# Intravenous Flow Rate Calculations Question From Viewer

I received an intriguing flow rate calculation question from one of our viewers. The way the question is framed, it really highlights several important elements when it comes to understanding flow rate calculations. In this blog, I'm going to show you how to solve this question.

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This question says a hospital pharmacy receives a medication order for 500 mg of aminophylline in 250 miL normal saline solution for a 132 lb patient. The aminophylline is to be administered at a dose of 300 µg/kg/hr using an IV set that delivers 60 drops/mL. The pharmacy has 20 mL vials of injection containing aminophylline, 25 mg/mL. Calculate the following

a) The milliliters of aminophylline injection that should be added to the normal saline solution.

b) The total volume of the intravenous infusion.

c) The milligrams of aminophylline administered per hour.

d) The duration in hours for complete infusion.

e) The number of milliliters of infusion delivered per hour. So that would be the flow rate, milliliters per hour.

f) The number of drops administered per minute, and that would be flow rate in drops per minute.

Now, the question is fairly long, so to make the solution easy to follow, I'm going to first solve A through C, and then I will solve D through F.

Before we start answering the question, let's quickly summarize all the important information that we've been given in the question.

The first thing we've been given is the amount of drug that the patient is going to receive, and that's the 500 mg of aminophylline.

We've also been given the volume of the bag in which we'll be putting the drug, which is the 250 mL of normal saline.

We also have the weight of the patient, which is 132 lb.

And then we have what is known as the normalized mass rate, which is the 300 µg/kg/hr.

We've also been given the calibration or drop factor, which is the 60 drops/mL.

Then we have the volume of the vial of injection containing aminophylline, which is the 20 mL.

And then, the concentration of the aminophylline in the vial is 25mg/mL.

### IV Flow Rate Calculation Question - Part A

So now, let's go ahead and solve part A of the question. And the question actually says, calculate the milliliters of aminophylline injection that should be added to the normal saline solution.

So for part A, what we actually need is the concentration of the aminophylline in the vial of injection, which is the 25 mg/mL. And then we also need the amount of drug, amount of aminophylline that you are going to give the patient.

And so the way that breaks down is we will take the 25 mg/mL, which implies that you have 25 mg of aminophylline in every milliliter of solution and that should be equal to the amount of drug that we want to give the patient, which is the 500 mg of aminophylline. But we do not know what the volume will be. So that would be X mL.

So we can go ahead and solve for x, which is the unknown here. X equals 500 mg, times 1 mL, divided by 25 mg, and that is equal to 20 mL.

So you need to take 20 mL of solution from the vials of injection containing aminophylline, and that is what will supply the 500 mg. So from the question, it basically means that you take one whole vial of injection containing aminophylline, and then you would transfer that using an injection into the 250 mL normal saline solution.

### IV Flow Rate Calculation Question - Part B

So for B, the total volume is going to be equal to the volume of the normal saline bag, plus the volume of drug added.

So that would imply that the volume of the normal saline bag is going to be the 250 mL.

And to that we need to add the volume of the drug added, which would be the 20 mL that we just calculated in part A.

So 250 plus 20, that gives us 270 mL.

### IV Flow Rate Calculation Question - Part C

So for C, we're actually looking for the mass rate. And the way we do that is we take the normalized mass rate, which is the 300 µg/kg/h, and we multiply that by the weight of the patient because it's normalized to body weight. So that would be 132 lb.

But the units are not consistent. You have pounds in the numerator, you have kilograms in the denominator.

So we need to change the pounds to kilograms. And so we will say 2.2 lb is equivalent to 1 kg.

So now the kilograms cancel out and the pounds cancel out. So now you are left in micrograms per hour, but the question is looking for milligrams per hour.

So we need to convert the milligrams. And so we make use of the conversion factor that the 1,000 µg is equivalent to 1 mg.

The micrograms cancel out and now you are in milligrams per hour.

Now, since we are using dimensional analysis, we can go ahead and multiply everything in the numerator, which would be 300 times the 132, times 1,  times 1 mg and divide that by everything in the denominator, which would be the hours times 2.2, times 1,000. And this should be equal to 18 mg/hr.

### IV Flow Rate Calculation Question - Part D

So the next step will be to solve part D of the question. And the question says, calculate the duration in hours for complete infusion. And so for D, we are actually interested in the duration in hours, which is basically the time. And so that is going to be given by the amount of drug divided by the mass rate that we just calculated.

And so that's going to be equal to 500 mg, which is the amount of drug, divided by 18 mg/hr, which is the mass rate which we calculated in part C of the question.

So if you go ahead and do the math, this should give us 27.78, which is approximately 27.8 hours.

### IV Flow Rate Calculation Question - Part E

The next thing we can do is solve part E of the question. The question says, calculate the number of milliliters of infusion delivered per hour. Basically flow rate in milliliters per hour.

So for part E, which is the flow rate in mL/hr, that's going to be equal to the volume divided by the time.

And so that's going to be equal to the total volume which we calculated in part B, and we found out to be 270 mL. And then we divide that by the time, which we just calculated to be 27.8 hours.

And so that gives us 9.71 mL/hr.

### IV Flow Rate Calculation Question - Part F

We can now solve part F of the question. That actually says, calculate the number of drops administered per minute. We are looking for flow rate, but this time flow rate in drops per minute.

For F, we are also looking for flow rate, but this time the flow rate is in drops per minute.

We go ahead and we take the flow rate in milliliters per hour, which we calculated from part E, so that would be the 9.71 milliliters per hour, and we convert that to drops per minute. So in one hour, you have 60 min.

And so the hour cancels out. You are now in milliliters per minute.

And then we can make use of the drop factor, which says you have 60 drops in 1 mL.

So the milliliter cancels out and you are now in drops per minute.

Now, because you have 60 in the denominator and 60 in the numerator, you actually end up with the same numeric value, which is 9.71. But the units are going to be in drops per minute.

So I hope you found this tutorial useful. Thank you so much, and I will see you on the next blog.

#### Q: What is an intravenous flow rate calculation?

A: An intravenous flow rate calculation is a calculation used to determine the rate at which a medication or fluid should be administered through an IV drip.

#### Q: What is an IV drip rate?

A: An IV drip rate refers to the number of drops per minute that should be administered through an IV tubing.

#### Q: How do you calculate the IV drip rate?

A: The IV drip rate can be calculated by using the drip factor of the tubing and the desired infusion rate. The formula is: (Drip factor × Number of milliliters to be infused) ÷ Infusion time (in minutes).

#### Q: What is a drip factor?

A: A drip factor is the number of drops of solution that equal 1 milliliter. It is usually printed on the IV tubing package and can vary depending on the type of tubing.

#### Q: What is an infusion pump?

A: An infusion pump is a medical device used to deliver fluids, such as medications or nutrients, into a patient's body in a controlled manner. It can automatically regulate the flow rate and provide more accurate administration compared to manual calculations.

#### Q: What is the purpose of IV tubing?

A: IV tubing is used to connect the IV bag or container to the patient's vein, allowing for the administration of fluids or medications directly into their bloodstream.

#### Q: What is the difference between macro drip and micro drip tubing?

A: Macro drip tubing has a large drip factor (usually around 10-20 drops per milliliter), while micro drip tubing has a smaller drip factor (usually around 60 drops per milliliter). The choice of tubing depends on the required flow rate and the volume of fluid being administered.

#### Q: How do you calculate the drops per minute?

A: To calculate the drops per minute, you can divide the total volume in milliliters by the infusion time in minutes and then multiply it by the drip factor of the tubing.

#### Q: How can I increase the IV flow rate?

A: To increase the IV flow rate, you can either increase the number of drops per minute or decrease the infusion time. However, it is important to consult with a healthcare professional before making any adjustments to the IV flow rate.

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