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 gtts = 10 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 gtts = 10 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 gtts = 10 gtt X 1000 ml X 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 gtts = 10 gtt X 1000 ml X 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 ml = 100 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