For today’s blog, I'm going to show you how to solve five different TPN calculations questions.

Related link: Milliequivalents Calculations

Related link: Pharmaceutical Calculations: 3 Reasons Why Students Get Questions Wrong

### IV Flow Rate Calculations - How to Solve 8 Important Examples

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### Calculation Practice Question #1

This question says, if the infusion rate for an IV is eight milliliters per hour and it is run for four and a half hours, how many milliliters has the patient received?

So to find the volume, what we need is the flow rate and the time component.

From the question, the flow rate is given as 80 mL/hr, and the time is given as four and a half hours. So we can multiply this by four and a half, which will be 4.5 hours.

The hours cancel out and you end up with 360 mL.

### Calculation Practice Question #2

This question says, a sterile solution request form is received for a large volume parenteral. The infusion rate is 125 mL/hr. 1 L bags are requested for the next 24 hours. How many bags do you make?

So here, the strategy will be to first determine the total volume that the patient would receive within the 24 hours. And then once we've determined that volume, we will use the volume of each bag to determine the number of bags that needs to be made.

So to determine the volume, we need the flow rate and we need the time.

The flow rate is given us 125 mL/hr and the time is 24 hours.

So the hours can cancel out and the volume is 3,000 mL.

So now that we know the volume, we can start off with the 3,000 mL. And from the question, each bag has a liter of sterile solution.

Now, the units need to be consistent, so we need to convert the liters to milliliters. And the conversion factor is such that one liter contains 1,000 mL.

And so the milliliters cancel out, the litters cancel out, and you end up with 3,000 times 1 bag, times 1, divided by 1 times 1,000.

So you multiply everything in the numerator, divide by everything in the denominator, and this ends up giving you 3 bags.

### Calculation Practice Question #3

This question says, how many drops per minute will a patient receive if an IV of 1,000 mL of 5% dextrose injection is run over eight hours? The drip factor is 15 drops/mL.

So here, the strategy would be to first find the flow rate in mL/hr, convert the hours to minutes, and multiply that result by the drip factor, also known as the calibration factor.

So let's see how that works. To find the flow rate, we need the volume component. So the volume in the question is given us 1,000 mL. So we start off with the 1,000 mL. We need to divide this by the number of hours that the dextrose injection is run over, and that's eight hours. So 1,000 mL divided by eight hours.

We need to convert the hours to minutes. So we use the conversion factor, 1 hour is 60 minutes.

So now the hours cancel out and then we multiply all of this by the drip factor. So that would be times 15 drops/mL.

So we are using dimensional analysis. So the units in the denominator cancel out the units in the numerator. So the milliliters will cancel out. And now we need to multiply everything in the numerator and divide it by what is in the denominator. So we have 1,000 times 1, times 15 drops, divided by 8, times 60 minutes.

So the units are now drops per minute. And if we multiply everything at the top and divide by everything in the denominator, we end up with 31.25 drops/min.

### Calculation Practice Question #4

Let's take a look at another question. This question says you have a 500 mL bottle of an 8% drug. The rate of infusion is 5 g/hr.

a) What is the rate of infusion in mL/hr?

b) How long would the bottle last?

A.

Let's start off with the solution to part A of the question. And the way we would approach this is to make use of the rate of infusion, which is a mass rate. So we start off with the 5 g/hr. And now we need a conversion factor to get us to mL/hr. And that information comes from the percentage strength.

So we have an 8% drug solution. And the 8% implies that you have eight grams of drug in every hundred milliliter of solution.

So now we can make use of that information and state that in every 100 mL of solution, you have eight grams of drug.

So now the grams cancel out. And since we are using dimensional analysis, we can essentially multiply all the terms in the numerator. So that would be 5 g times 100 mL, divided by 1 hr, times 8. And that should be equal to 62.5 mL/hr.

B.

Let's now take a look at part B of the question. And here we are required to find how long the bottle will last. So the approach would be to take the 500 mL bottle and essentially divide that by the flow rate that we found in part A.

But since we are using dimensional analysis, this is how it's going to look. We will start off with a 500 mL bottle, and we will make use of the flow rate information from part A, which tells us that in every hour, the patient is going to receive 62.5 mL.

So now the mL can cancel out, and we essentially have 500 times 1 hr, divided by 62.5.

So you multiply everything in the numerator and divide by what is in the denominator. And so the answer is 8 hr.

### Calculation Practice Question #5

This question says, a physician orders a drug to be infused at 10 mcg/kg/min. The patient weighs 70 kg. The total dose the patient is to receive is 21 mg. How long must the IV continue for the patient to receive this dose?

So the first thing we need to do is to determine the rate for this particular patient. And so we will start off with the normalized mass rate, which is given as 10 mcg/kg/min.

And we multiply this normalized mass rate by the patient's weight. That gives us 70 kg.

The kilograms cancel out. And so now we have 10 mcg times 70, divided by minutes. And that gives 700 mcg/min.

Now that is the mass rate for this 70 kg patient. However, the dose to be given the patient is in milligrams, is 21 mg. So we want to convert the micrograms to milligrams to make the next step easier.

So we make use of the conversion factor, which states that 1,000 mcg make up 1 mg.

So the micrograms cancel out, and that is equal to 0.7 mcg/min.

So now we can determine the time by dividing the total dose that the patient receives, which is 21 mg, by the mass rate determined in the earlier step.

So now, since we are using dimensional analysis, we'll start off with the 21 mg, and then the mass rate is 0.7 mg/min, which means that in 1 minute, the patient would receive 0.7 mg of drug.

So the milligrams cancel out and that implies you have 21 times 1 minute, divided by 0.7 and that is equal to 30 minutes.

### Calculation Practice Question #6

This question says, an order for a patient with a 3 L daily IV fluid limit calls for 3 L of D5W with a 100 mL IVPB antibiotic to be running alone over a 1 hour period administered every 6 hours. The administration set is calibrated to deliver 10 drops per milliliter. Calculate:

a) The flow rate of the IVPB antibiotic.

b) The total flow time for the IV antibiotic.

c) The total volume of the IV antibiotic.

d) The total flow time for the D5W

e) The total volume for the D5W

f) The flow time for the D5W.

So the question has six parts. The first three have to do with the IVBP, which is your IV piggyback.

And then the last three from D to F have to do with the large volume parenteral, which is your D5W.

Part A

So we can start off by solving part A. And A is asking for the flow rate of the IVPB antibiotic. So the strategy will be to take the volume of the IVPB, which is 100 mL, divide that by how long you are running it, which is 1 hr, convert the hours to minutes, and multiply that result by the drip factor, which is 10 drops/mL.

And so what that would look like is you have 100 mL, which is the volume of the IVPB, divide that by how long you are running it, which is going to be 1 hr. We convert the hours to minutes, 1 hr is 60 min, and we multiply this result by the drip factor, which is 10 drops/mL.

So the milliliters cancel out, the hour cancels out, and now you're in drops per minute.

So since we are using dimensional analysis, we are going to multiply everything in the numerator. So that would be 100 times 1, times 10 drops, divided by everything in the denominator. So that would be 1 times 60 minutes.

Now that should be equal to 16.67 drops/min or approximately 17 drops/min.

Part B

So we can now solve part B of the question, which is asking for the total flow time of the antibiotic. And the way we find the total flow time is to multiply the number of times that you are running the IVPB by how long you run each bag.

And so what that would look like is you have a total time of 24 hrs.

You run the IVPB every six hours. And each bag is run for one hour. And so the total flow time will be four hours.

Part C

So we can now go ahead and solve part C of the question, which is asking for the total volume of the antibiotic. And the way you find the total volume is to multiply the number of times that you run the IVPB by the volume of each bag.

So what that would look like is you have a total time of 24 hr

and every 6 hrs you run one IVPB, one bag.

So this ratio gives us the number of times that you would run the bag, and the volume of each bag is given us 100 mL.

So the hours cancel out and your total volume will be 400 mL.

Part D

We can now solve part D of the question, which is asking for the total flow time for the D5W.

And the way we would approach that is to take the 24 hr, which is how many hours you have in one day,

and subtract from that the total flow time of the antibiotic, which is given in part B to be 4 hr. So that will end up giving us 20 hr.

Part E

So we can now go ahead and solve part E of the question, which is asking for the total volume for the D5W. And the way we would approach this is to take the patient's daily IV fluid limit, which is 3 L, and subtract from that the total volume of the antibiotic, which is 400 mL.

Now, for the units to be consistent, we first need to convert the 3 L to mL. So 3 L multiplied by the conversion factor, one liter is 1,000 mL.

The litters cancel out and that gives 3,000 mL.

So from this 3,000 mL, we will subtract the total volume of the antibiotic, which is 400 mL,

and that should be equal to 2,600 mL.

Part F

We can now solve part F of the question, which is asking for the flow rate for the D5W. Now, the way we will do that is to take the total volume for the D5W, which we calculated in part E to be equal to 2,600 mL, divide that by the total flow time for the D5W, which we calculated in part D to be equal to the 20 hrs and then convert the hours to minutes and multiply that result by the drip factor.

So what that would look like is we have 2,600 mL divided by 20 hr. We convert the hours to minutes. In 1 hr, you have 60 min.

The hours cancel out and we multiply this result by the drip factor, also known as the calibration factor, which is 10 drops/mL.

So the milliliter also cancels out and now you're in drops/min.

So since this is dimensional analysis, we will multiply everything in the numerator. So you have 2600 times 1, times 10 drops, and divide that by everything in the denominator, which would be 20 times 60 min. And that is equal to 21.67 drop/min, which is approximately 22 drops/min.

### Calculation Practice Question #7

This question says a 250 mL bag of D5W is to be infused at 40 drops/min. The IV set drop factor is 60 drops/mL. The IV is started at 6 AM. When will the next bag be needed?

The way we want to approach this question is to first calculate how long it's going to take to infuse the 250 mL bag of D5W. Now, once we've calculated that, we can then determine when the next bag will be needed.

To do that, we need to identify from the question any parameter that has a time component. And we see that the flow rate, which is 40 drops/min, has a time element being the minutes.

So the first thing we want to do is to start off with the flow rate 40 drops/min. And what that implies is that in every single minute, you're able to give 40 drops. Now we are using dimensional analysis, so we can go ahead and multiply this ratio by the drop factor, which is 60 drops/mL.

Now at this point, the drops can cancel out and we are now left with min/mL. So we can go ahead and multiply this by the volume of the bag, which is 250 mL.

So now the milliliters cancel out. So we are using dimensional analysis. So we can go ahead and multiply all the terms in the numerator. So that will be 1 min times 60, times 250, divided by 40. And that is equal to 375 minutes.

So to make the calculation easier, we can go ahead and convert the minutes to hours, which would imply that we have 375 min. We convert that to hours. So the conversion factor is 1 hr contains 60 min.

The minutes cancel out, and that is equal to 6.25 hr.

So the 0.25 is not 25 min, but rather is a quarter of an hour. So just to be clear, we can go ahead and convert the 0.25 hr to minutes. So that would imply that your 0.25 hr, we convert that to minutes. 1 hr is equivalent to 60 min.

The hours cancel out. That means you have 15 min.

And so this implies that you're actually going to be infusing the 250 mL bag of D5W for 6 hr and 15 min.

If you started the IV at 6 AM, then 6 hr later will be 12 noon and 15 min later will be 12.15.

So that would imply that the next bag would be needed at 12.15 PM.

### Calculation Practice Question #8

This question says, a medication is ordered by the physician 2 g in 250 mL normal saline to be administered by a continuous IV around the clock for 24 hr. The rate of infusion is 100 mL/hr. If the first bag started at 0800, how many bags in total would be needed?

And so the strategy here would be to first determine the volume administered in 24 hr. And the way you do that is to use the rate of infusion, which is 100 mL/hr, multiply that by the total time, which is 24 hr, and that will give the volume administered.

Once we found this volume, we will divide that by the volume of each bug to give the number of bags.

Let's see how that looks like. So we can start with the rate of infusion, which is 100 mL per hour. We multiply this ratio by the time, which is 24 hr, and make use of the information provided, which states that each bag has 250 mL.

Now the milliliters can cancel out, the hours cancel out. And what we can do next, since this is dimensional analysis, is to multiply all the terms in the numerator. So we have 100 times 24, times 1 bag and divide that by all the terms in the denominator. So divide that by 250.

So this will be equal to 9.6 bags, which is approximately 10 bags.

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

### Frequently Asked Questions

#### Q: What is the significance of IV Flow Rate Calculations?

A: IV Flow Rate Calculations are essential in determining the rate at which intravenous fluids should be administered to a patient.

#### Q: What is the significance of IV Flow Rate Calculations?

A: To calculate the IV flow rate, you need to know the drip factor of the tubing and the amount of fluid to be infused. Using the formula: IV Flow Rate (gtt/min) = Drip Factor (gtt/mL) x Volume to be Infused (mL) / Time (min).

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

A: A drip factor refers to the number of drops per milliliter (gtt/mL) that a particular tubing allows. It is a crucial factor in IV flow rate calculations.

#### Q: How can I determine the drip factor of my IV tubing?

A: The drip factor is usually indicated on the packaging of the IV tubing. If it is not, you can consult the manufacturer's instructions or ask your healthcare provider for assistance.

#### Q: How can I ensure the right amount of fluid is being infused?

A: You can use an IV pump to ensure the accurate administration of intravenous fluids. The pump can be set according to the calculated IV Flow Rate to deliver the right amount of fluid over the desired time.

#### Q: What should I do if I don't have an IV pump?

A: If you don't have an IV pump, you can manually regulate the drip rate by counting the number of drops per minute and adjusting accordingly. However, this method may not be as accurate as using an IV pump.

#### Q: What should I do if the calculated drip rate seems unusually high or low?

A: If the calculated drip rate seems unusually high or low, double-check your calculations and ensure that the units are consistent. If you are still unsure, consult with your professor or healthcare professional for guidance.

#### Q: Are there any risks associated with incorrect IV flow rate calculations?

A: Yes, incorrect IV flow rate calculations can result in over- or under-infusion of fluids, leading to potential complications such as fluid overload or inadequate hydration. It is essential to ensure accurate calculations to prevent such risks.

#### Q: Are there any risks associated with incorrect IV flow rate calculations?

A: Practice is the key to improving your IV flow rate calculation skills. You can find various online resources and practice quizzes such as the NAPLEX Calculations Question Bank to test your knowledge and enhance your understanding of the calculations involved.

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