Dimensional Analysis 

                                        (DA)

 

 

   The Dimensional Analysis (DA) is a method used to calculate math problems by cancelling out the unwanted units to get to our final unit which would be our answer. I personally do not like this method but I thought I will create a tutorial about it for those who are interested and rather much like challenging calculations.

 

 

                                                

 

Ex 1.) A nurse must infuse 1000 ml of IV fluids over 8 hours. The tubing drop factor is 10 gtt/ml. How many gtts/min will there be?

 

Step 1: On the left place what you are solving for by placing an X for the unknown

                 X gtts 

                              min

Step 2: Next to that place information dealing with drops (gtts) on the right 

 

                X gtts =   10 gtt

                            min              1 ml

 

Step 3: Next to that place information dealing with ml and time

 

             X gtts10 gtt  X  1000 ml

                            min             1 ml          8 hrs

 

Step 4: Next to that place information dealing with time conversion because as you can see the problem provided time in hours and we need an answer that will have a time in minutes

 

            X gtts10 gtt  X  1000 ml  X  1 hr

             min      1 ml          8 hrs        60 min

 

Step 5: Cross out units that we do not need. Remember we need to leave units open that deal with our answer which is gtt/min

 

            X gtts10 gtt  X  1000 ml 1 hr

             min      1 ml          8 hrs        60 min

 

Step 6: Now we can calculate by multiplying the first row, and the second row

 

           X gtts10 gtt  X  1000 ml 1 hr

            min      1 ml          8 hrs        60 min

 

 1st Row - 10 gtt x 1000 ml x 1 hr = 10,000 gtts

 2nd Row - 1ml x 8 hrs x 60 min = 480 min

 

Step 7: Divide 1st and 2nd row together to get our final answer

 

           10,000 gtts / 480 min = 21 gtts/min

 

 

Ex 2.) A patient with hyperglycemia has an order for regular insulin IV at a rate 8 units/hr. The concentration is insulin 50 units in 100 ml of 0.9% NS. At what rate in milliliters per hour, will the IV pump be programmed? 

 

Step 1: On the left place what you are solving for by placing an X for the unknown

                 X ml 

                               hr

Step 2: Next to that place information dealing with ml and units

 

                 X ml100 ml

                               hr          50 units

 

Step 3: Next to that place information dealing with units and time

 

              X ml 100 ml      X   8 units

               hr     50 units       1 hr

 

     If you noticed we will not need to convert the time since the question provided us with the hour and the answer is also asking for hours instead of minutes

 

Step 4: Cross out units that we do not need. Remember we need to leave units open that deal with our answer which is ml/hr

 

             X ml 100 ml      X   8 units

              hr     50 units       1 hr

 

Step 5: Now we can calculate by multiplying the first row, and the second row

 

            X ml 100 ml      X   8 units

             hr     50 units       1 hr

 

 1st Row - 100 ml x 8 units = 800 ml

 2nd Row - 50 units x 1 hr = 50 hrs

 

Step 6: Divide 1st and 2nd row together to get our final answer

 

              800 ml / 50 hrs = 16 ml/hr

 

                                                                            

 

1.) A postoperative patient has an order for 200 ml 0.9% normal saline solution (NS) over 2 hours. The tubing drop factor is 10 gtt/ml. At what rate in drops per minute should the NS be infused?

 

Answer: 17 gtts/min

 

2.) A patient has an order for regular insulin IV at a rate of 5 units/hr. The concentration is insulin 100 units/100 ml 0.9% NS. At what rate in milliliters per hour should the IV pump be programmed?

 

Answer: 5 ml/hr