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# Math help from the Learning Centre

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.

## Intravenous Flow Rate

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.

## Calculating using the Drop Factor

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?

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

In two hours, 120 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.