Steps for Dimensional Analysis for Dosage Calculations

Furosemide 50mg IV push now.
Available: Furosemide 40mg/10mL
How many mL will you give using dimensional analysis?

To calculate the volume in milliliters (mL) of Furosemide 50mg, using dimensional analysis, we can set up a proportion based on the given information. Here’s how you can do it:

Step 1: Determine the given values and the desired value:
Given:
– Furosemide concentration: 40mg/10mL
– Desired Furosemide dose: 50mg

Desired:
– Volume of Furosemide to be administered (in mL)

Step 2: Set up the proportion:
We can set up a proportion to relate the available concentration to the desired dose.

40mg/10mL = 50mg/x mL

Step 3: Solve the proportion:
Cross-multiply and solve for x:

40mg * x mL = 10mL * 50mg

40x = 500

Step 4: Solve for x:
Divide both sides by 40 to isolate x:

x = 500 / 40

x = 12.5 mL

So, using dimensional analysis, you would need to administer 12.5 mL of Furosemide to achieve a dose of 50mg.

The IV order is for D5W to infuse at 100 mL/hr. The drop factor is 10 gtt/mL. How many drops per minute (gtt/min) should the IV be regulated using Dimensional analysis?

To calculate the number of drops per minute (gtt/min) for an IV infusion of D5W at a rate of 100 mL/hr, using dimensional analysis and the given drop factor of 10 gtt/mL, you can follow these steps:

Step 1: Determine the given values and the desired value:
Given:
– IV infusion rate: 100 mL/hr
– Drop factor: 10 gtt/mL

Desired:
– Number of drops per minute (gtt/min)

Step 2: Convert the given rate from mL/hr to mL/min:
Since we need the rate in minutes, we have to convert the given rate from hours to minutes. There are 60 minutes in 1 hour, so:

100 mL/hr * (1 hr / 60 min) = 100/60 mL/min

Simplifying, we have:
100/60 mL/min = 5/3 mL/min

Step 3: Convert mL/min to gtt/min using the drop factor:
To convert mL/min to gtt/min, we need to multiply by the drop factor (10 gtt/mL):

5/3 mL/min * 10 gtt/mL = 50/3 gtt/min

Step 4: Simplify the fraction:
To simplify the fraction, divide the numerator by the denominator:

50/3 gtt/min ≈ 16.7 gtt/min

Step 5: Round the value:
Since the drop count must be a whole number, we should round down the value to the nearest whole number (integer):

16.7 gtt/min ≈ 16 gtt/min

So, using dimensional analysis, you should regulate the IV infusion at a rate of 16 drops per minute (gtt/min).