CLOates

Revised:

Vastly expanded solution to WS 26,
Problem 15b --CLO

OCCC APPM 1313

Some Solved IV Drip Rate
Problems (Chapter 10)

Below
are excerpts from e-mails I’ve sent to your predecessors over the past few
semesters, answering requests for solutions to the indicated problems. These should be of some use to you in working
the Module 3 homework assignments and in studying for the Module 3 test. Note that some of this information is in the
hard-copy handouts for Chapter 10, also.

--------------------------------

**Problem #1 on p. 168**

Let's see, they asked us for a flow
rate (gtt/mL), so let's start with a flow rate.
We have 1000 mL to be delivered in 4 hours, so

1000 mL

------------- .

4
hr

Now, we're going for gtt/min (the problem doesn't explicitly say that, but I
will for sure tell you what units I want on the test). So, let's take
care of the conversion of hours to minutes, as follows (I'll put the conversion
on the left side to make it look like what they do in the book):

1
hr 1000 mL

---------
x ------------- .

60
min 4 hr

Well, okay, we're in mL / min after we
divide out the hours. That's closer to gtt /
min, but we need to convert the mL to gtt. We
can do that with the drop factor, as follows:

1 hr 1000
mL 15 gtt

---------
x ------------- x -----------.

60
min 4 hr 1
mL

Now, the surviving units, after
dividing out the hours and the milliliters are gtt /
min, and those are the desired answer units.

We'll separate the numeric stuff like
this:

1 x
1000 x 15 gtt 15,000 gtt

-------------------------
= ---------- -----
= 62.5 gtt / min ~=
63 gtt /min

60 x
4 x
1 min 240 min

We rounded to the nearest whole drop
per minute, since it's just about impossible to count fractional drops being
delivered to the drip chamber. Notice that we didn't use the amount of medication
in the calculation, because, thought the medication needs to be there, all they
asked us for was the flow rat to deliver the 1000 mL of fluid (D5NS in this
case) in 4 hours. Later problems will ask us for more complicated rates
of delivery and we'll need to use the amount of medication in those, but in
this case we can answer the question quite simply.

--------------------------------

The problems on p. 168 have more information
than is needed to do the calculation (though you need all of the info to be
sure you're giving the right amount of medication when actually administering
an IV).

For instance, in **problem #2, p. 168**, we need to infuse 250 mL of D5W, that
happens to have 0.5g of Aminophylline dissolved in
it, over a two hour period. All that's required is an application of
"Chuck's Flow Rate Rule" which states, "if they're asking for a
flow rate, start with a flow rate." These problems are looking for
flow rates in gtt/min, though they don't explicitly
say that (I'll be explicit on the test).

So let's see, we have 250 mL of fluid
to be infused in 2 hours. That's a flow rate of 125 mL/hr ( = 250 mL / 2 hr). Well, 125 mL/hr is a flow rate,
but it's not in gtt/min, so let's remedy that.

We need the flow rate to be "per
minute," so let's use the conversion factor 1 hr / 60 min. The
equation would look like this:

1 hr / 60 min *
250 mL / 2 hr ( <-- You may want
to write this out by hand in standard fraction notation--that's tough for me to
do on a typewriter-like device.)

We're pretty close now. The
surviving units, after dividing out hours, are mL / min. If we can
convert the mL to drops (gtt), we'll be home
free. Since they gave us a drop factor of 60 drops to 1 mL, we can
add that factor to the above equation to get

1 hr / 60
min * 250 mL / 2 hr * 60 gtt / 1 mL which has the surviving units gtt/min.

We can now collect the numeric stuff as
follows:

1 * 250 *
60 gtt

-------------- ------
.

60 * 2 *
1 min

If we note that 60 / 60 =1, this yields
125 ( = 250 / 2 ) gtt / min.

Notice a couple of things about this
answer. First, the number of drops per minute is equal to the number of
milliliters per hour that we calculated at the very first. This will be
true any time the drop factor is 60 gtt / mL, because
the 60 in the drop factor and the 60 in the 1 hr
/ 60 min conversion factor will divide out. Second, we never used
the fact that 0.5 g of medication happens to be dissolved in the D5W. The
pharmacy or, perhaps, the manufacturer of the medication pre-loaded the
medication, so we don't need to do anything in the calculation to take it into
account. (This is the usually case in practice.) The medication
information is just there in the order to make sure that we giving the correct
medication to Mrs. Brown in bed A in Room 278 (or
wherever).

Also, for a sanity check on the
calculation, notice that the 125 mL/hr = 125 gtt/min
is a pretty reasonable flow rate for an IV. One or two hundred mL / hr is
about a high as they usually go, although you'll see small amounts (50 mL)
infused at 300 mL/hr sometimes. Anything higher is probably a candidate
for administration with a garden hose, not an IV tube.

The rest of the problems on p. 168 work
pretty much the same way. Form a rate in mL / hr, then convert it to gtt / min using the drop factor (none of the others happen
to be 60 gtt / mL) and the 1 hr / 60 min conversion
factor.

--------------------------------

**Problem 3, p. 172:**

Let's see, we need to give 150 mg of
Ampicillin and we need concentration information from the medication label to
figure the number of mL. The label says to add 5 mL of diluent to 250 mg
of ampicillin. Since the label doesn't directly tell us the
concentration, we'll have to calculate the concentration (strength) as 250 mg /
5 mL. That gives

150 mg x 5 mL /
250 mg = ( 750 / 250)
mL = 3 mL.

In 3b, we're asked for a flow rate (in gtt/min), so let's start with a flow rate. The
problem hands us a flowrate in the order without
any need to calculate it: 150 mL / hr, so let's start with that and
transform its units into gtt/min.

We can transform the "per
hour" part to "per minute" by the usual
1 hr = 60 min equivalence. I'll write it in front of the 150
mL / hr starting factor so that it'll look like the book's method, as follows:

1 hr / 60 min x
150 mL / hr .

Dividing out the hours in the
numerator and denominator shows that the units are now in
mL/min. That's close to gtt/min, but obviously
we need to convert mL to drops, using the 15 gtt / mL
drop factor, as follows:

1 hr / 60 min x
150 mL / hr x 15 gtt /
mL

= (150 x 15) /
60 gtt / min

= 37.5 gtt / min

~= 38 gtt /
min

--------------------------------

**Problem 4, Page 172: **

4a) 30 mEq
x 1 mL / 2 mEq = 15 mL

4b) They've
asked for a flow rate (gtt / min, given in the gold
box at the top of each page 172 - 175), so let's start with a flow
rate. Let's see we're supposed to deliver 1000 mL in 6 hours. Ah,
that's a valid flow rate, so let's write it as:

1000 mL

------------- .

6
hr

Now, we're going for gtt / min, so we'll need to convert the hours to minutes.
Again, I'll write the conversion factor on the left so that it will look
like the text's method, but you could write the conversion factor on the left
if you prefer.

1 hr
1000 mL

-------- x ------------- .

60 min
6 hr

After dividing out the hours, the
surviving units are mL / min. That's close, but we need gtt / min, so we'll need to convert the mL to gtt. The drop factor of 10 gtt
/ mL should do that nicely, as follows:

1 hr
1000 mL 10 gtt

-------- x
------------- x
--------------

60 min
6 hr
1 mL

1
x 1000 x 10 gtt

= ----------------- ------- .

60 x 6 1 min

After a bit of somewhat painful
arithmetic, this yields

27.78 gtt / min

~= 28
gtt / min to the nearest drop, since
fractional drops are very difficult to count. :^)

--------------------------------

How about **problem 6, p.**** ****178** ? It's just a lot of extraneous
information packed around 100 mL / 60
min =
100 mL / hr, right?

--------------------------------

**Problems 6,
7, 8, p. 178-179**

… in problems six, seven, and
eight, they’ve given you extraneous information (for purposes of calculating
the flow rate, at least).

For example, in problem six, observe that 100 mL of D5W must
be infused in 60 minutes (1 hour); therefore, the required flow rate is 100 ml
/ 1 hour = 100 mL/hr. All the rest of the information is irrelevant to
the flow rate calculation.

In problem seven, it’s the same story: 50 mL of
Ringers Solution has to be delivered in 30 minutes (1/2 hour), so the flow rate
needs to be 50 mL / 0.5 hour = 100 mL/hr. Problem eight is similar.

Problem nine takes a bit more doin’,
but it’s not too bad. The flow rate is given as a weight (mass) flow
rate, 30 mg / min. I’d start there and try to transform the weight flow
rate (mg/min) into the required volume flow rate (mL/hr). Here’s how that
would look:

9a. (30 mg of Cleocin
/ 1 min) x (60 min / 1 hr) x
(50 mL of D5W / 300 mg of Cleocin) =
300 mL of D5W / hr .

^--- from information in the statement of the problem

Now that we know the volume flow rate, the time-to-deliver
calculation is easy enough (“how long to drive 240 miles to

9b. 50 mL of D5W x
( 1 hour / 300 mL of D5W) x ( 60 min. / 1 hour) = 10
min.

^--- from 9a, above

You may want to write the above expressions out on paper in
traditional fraction form or in a ladder/monorail diagram form to make them
clearer.

--------------------------------

**Problem 9b,
p. 179**

The Student’s Question

… The answer book had two different ways to work the problem and neither make logical sense to me.

Answer way 1 was 50mL X 1hr./300mL
X 60min/1hr = 10 min

Where in the sam hill did the 300
mL come from?

Answer way 2 was 300mg X 1min/30mg = 10 min.

At least these numbers were in my problem BUT why would you
use 300mg instead of the 50mL. I would never have thought to use
that. Do you just use it because it is mg and so is 30mg?

…

The Answer

With respect to p. 179, problem
9b, consider the analogy I used in class. If it's
240 miles to

In dimensional analysis form, this is
stated as

240 mi x
1 hr / 60 mi = 4 hr.

Now, in problem 9b, we're
consuming what? Well, we could view the infusion as a
consumption of 50 mL of D5W. In that view, we're consuming 50 mL of D5W
at the rate of 300 mL / hr (the rate calculated
in 9a), for a total time of 1/6 hr or 10 min. That's the logic of
"way 1."

On the other hand, we could view the
infusion as a consumption of the 300 mg of Cleocin
that's dissolved in the D5W. In that view, we're consuming 300 mg of Cleocin at the ordered rate of 30 mg / min. That's
the logic of "way2."

Either way works. Way 2 is a
little safer, I suppose, in the sense that it uses only quantities from the
order itself in the calculation, instead of depending on a previous calculation
for the flow rate in mL / hr.

--------------------------------

__Handout 25__

**13 b****.** it
gives 10 mL/hr. Is this the flow rate or do I need to calculate gtt/min?

I believe all it’s asking for is the
volume flow rate that’s stated in the problem, that is, 10 mL/hr. That’s
what you’d need to set the infusion pump. It’s certainly possible to
calculate a drug weight flow rate in Units of Heparin / hour, since we know
that 30,000 Units of Heparin are dissolved in the 250 mL of D5W, but I don’t
think that’s what they’re asking. I’ll be very specific about the answer
units on the test, so there shouldn’t be any doubt.

__Handout 26__

**15 b**. (vastly revised and expanded)

Let’s work this problem by a more orthodox solution
technique than the one I first posted.
Here’s the Revised Standard Version.

Since
they asked us for a flow rate, let's start with a flow rate. The only one
available seems to be the WEIGHT flow rate, 1000 Units/hr. Well, that
means we're going to need the concentration in the "big bag," so let's just calculate it now:

20,000
Units

---------------- = concentration of medication in the IV
infusion bag or bottle

500
mL

Now,
let's start with the flow rate specified,

1000
Units / hr .

We're
going for gtt / min as the answer units, so let's
take care of the time conversion first. To get hr --> min,

1
hr / 60 min x 1000 Units / hr .

The
surviving units are now Units/min, which is closer, but still no cigar awarded.

Okay
we're going to have to get the weight units of "Units" converted to
mL, so we may as well do that now using the concentration in the big bag,
calculated above. It'll look like this:

1
hr / 60 min x 1000 Units / hr x
500 mL / 20,000 Units .

The
surviving units are now mL/min, so we're getting closer, but the volume unit
required is gtt, not mL. Well, we have the drop
factor of 60 gtt/mL, so we
can take care of that, as follows:

1
hr / 60 min x 1000 Units / hr x
500 mL / 20,000 Units x 60 gtt / mL .

Finally!
Our surviving units are now gtt / min, and
that's what we're after. Let's collect numeric quantities and see if we
can get an answer.

1
x 1000 x 500 x 60 gtt

--------------------------
---

60
x 1 x 20,000 x 1 min

=
500 / 20 gtt / min

=
25 gtt / min.

Whew!
We got there.

---------------------------------------------------------------

For those of you who want additional
depth, let’s look at how the unorthodox, but quite correct solution I originally
posted for this problem works.

Since
we're given a weight flow rate, let's first figure out how long it will take to
infuse the medication at the ordered rate. Once we know how long, we can
use that, along with the number of mL to be administered, to get a VOLUME
flow rate and life will be easier. Here's how it looks.

20,000
Units must be delivered at 1000 Units / hr. Therefore, it'll
take

20,000
Units x 1 hr / 1000 Units = 20 hr to infuse the
medication.

Now
that we know it'll take 20 hours, we can form a volume flow rate as follows:

500
mL / 20 hr .

For
some reason, my previous student chose to divide both numerator
and denominator by 5 (I'd have divided by 20 to yield 25 mL/hr, but .. oh, well). This yields

100 mL / 4 hr.

We
can convert this to gtt/min by applying first the 1
hr / 60 min conversion factor and then the 60 gtt/mL
drop factor, like this:

1
hr / 60 min x 100 mL / 4 hr x
60 gtt / mL

100 x 60 gtt

=
------------- ------

60 x 4 min

= 25 gtt / min .

---------------------------------------------------------------

Now the original answer to this problem, re-posted below,
may make more sense.

(Student: ) I came up with a flow rate of
500 gtt/min and that seems a little high. Is
that correct or did I get my figures messed up?

Here's how I did
it: (60 gtt/1 mL) x (100 mL/4 hr) x (1 hr/60 min) = 500
gtt/min

(Prof. Oates: ) Your setup is correct, but I believe if
you’ll do the arithmetic again you’ll find that the flow rate is (60 / 60) x
(100 / 4) = 25 gtt/min (and 25 mL/hr, too, since the
drop factor is 60 gtt/mL). That’s a more
reasonable value for an IV flow rate.

__Handout 27__

**21 b****.** Again, I am questioning my flow
rate calculation this one seems low & really long.

Here it
is: (60 gtt/1 mL) x (250 mL/1 g) x (1 g/1000 mg) x (2 mg/1
min) = 30 gtt/min

That’s what I get, too. Let’s see if it’s
reasonable. Since the drop factor is 60 gtt/mL, the flow rate would be 30 mL/hr or 0.5
mL/min (from 21a). Since the Lidocaine is dissolved in at least 250 mL of
D5W (the problem doesn’t directly say this, but I’m pretty sure that’s a
reasonable deduction from the label info.), it would take about 8 hours and 20
minutes [= 250 mL x (1 hr / 30 mL) ] to
deliver the whole 250 mL. That’s probably reasonable, assuming that the
Lidocaine is being given for medium-term pain relief.