Flow Rates

[Pages:22]CHAPTER

8

Flow Rates

L earning Objectives

After completing this chapter, you should be able to:

? Define flow rates. ? Illustrate the dimensional

analysis for flow rates. ? Calculate flow rates to

determine drops/minute. ? Calculate flow rates in

milliliters/hour.

INTRODUCTION

Flow rates are calculated to determine at what rate, usually stated in drops per minute, a medication will flow through IV tubing to the patient. Dimensional analysis is commonly used to perform these calculations. Dimensional analysis uses logical sequencing and placement of units so that they can be canceled out to leave the desired terms for the final answer.

68

Basic Dimensional Analysis

It is common for individuals to become overwhelmed and confused when approaching complex pharmacy calculations. The truth is, however, that while many pharmacy calculations can appear to be complex, they are, in actuality, very simple.

Sterile product calculations and flow rates are typically viewed as among the most difficult, but each problem can be solved either by using basic dimensional analysis or ratios/proportions. We have covered ratios/proportions extensively in earlier chapters of this book, so now we will cover the basics of dimensional analysis.

Before moving forward, however, let's review several fundamental math principles.

1. Any number multiplied by 1 retains the same value.

ex. 4 * 1 = 4

ex.

1 2

*

1

=

1 2

2. Any whole number can be expressed as a fraction by placing a 1 as the denominator.

ex. 3 = 3>1

ex. 18 = 18>1

3. Any number divided by itself equals 1. ex. 4 , 4 = 1 ex. 2>2 = 1

The first set of examples and practice problems in this chapter will not appear to have anything at all to do with sterile product calculations, but be patient and realize that these early examples are laying a foundation for you to easily comprehend more "advanced" flow rate calculations.

EXAMPLE 8.1

How many hours are there in 6 days? In this problem we are working with days and hours. What

information, or facts, do we know about days and hours?

? There are 24 hours in 1 day.

This could be written as:

? 24 hours 1 day 1 day

? 24 hours 24 hours

? 1 day

Using the principle of dimensional analysis, we can use this information to solve the problem.

6 days 24 hours

6 days =

*

=?

1

1 day

Chapter Eight Flow Rates 69

After setting the problem up, we can cancel out like units and/or numbers.

6 days 24 hours

6 days =

*

=?

1

1 day

which can now be written as:

6 days = 6 * 24 = ?

Therefore, 6 days is equivalent to 144 hours.

6 days = 6 * 24 = 144

EXAMPLE 8.2

How many minutes are there in 5 hours? In this problem we are working with minutes and hours. What

information, or facts, do we know about minutes and hours?

? There are 60 minutes in 1 hour.

This could be written as:

? 1 hour 60 minutes 1 hour

? 60 minutes 60 minutes

? 1 hour

Using the principle of dimensional analysis, we can use this information to solve the problem.

5 hours 60 minutes

5 hours =

*

=?

1

1 hour

After setting the problem up, we can cancel out like units and/or numbers.

5 hours 60 minutes

5 hours =

*

=?

1

1 hour

which can now be written as:

5 hours = 5 * 60 = ?

Therefore, 5 hours is equivalent to 300 minutes.

5 hours = 5 * 60 = 300

EXAMPLE 8.3

45 minutes is equal to how many seconds? We know that there are 60 seconds in every 1 minute, this could

be written as:

? 1 minute = 60 seconds 1 minute

? 60 seconds 60 seconds

? 1 minute

70 Chapter Eight Flow Rates

Using the principle of dimensional analysis, we can use this information to solve the problem.

45 minutes 60 seconds

45 minutes =

*

=?

1

1 minute

After setting the problem up, we can cancel out like units and/or numbers.

45 minutes 60 seconds

45 minutes =

*

=?

1

1 minute

which can now be written as:

45 minutes = 45 * 60 = ?

Therefore, 45 minutes is equivalent to 2700 seconds.

45 minutes = 45 * 60 = 2700

EXAMPLE 8.4

How many seconds are there in 3 hours? We know that there are 60 seconds in every 1 minute and that

there are 60 minutes in every hour. Using the principle of dimensional analysis, we can use this

information to solve the problem, but to solve this problem we will now have to add a third component.

3 hours 60 minutes 60 seconds

3 hours =

*

*

=?

1

1 hour

1 minute

After setting the problem up, we can cancel out like units and/or numbers.

3 hours 60 minutes 60 seconds

3 hours =

*

*

=?

1

1 hour

1 minute

which can now be written as:

3 hours = 3 * 60 * 60 = ?

Therefore, there are 10,800 seconds in 3 hours.

3 hours = 3 * 60 * 60 = 10,800

EXAMPLE 8.5

How many seconds are there in 4 days? We know that there are 60 seconds in every 1 minute,

60 minutes in every hour, and 24 hours in every 1 day. Using the principle of dimensional analysis, we can use this

information to solve the problem, but once again we will need to add another component compared to previous examples.

4 days 24 hours 60 minutes 60 seconds

4 days =

*

*

*

=?

1

1 day

1 hour

1 minute

Chapter Eight Flow Rates 71

After setting the problem up, we can cancel out like units and/or numbers.

4 days 24 hours 60 minutes

4 days =

*

*

1

1 day

1 hour

60 seconds

*

=?

1 minute

which can now be written as: 4 days = 4 * 24 * 60 * 60 = ?

Now we know . . . there are 345,600 seconds in 4 days. 4 days = 4 * 24 * 60 * 60 = 345,600

PRACTICE PROBLEMS 8.1

1. How many hours are there in 8 days? ________________ 2. How many minutes are there in 14 hours? ________________ 3. How many minutes are there in a day? ________________ 4. Ten minutes is equivalent to how many seconds? ________________ 5. How many seconds are there in 50 minutes? ________________ 6. 1.5 days is equal to________________ hours. 7. There are ________________ minutes in 2.1 hours. 8. How many seconds are there in 8 hours? ________________ 9. One hour is equal to ________________ seconds. 10. How many seconds make up a full day? ________________

Flow Rate Duration

EXAMPLE 8.6

A 1-L IV bag is being administered at a rate of 200 mL per hour. How long will this IV bag last?

Do not get overwhelmed or confused now that the problems are talking about IV bags instead of days, hours, and seconds. Just as before, we can use dimensional analysis to solve this problem. In essence, the problem being asked is 1 L is equal to how many hours?

Again, we should start by looking at the information, or facts, that we know.

We know that there are 1000 mL in every 1 L, which could be written as:

? 1 L = 1000 mL 1 L

? 1000 mL

1000 mL ? 1L

72 Chapter Eight Flow Rates

We also know, according to the problem, that 200 mL are being administered per hour, which can be written as:

? 1 hr = 200 mL ? 1 hr

200 mL ? 200 mL

1 hr Using the principle of dimensional analysis, we can use this information to solve the problem.

1 L 1000 mL 1 hr

1L = *

*

=?

1

1 L

200 mL

After setting the problem up, we can cancel out like units and/or numbers.

1 L 1000 mL 1 hr

1L = *

*

=?

1

1 L

200 mL

which can now be written as:

1 * 1000 * 1 hr

1L =

=?

200

Therefore, the 1-L bag will last 5 hours

1000

1L =

= 5 hr

200

EXAMPLE 8.7

A 2-L IV is to be administered at 250 mL>hr. How long will the IV last? Let's start by looking at the information, or facts, that we know. We know that there are 1000 mL in every 1 L, which could be

written as:

? 1 L = 1000 mL ? 1L

1000 mL ? `1000 mL

1 L

We also know, according to the problem, that 250 mL are being administered per hour, which can be written as:

? 1 hr = 250 mL ? 1 hr

250 mL ? 250 mL

1 hr

Using the principle of dimensional analysis, we can use this information to solve the problem.

2 L 1000 mL 1 hr

2L = *

*

=?

1

1 L

250 mL

Chapter Eight Flow Rates 73

After setting the problem up, we can cancel out like units and/or numbers.

2 L 1000 mL 1 hr

2L = *

*

=?

1

1 L

250 mL

which can now be written as:

2 * 1000 * 1 hr

2L =

=?

250

Therefore, the 2-L bag will last 8 hours.

2000

2L =

= 8 hrs

250

EXAMPLE 8.8

A patient is set to start a 500-mL infusion of cimetidine in lactated ringers 5% at 10:00 a.m. The bag is to be administered at a rate of 125 mL per hour. At what time will the infusion be complete?

This example provides us with additional information concerning the drug name, solution strength, and administration start time. As always, let's start by looking at the information that we know and that we will need to calculate the problem.

We know that:

? the bag contains a total of 500 mL ? 125 mL are being administered per hour ? the infusion is scheduled to start at 10:00 a.m.

Using the principle of dimensional analysis, we can use this information to determine how long the infusion will last.

500 mL 1 hr

500 mL =

*

=?

1

250 mL

After setting the problem up, we can cancel out like units and/or numbers.

500 mL 1 hr

500 mL =

*

=?

1

250 mL

which can now be written as:

500 500 mL = * 1 hr = ?

250

Therefore, the 500 mL bag will last 4 hours.

500 500 mL = * 1 hr = 4

250

The question being asked, however, is what time will the infusion be completed?

To answer this question simply take the start time (10:00 a.m.) and add the length of duration (4 hours).

10:00 a.m. + 4 hr = 14:00 hr, or 2:00 p.m.

74 Chapter Eight Flow Rates

EXAMPLE 8.9

Three 1 L IV bags are to be infused at a rate of 150 mL/hour. How long will these three bags last?

Let's start by looking at the information, or facts, that we know. We know that:

? 1 IV bag contains 1 L ? there are 1000 mL in every 1 L ? 150 mL are being administered per hour

Using the principle of dimensional analysis, we can use this information to solve the problem.

3 bags 1 L 1000 mL 1 hr

3 bags =

*

*

*

=?

1

1 bag

1 L

150 mL

After setting the problem up, we can cancel out like units and/or numbers.

3 bags 1 L 1000 mL 1 hr

3 bags =

*

*

*

=?

1

1 bag

1 L

150 mL

which can now be written as:

3 * 1 * 1000 * 1 hr

3 bags =

=?

150

Therefore, the 3 bags will last 20 hours.

3 bags = 3 * 1 * 1000 * 1 hr = 20

EXAMPLE 8.10

Two 2-L IV bags containing heparin sodium and NS are set to be administered at a rate of 250 mL per hour at 7:00 a.m. When will both bags be completely administered?

Let's start by looking at the information, or facts, that we know. We know that:

? 1 IV bag contains 2 L ? there are 1000 mL in every 1 L ? 250 mL are being administered per hour

Using the principle of dimensional analysis, we can use this information to solve the problem.

2 bags 2 L 1000 mL 1 hr

2 bags =

*

*

*

=?

1

1 bag

1 L

250 mL

After setting the problem up, we can cancel out like units and/or numbers.

2 bags 2 L 1000 mL 1 hr

2 bags =

*

*

*

=?

1

1 bag

1 L

250 mL

which can now be written as:

2 * 2 * 1000 * 1 hr

2 bags =

=?

250

Chapter Eight Flow Rates 75

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