000\,mL}{1}\times \frac{h}{50\,mL}\\Time&=20h\end{align}

The IV will be administered for 20 hours starting at 12 pm on Monday.

12 hours after will be 12 am on Tuesday. This leaves 8 hours which will make it 8 am on Tuesday.

**3. The prescriber ordered \(\frac{1}{4}\) NS 850 mL IV in 8 hours. The label on the box containing the IV set to use for this infusion is shown below. Calculate the flow rate in drops per minute. **

We want to find the flow rate given the volume of 850 mL, and the time of 8h.

\begin{align}Flow\,Rate&=\frac{Volume}{Time}\\&=\frac{850\,mL}{8h}\end{align}

Now, we want to calculate the drops per minute using the flow rate. We know the flow rate is equivalent to the drops per minute so we can set up the following.

\[\frac{850\,mL}{8h}=\frac{?\,gtt}{min}\]

There are a few items we need in order to convert the flow rate into drops per minute. On the label, the solution states a drop factor of 10 drops per mL, or 10 gtt/mL. We can use this to convert the flow rate.

\[\frac{850\,mL}{8h}\times\frac{10\,gtt}{1\,mL}=1062.5\frac{gtt}{h}\]

We have to convert hours into minutes knowing that 1 hour is equivalent to 60 minutes.

\[\frac{1062.5\,gtt}{h}\times\frac{1\,h}{60\,min}=17.7\frac{gtt}{min}\]

The flow rate is approximately 18 drops per minute.

The previous example calculated the drip rate in drops per minute (gtt/min). A drop factor was used in the calculation from the label. The drop factor is the number of drops required to make up 1 mL.

A macrodrip is used for flow rates of 125 mL/h or more. Macrodrips can be used for large volumes of fluid to be infused and usually have drop factors of 10, 15, or 20 gtt/mL.

A microdrip is used for flow rates of 50 mL/h or less. A drop factor related to microdrips is 60 gtt/mL.

We can use the drop factor to calculate volume and duration of IV administration.

\[\frac{Volume\,(mL)}{Time\,(min)}\times Drop\,factor\,(gtt/mL)=Drip\,rate\,(gtt/min)\]

The equation can be rearranged to solve for volume and time.

\[Volume=\frac{Drip\,rate}{Drop\,factor}\times Time\]

\[Time=Volume\times \frac{Drop\,factor}{Drip\,rate}\]

**Examples:**

1. How many millilitres will infuse in 2 hours at the rate of 30 gtt/min with a drop factor of 15 gtt/mL?

\[Volume=\frac{30\,gtt}{1\,min}\times\frac{1\,mL}{15\,gtt}\times \frac{120\,min}{2h}=240\,mL/2h\]

In two hours, 240 mL will be infused.

2. A 500 mL IV starts at 9 pm and runs at 33 gtt/min with a drop factor of 10 gtt/mL. At what time will it finish?

\[Time=500\,mL\times\frac{10\,gtt}{1\,mL}\times\frac{1\,min}{33\,gtt}=151.515152\,min\]

The IV will finish approximately 152 minutes after. To find the hours.

Two hours is 120 minutes. \(152-120\) minutes equals 31 minutes. Thus, the IV will end 2 hour 31 minutes after 9pm or 11:31 pm.

Designed by Matthew Cheung. This work is licensed under a Creative Commons Attribution 4.0 International License.

- Last Updated: Sep 22, 2023 2:04 PM
- URL: https://libraryguides.centennialcollege.ca/mathhelp
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