This article will demonstrate you how to determine hole size by fluid caliper. First of all, you need to know what is the fluid caliper is. The fluid caliper is one simple way to calculate hole diameter. The concept is based on hole volume, annular capacity, and inner capacity. You pump any substance and when you seen it on surface, you back calculate the hole size based on strokes pumped. It is quite tricky to explain so I would like you to see the example below which it will make you clear about what I say.
7” casing shoe is set at 5000’MD/4500’TVD
7” casing 23 ppf, ID 6.33 inch
4” drill pipe is used to drill the well and its ID is 3.34 inch.
4-3/4” drill collar is used as BHA and its ID is 2.5 inch. The length of drill collar is 500 ft.
This hole section is used water based mud and the bit size is 6-1/8”
Drill to section TD at 10,000’MD/9,000’TVD then drop carbide once TD is reached.
Pump output is 0.1 bbl/stroke.
Surface line from pumps to rig floor is 20 bbl.
Carbide is detected by a gas sensor on surface after 4,000 strokes pump.
With the given information, determine what is the hole size of the open hole section.
The basic drilling formulas that you need to know are inner capacity and annular capacity calculation.
1st step – Determine Inner Capacity and Annular Capacity of All Parts
Inner capacity of 4”DP
Inner capacity of 4”DP = 0.01084 bbl/ft
Inner capacity of 4-3/4”DC
Inner capacity of 4-3/4”DC = 0.00607 bbl/ft
Annular capacity between 4” DP and 7” Casing
Annular capacity between 4” DP and 7” Casing = 0.02383 bbl/ft
I assign “d” is the open hole diameter.
Annular capacity between 4” DP and open hole
Annular capacity between 4 3/4” DP and open hole
2nd step – Determine Volume of All Parts
Volume in 4”DP = Inner capacity of 4”DP x length of 4” DP
Volume in 4”DP = 0.01084 x 9,500 = 103 bbl
Volume in 4-3/4”DC = Inner capacity of 4-3/4”DC x length of 4-3/4”DC
Volume in 4-3/4”DC = 0.00607 x 500 = 3 bbl
Volume between 4”DP and 7” Casing = Annular capacity between 4” DP and 7” Casing x length of 4” DP inside 7” casing
Volume between 4”DP and 7” Casing = 0.02383 x 5,000 = 119 bbl
Volume between 4”DP and open hole = Annular capacity between 4” DP and open hole x length of 4” DP inside open hole
Volume between 4-3/4”DC and open hole = Annular capacity between 4-3/4”DC and open hole x length of 4-3/4”DC inside open hole
3rd step – determine hole size. The total volume pump is equal to total volume in the system.
With the pump output of 0.1 bbl/stroke, 4000 strokes equate to 400 bbl.
In the following equation, I account for the surface volume from the pump to the rig floor.
Solve the equation to get d, d is equal to 6.97”.
Answer: You will get the hole size based on the fluid caliper of 6.97 inch.
I wish this article will give you idea on how to calculate hole size based on the fluid caliper.
Reference book: 
Formulas and Calculations for Drilling, Production and Workover, Second Edition