**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 **

** 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 **

** min 1 ml 8 hrs 60 min**

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

2nd Row - 1~~ml~~ 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 **

** 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 **

** 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