25 March 2008

Revised: 30 Mar 2008

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



Some Solved IV Drip Rate Problems (Chapter 10)


Below are excerpts from e-mails Iíve 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

Ö in problems six, seven, and eight, theyíve 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, itís 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 doiní, but itís not too bad.  The flow rate is given as a weight (mass) flow rate, 30 mg / min.  Iíd start there and try to transform the weight flow rate (mg/min) into the required volume flow rate (mL/hr).  Hereís 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 (ďhow long to drive 240 miles to Amarillo at 60 mi/hrĒ or 1 hour per 60 miles):

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 Studentís Question

Ö 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 Amarillo and my bucket-of-bolts jalopy will go only 60 mi / hr, then I'll "consume" the 240 miles at the rate of 60 miles each hour until 4 hours have passed and all the miles have been consumed.


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 itís asking for is the volume flow rate thatís stated in the problem, that is, 10 mL/hr.  Thatís what youíd need to set the infusion pump.  Itís 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 donít think thatís what theyíre asking.  Iíll be very specific about the answer units on the test, so there shouldnít be any doubt.

Handout 26

15 b.(vastly revised and expanded) 

Letís work this problem by a more orthodox solution technique than the one I first posted.Hereís 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, letís 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 youíll do the arithmetic again youíll 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).  Thatís 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

Thatís what I get, too.  Letís see if itís 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 doesnít directly say this, but Iím pretty sure thatís 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.  Thatís probably reasonable, assuming that the Lidocaine is being given for medium-term pain relief.