Calculation of water volume in a well casing:

Here we explain how to calculate the volume of water in a well casing. We provide a Table of Volume of Water in a Well as well as the formulas for calculating the static head and total dynamic head of a well.

Well Water Volume Calculations

This article series describes how we measure the amount of water available and the water delivery rate ability of various types of drinking water sources like wells, cisterns, dug wells, drilled wells, artesian wells and well and water pump equipment.

How is well quantity measured? How do well static head volume, height, pressure vary over time?

Question: What happens to well flow when we install a more powerful water pump? Answer: We exhaust the well static head volume more quickly.

[Click to enlarge any image]

This sketch, courtesy of Carson Dunlop Associates offers a graphic explanation of well static head. The static head in a well is is not the total amount of water than can be pumped out of the well, it's just where we start.

Article Contents

• CALCULATE WATER VOLUME per FOOT of WELL CASING
• TABLE OF WELL WATER VOLUME / QUANTITY per FOOT
• VOLUME of WATER IN a PIPE - CALCULATION
• VOLUME of WATER IN a CYLINDER - CALCULATION
• STATIC HEAD HEIGHT VOLUME CALCULATION
• TOTAL DYNAMIC HEAD CALCULATION

How to Calculate the Gallons of Water per Foot of a Well Casing

We have about 1.5 gallons of water per foot of depth of a well when we're using a standard residential 6" well casing. The height of water column inside the well and available to the pump is less than the total well depth.

[Click to enlarge any image]

With the exception of artesian wells, the well water column height does not extend from the well bottom to the top of the ground. Rather the top of the water in a conventional drilled or dug well at rest will be somewhere between the well bottom and well top, depending on the seasonal water table and other factors.

In an artesian well natural water pressures in the aquifer would force well water out at the top of the well casing.

For artesian wells the well is usually constructed with a seal inside the well casing to prevent water from rising above the point at which a water supply pipe exits the well casing. In an artesian well the static head water height will normally be from the well bottom to the point at which the casing seal has been installed.

Static head location in a well

In this sketch, distance (h) is the "static head" which is the total volume of water available to the pump.

The static head in a drilled well extends from the water intake at the pump (since water can't jump up to the pump intake) upwards to the highest point that water reaches inside the well casing when the well has rested and reached its normal maximum height.

Well water quantity calculation at pump startup

• (a) air in top of the well casing: water rises only to a height somewhere below the very top of the well.
• (h) static head: explained above
• (c) well bottom clearance: our well pump or foot valve (if the pump is not in the well) was placed 5' off of the well bottom © in the sketch, a distance to avoid drawing mud into the pump
• (d) total well depth: measured from the top of the ground to the bottom of the well. More about measuring the depth of a well is
  
  at DEPTH of a WELL, HOW TO MEASURE.

Table of Volume of Water in a Well or Pipe Per Foot or Meter

Notes to the table above

Notes:

Pipe diameters used here are the nominal or internal diameter or I.D. of the pipe.

The Static Head height or Actual Water Volume in the Well Bore is normally Less Than Total Well Bore Volume

The table above gives the volume of a cylinder (or well bore) of various diameters per foot of height or per meter of height.

Watch out: The volume of water inside of a well bore or well casing is normally less than the total volume inside the well bore cylinder.

The actual water volume is just for the portion of the casing that actually contains water when the well is at rest - don't count the air.

The portion of the well casing that is filled with water, or slightly more narrowly, the cylinder of water that extends from the pickup bottom point of the foot valve or submersible pump (the bottom of the usable water column) up to the top of the water column when the well is fully rested and recovered, is the well's static head.

The static head will generally be less than the volume of the whole well bore since water in the well does not rise to the top of the well bore.

Exception: the level of water in artesian wells will, if not deliberately blocked from doing so, rise to the top of the well bore.

1. Special thanks to readers Steven (October 17 2017) and Valerie (5 August 2017) for correcting our arithmetic errors.

2. 1 U.S. gallon contains 231 cubic inches

3. 1 Litre or liter contains 1000 cc's or cm³

4. 1 cubic foot contains 1728 cubic inches

The formulas for volume of a cylinder and thus of water in a well casing are shown and a examples are calculated below.

Calculate the volume of a Cylinder, Tank, Well or Pipe

E.g. volume of water or gallons of water stored in water piping or in a well bore

In some circumstances such as deciding how much water to flush out of a pipe for certain water tests, it is useful to know the volume of water required to fill well piping or water piping.

But let's be clear - the volume of water resting in well piping does not increase the volume of water available at a property. That is, the water stored in well piping does not increase (nor decrease) the well's static head as we defined it above.

For long runs of well piping there may be a significant volume of water in the piping itself. Using 600' of plastic well piping as an example, we need simply to calculate the volume of a cylinder (the inside of a water pipe) into cubic inches per foot.

The volume of a cylinder V = pi x r² x h 

where pi = 3.1416,

r = cylinder radius (1/2 the diameter)

h = the cylinder height or length of pipe in our case and

G = the volume of water in U.S. gallons = 0.004329 gallons per cubic inch or more conveniently 1 U.S. gallon contains 231 cubic inches of liquid.

For U.K. readers,

G_U.K. = the volume of an imperial gallon is 277.419 cubic inches.

There is more water in long piping runs than one would have guessed.

To translate cubic inches of water inside of a pipe, 1 cu. in. is about 0.004329 gallons

• 1/2" internal diameter piping (that's a radius of 0.25") contains
  
  V = π r² h = π x 0.25² x 12 ≈ 2.35619 cubic inches

Divide the cubic inches by 231 (cu. in. per gallon)

G = 0.01 gallons per linear foot of pipe

• 3/4" internal diameter piping contains (.75/2)² x 3.1416 x 12 / 231 = 0.02 gallons per linear foot
• 1" internal diameter piping contains (1/2)² x 3.1416 x 12 / 231 = 0.04 gallons per linear foot

How to Calculate the Volume of Water Inside a Cylinder

The formula to calculate the volume of water in a cylinder is

Vcyl = pi x r² x h 

where

pi = 3.1416,

r = the radius of the circle formed by the cylinder (the well shaft or casing), and is simply 1/2 of the well diameter

h = the height of the cylinder of water (the static head height that we measured above).

Watch out! be sure to write the radius and height in the same units of measure - here we're going to use inches.

Vcyl_inches = 3.1416 x r²_inches x h_inches

So for a 12-inch (one foot) height of 6" diameter steel well casing,

r = the radius = 1/2 of the diameter of the pipe, or 3" and

h = the height is 12"

Now we can calculate the static head water volume in cubic inches:

Vcyl_inches= 3.1416 x 3²_inches x 12_inches

Vcyl_inches = 339.29 cubic inches (in this example, for a one foot high, 6" diameter cylinder of water in a well casing)

How to convert cubic inches to gallons

1 U.S. gallon contains 231 cubic inches

so for our 6-inch well casing that contains 339 cubic inches per foot,

339 / 231 = 1.4675 gallons per foot or about 1.5 gallons.

Alternatively:

How to convert cubic inches to cubic feet

Since there are 1728 cubic inches in a cubic foot (12 x 12 x 12) we divide:

Vc_feet = 339 / 1728

Vc_feet = 0.196 cubic feet

How to Convert Cubic Feet to Gallons

since 1 ft³ = 7.48051 gal(US Liq),

Vc_gallons = 0.196 x 7.4 = 1.46 gallons

That's why we use an easy to remember "rule of thumb" of 1.5 gallons per foot of static head of water found inside of a 6" drilled well casing.

Metric Calculation of Well Casing Volume

Using the formula for the volume of a cylinder

For a well casing that is 15cm in diameter and 1 meter in height:

Radius r = 1/2 the diameter or 7.5 cm

Vcyl = pi x r2 x h

Vc_{in cc} = pi x (7.5cm)2 x (100cm)

Vc_{in cc} = 3.1416 x 56.25cm [the bore radius in cm, squared] x 100cm [the bore height in cm) = 17,671 cc or cubic centimetres

1 cc = 0.001

1 m of a 15cm diameter well bore will contain 17.671 L - that would be the correct entry in our table

Water volume calculation for other metric well diameters:

1m of a 13cm well bore will contain 3.1416 x (13/2)² x 100 ccs [per L] = 1.1416 x 42.25 x 100 = 13,273 ccs or 13.2L of water per meter

1 m (or 100 cm) of a 20 cm diameter well bore will contain 3.1416 x (20/2)² x 100 ccs = 3.1416 x 100 x 100 = 31,416 ccs or 31.4L of water per meter

1 m of a 120cm diameter dug well will contain 3.1416 x (120/2)² x 100 ccs = 3.1416 x 3600 x 100 = 130,976 ccs or 130L of water per meter

Formula to Calculate the Static Head of Water in a Well

To find the amount of water in the static head of a well, we find (h), the depth of the column of water in the well when the well is at rest, and then based on the well diameter we calculate the volume of (h) in cubic meters, feet, or inches. Last we convert that volume into common liquid measures such as liters or gallons.

Using the symbols and definitions given just above, the formula to express the size of the static head of water in a well first in feet of height is simply:

(h) = (d) - [(a) + (c)] - we subtract the well top air space and pump to bottom clearance distances from total well depth.

The actual water quantity in (h) is calculated based on the volume of the well cylinder interior.

In a standard 6" steel casing well, the water volume is about 1.5 gallons per foot of height of the static head.

Formula for Static Head Volume in Gallons of Water in a Typical 6" Steel Well Casing

Static Head (h)_gallons = (1.5 gallons per foot) x (h) measured in feet

Here's a simple example to calculate the volume of water in the static head of a particular 100 foot deep well. Remember that for your well you'll need to plug in the actual measurements.

(d) = total well depth = 100 ft.

(a) = air in top of well casing = 45 ft.|

(c) = well bottom clearance between pump intake and well bottom = 5 ft.

We want to calculate (h), the static head, in gallons of water - we just need to calculate the height of the column of water (in feet) inside the 6" diameter well casing and multiply it by 1.5 (gallons per foot)

Static head water quantity (h)_gallons = (Total well depth (d) - Air (a) - Clearance at bottom (c) ) x 1.5

Or if you prefer

(h)_gallons = (h)_feet x 1.5

For this example, using the (d), (a), and (c) measurements from above, we calculate (h)_feet and multiply it by 1.5 to find the static head in gallons - (h)_gallons

(h)_gallons = [(100 - 45 - 5) feet of height of static head ] x [1.5 gallons per foot]

(h)_gallons = (50) x 1.5

(h)_gallons = 75 gallons of water - that's how much water is in the static head of the example well.

Static Head Height, Volume Measurements for Other Well Types

Note that the static head description and calculations given in this article apply to round drilled wells and round dug wells.

If your dug well is a different shape, say a rectangle, the principles are the same but you'll need to use the formula for volume of a rectangular shape V= length x width x height rather than a cylindrical shape given above and again just below.

The static head of a driven point well is practically zero - just the volume of water inside the lower section of the driven well point (a pipe) below ground. For a driven point well, if you still want to know its static head, you might try the calculation of volume of water stored in water piping, just below.

How to Calculate Total Dynamic Head (TDH)

Question: How to Calculate TDH Total Dynamic Head for a flowing artesian water well

2021/02/05 Zakaria Hofra said:

We have a new flowing artesian well, and we want to size the perfect pump for it.
What is the perfect pump (submersible or centrifugal) kind for it?

What is the best depth to install the pump?
How to calculate total dynamic head of the system in such case?

This Q&A were posted originally at PUMP, SUBMERSIBLE OPERATION

Moderator reply: example calcuation of total dynamic head for a flowing artesian water well

Zak

Thank you for the artesian well questions including the calculation of TDH total dynamic head.

You will see that without knowing specifics of your well such as its bore depth and the height of its water column, nobody can tell you its TDH or Total Dynamic Head.

As a mere example, if your artesian well is producing water flowing at a rate of 1 liter per second through a 1-inch diameter 200 foot long plastic pipe through which water rises a total of 100 feet, then the total dynamic head or TDH could be calculated as 40.24 meters (132.021 feet) ³.

For other readers, TDH or "Total Dynamic Head" in a water well is defined as the total pressure measured when water is actually flowing through a system, made up of the vertical rise-height of water and the friction loss through the system.

The friction loss will be a function of pipe diameter, material, and should include the effects of elbows and fittings too.

• TDH = static water height + static water lift + friction losses in the system
• TDH = the pressure difference between the pressure at the inlet and outlet of a well pump when that pressure is measured at the same height or elevation and when the inlet and outlet pipes or openings are of the same diameter.
• TDH = the height of column of water that is to be pumped out of a well bore.

In a practical sense we would treat TDH similarly to as Static Head in a water well, that we define and describe in detail on this page.

There, Zakaria, you'll find sketches and formulas for calculating the TDH or total dynamic head or static head.

A careful calculation of TDH or total dynamic head will also include the effects of Friction Loss, also referred to as Head Loss - the restriction on water flow due to friction of water against the piping surfaces as well as losses due to fittings such as elbows and valves.

Watch out: there is a difference between Static or Total Dynamic Head in a well - the column of water from top of water of a well at rest to the point of intake into the well pump or footvalve - and what other sources might call "static head" but that properly would be called

Static Lift: the total height inside the well that water rises from the point of water entry into the submersible pump up to the pitless adapter where the well pipe leaves the casing.

Static Height: also referred to as Discharge Height: the total or maximum height from the outlet of a submersible pump to the point at which the piping turns horizontal to enter the building served.

The total amount of water from a conventional (not-artesian or not-flowing) well is the sum of the static head and the average flow rate or minimum flow rate of the well - the rate at which water flows into the well.

Watch out: there is no single "correct" flow rate for most wells. More accurately, flow rates, whether for a non-flowing well OR even for an artesian well are never a single simple number like "GPM". The flow rate into a well bore varies seasonally as well as at various points along the depth of the well bore and is more permanently affected by long term changes in the level of the water table that feeds the well.

Details are

at WELL YIELD DEFINITION where we describe the maximum amount of water one can get out of a well.

For example, in areas of Guanajuato, Mexico, outside San Miguel de Allende, once a few large factory farm companies bought up farmland and began industrial-level farming of crops, the rate of pumping of groundwater increased so dramatically (over the last 15-20 years) that the water table in that area dropped so percipitously that the older less-deep water wells used by local farmers dried-up and even trees in the area have all died from lack of water.

So, Zak, there is no possible single "right" or "best" generic answer to your question of the best depth at which to place your pump in an artesian well.

But in general, when using a submersible (in-well) water pump we put the pump 4-6 feet or a couple of meters above the well bottom. That gives us the maximum practical static head of water available to the pump while avoiding having the pump pick up sediment from the bottom of the well bore.

See more details

at WELL FLOW RATE

The flow rate of your flowing artesian well can and should be measured by the well driller: that's the rate of water naturally exiting the well before making any use of a well pump whatsoever. But as I warn above, that flow rate will vary over time and season and usage.

About your question of what is the "perfect pump", again I fear you're asking for Karnough the magician to give an answer to an unanswerable question. There is no perfect pump, since the best pump to use varies by individual well and water situation.

In general, shallow wells use an above-ground 1 line jet pump;

Deep wells use a 2-line jet pump or a submersible pump;

You'll probably get maximum pumping capacity from a submersible pump.

but

Watch out: if you try pumping water faster than the well's yield or flow-rate, you'll simply exhaust the well and unless a pump protection device is installed you'll damage or destroy your pump.

 

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