### Ex: IV Dosage Calculation – Flow Rate Requiring Five Steps

#### By Bryan Wright

You receive an order for 10 milliunits per

kilogram per minute. The solution is labeled 40

units per 100 milliliters. The patient weights 198 pounds. What is the correct rate or flow rate in milliliters per hour? So to find the flow rate, we’ll have to perform several conversions. Notice how the order is given

in milliunits per kilogram but the weight is given in pounds. Let’s begin by converting

198 pounds to kilograms, and we’ll do this using a proportion. Looking at our conversions below, notice that one kilogram

is equal to 2.2 pounds, so we can say one

kilogram is to 2.2 pounds as an unknown number of kilograms, which I’ll call X kilograms,

to the weight at 198 pounds. And before we cross

multiply and solve for X, it’s important to recognize that we have the same units on the top and

the same units on the bottom. If we did not have this, we’d have to perform a conversion first. But because we do, 2.2 times X is 2.2 X must equal one times 198. Dividing both sides by 2.2, this comes out very nicely on the right. This is equal to 90, so 90 kilograms is equal to 198 pounds. Now that we know the

patient’s weight in kilograms, let’s determine how many milliunits the patient needs per minute. The order calls for 10

milliunits per kilogram, so 10 milliunits per one kilogram must equal an unknown

number of milliunits, we’ll call it Y milliunits, to the patient’s weight of 90 kilograms. Once again, we have the same units on top, same units on the bottom, so we can cross multiply and solve for Y. So one times Y is Y. 10 times 90 is 900. Which means the patient needs

900 milliunits per minute. So again, we can write the order

for this particular patient as 900 milliunits per minute, but notice how we want the flow

rate in milliliters per hour so now let’s convert this

rate into milliunits per hour, and then we’ll determine how

many milliliters we need. So for the next proportion,

900 milliunits per one minute must be equal to some

number of milliunits, we’ll call it Z milliunits, per one hour, but because we need the

same units on the bottom, notice here we have minutes,

instead of writing one hour, one hour is equal to 60 minutes, so I’ll write this as 60 minutes. Again, we have the same

units on the bottom, same units on the top, so now we can cross

multiply and solve for Z. One times Z is Z. 900 times 60 is equal to 54,000, which means now we can write the order as 54,000 milliunits per one hour. For the next step, we’ll

convert the 54,000 milliunits to units, then once we

find the number of units, we can determine the number

of milliliters per hour. Let’s go and continue

this one the next slide. Again, now we’re going to

convert milliunits to units. Going back to the previous

slide just for a moment, notice how 1,000 milliunits

is equal to one unit. So this will give us the

left side of the proportion. 1,000 milliunits is to one

unit as 54,000 milliunits is to an unknown number of

units, we’ll say A units. Once again, we have the same units on top, same units on the bottom. Cross multiply and solve for A. 1,000 times A, or 1,000 A

must equal one times 54,000. Divide both sides by 1,000. So we have A equals 54. So if A’s equal to 54, that

means 54,000 milliunits is equal to 54 units, and therefore, we can now write the order

as 54 units per hour. Now we need one more proportion. We need to determine how many milliliters is required for 54 units. So going back to the given

information just for a moment, notice how the solution has a rate of 40 units per 100 milliliters. So they can say 40 units

is to 100 milliliters as 54 units is equal to an

unknown number of milliliters, which we’ll say B milliliters. And finally, once again, we

have the same units on the top, same units on the bottom, so now we can cross

multiply and solve for B. So we have 40 times B, that’s 40 B, equals 100 times 54, that’s 5,400. Divide both sides by 40. 5,400 divided by 40 is equal to 135. Which means that the

patient requires 54 units, that would be equivalent to

135 milliliters of the solution and therefore, the flow

rate for this patient is 135 milliliters per hour. I hope you found this explanation helpful.