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Welcome to our new and updated site. Browsing through the site you will find information on mass and liquid measurement as well as discussions on many of the latest consumer measurement issues. Take a look at our ever popular and expanding calculators & conversion sections.

We have just added sections on calibrating open neck provers and made available our Gravimetric Proving Worksheet. Also now available is the H2O density reference book and an open neck proving worksheet. There is so much to see, please look around and don't hesitate to contact us with your comments or to enquire about your custom metrology software needs.

Come back often as we are still editing daily and there will always be lots of new information. Please drop us an email and let us know what you think.

Volume Standards

Proving (static)    Proving (dynamic)

Proving Methods (Static)

Open Neck Provers    Gravimetric Provers   
Vapour Displacement

Static meter proving most commonly utilizes open neck prover vessels for low Vp products. Static proving of high Vp products generally is performed with Gravimetric or Vapour Displacement Provers.

The disadvantage of using a static prover is that the entire volume of a single proving run must be contained within the proving vessel. For small flow rate meters this is not too much of a concern, but as the size of the meter increases, so too must the size of the prover. The rule of thumb is that the prover must be capable of containg at least 1 minute flow at the maximum rated capacity of the meter. Although they are available in larger sizes (up to about 4 500 litres), open neck provers are commonly available up to about 2 500 litres. Above this size they become too large to be practical and you must look to a dynamic proving method.

Mass Flow meters may be proved using a scale or scales and, if results are to be displayed in units of volume rather than mass, some method of determining product density (pycnometer).

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Open Neck Provers

1 500 litre prover

Using an open neck prover requires the operator to make an adjustment for the effect of temperature on the steel in the proving vessel (CTS).

The correction for the effect of temperature on the proving vessel can be made using the formula

CTS = 1 + (Tp-15)Em

Tp = temperature of the prover shell in degrees Celsius. (This is essentially the same as the temperature of the liquid in the prover.)
Em = Coefficient of Cubical Expansion/degree Celsius of the material of which the prover shell is constructed.

This particular prover is constructed from type 304 Stainless Steel which has a cubical coefficient of expansion of 0.000 051 84/ °Celsius.

As the product in this prover is open to the atmosphere (Low Vapour Pressure), corrections for Pressure (CPL, CPS) are not required. The correction for effect of temperature on the product is quite often accounted for in Canada as most commercial/retail fuel sales are "Compensated to 15 °Celsius." This correction, CTL (Correction for the temperature of the liquid) is made using the appropriate API Volume Reduction Tables.

The prover is rated as "to deliver" 1 500 litres at 15 °Celsius, providing it has first been completely "wet down" with product, drained and allowed to "drip" for 1 minute after final draining. This ensures that all subsequent measurements are taken from a common zero or reference point. A slightly different design utilizes a second sight glass at the bottom to establish the zero mark.

Calibration of Open Neck Provers

Volumetric standards, except milk meters used in the milk industry, are calibrated to a reference temperature of 15 °C. Stainless steel provers used for the inspection of milk meters are calibrated to a reference temperatures of 4.4 °C.

Volumetric calibration is usually done using water at a temperature which will likely not be 15 °C. Therefore, it is imperative to compensate for the difference between the actual test temperature and 15 °C. Correction factors are used to take into account the thermal expansion or contraction of the water and of both the prover and the master standard.

To find the cubical coefficient of thermal expansion for the prover and the master standard, you should consult the manufacturer's specifications or the measure itself which is often stamped with this information. The following table will provide some commonly used values.

Cubical Coefficient of Thermal Expansion
Material CCE per °C
Stainless steel type 304 5.184 x 10-5
Stainless steel type 316 4.54 x 10-5
Seraphin™ Stainless steel 4.77 x 10-5
Mild steel 3.35 x 10-5
Invar™ (used in some small volume provers) 4.32 x 10-6
Aluminium (not suitable for most provers) 7.14 x 10-5
Brass (may be used in smaller measures) 5.72 x 10-5

Note: The cubical coefficient of thermal expansion (CCE) of a material is related to its linear coefficient of thermal expansion (LCE) by a factor of 3:

CCE = 3 x LCE or LCE = 1/3 x CCE

Densities of water at different temperatures provided in Wagenbreth and Blanke table are used to calculate coefficients of expansion for calculating the volume correction of volumetric standards.

click for larger version...

A PDF copy of the Wagenbreth & Blanke densities from 0.01 °Celsius to 40 °Celsius in 0.01 °C increments, is available from APLJaK Ventures. APLJaK Ventures can also supply worksheets (MS Excel or Lotus 123) to complete these calculations. Please contact us for more information.

Volume Correction to 15 °Celsius

VCF = [1 + (Tr - 15) (a)] Dr ÷ [1 + (Tp - 15) (b)] Dp


Tr = average temperature in the master standard
Tp = temperature in the prover under calibration
a = cubical coefficient of expansion/°C of the master standard
b = cubical coefficient of expansion/°C of the prover to be calibrated
Dr = water density in the master standard from the Wagenbreth and Blanke table
Dp = Water density in the prover to be calibrated from the Wagenbreth and Blanke table


A 1500-litre prover made of mild steel is calibrated using a 500 litre master standard made of stainless steel. The temperature recorded in the master standard for each draft is respectively 6.0, 7.0, 8.0 °C. The temperature recorded in the prover to be calibrated after filling is 8.5 °C.

It is clear that it will take three drops from the master standard to fill the prover to be calibrated. The calculations are:

Drop #1 (full calculations)

VCF = [ 1+ ( 6.0 - 15 )( 0.00005184) ] 999.9400 ÷ [ 1+ ( 8.5 - 15 )( 0.0000335) ] 999.8157

VCF = [ 1+ (-9.0)(0.00005184) ] 999.9400 ÷ [ 1+ (-6.8)(0.0000335) ] 999.8157

VCF = 0.999533 x 999.9400 ÷ 0.999782 x 999.8157

VCF = 999.4734 ÷ 999.5980 = 0.999875

Calculated volume = Nominal Volume x VCF

Calculated volume = 500 litres x 0.999875 = 499.938 L

Drop #2 (abbreviated)

VCF = [ 1+ ( 7.0 - 15 )( 0.00005184) ] 999.9011 ÷ [ 1+ ( 8.5 - 15 )( 0.0000335) ] 999.8157

VCF = 0.999889

Calculated volume = 500 litres x 0.999889 = 499.944 L

Drop #3 (abbreviated)

VCF = [ 1+ ( 8.0 - 15 )( 0.00005184) ] 999.8477 ÷ [ 1+ ( 8.5 - 15 )( 0.0000335) ] 999.8157

VCF = 0.999887

Calculated volume = 500 litres x 0.999887 = 499.943 L

Total Volume = Drop 1 + Drop 2 + Drop 3

Total Volume = 499.938 + 499.944 + 499.943 = 1499.825 L

Correction = Prover Nominal Volume - True Volume

Correction = 1500 litres - 1499.825 litres = 0.175 litres


An additional 175 ml of water (at 15 °C) must be added to achieve a true 1500 litres at 15 °C.

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Gravimetric Provers

Gravimetric Proving is done with a Gravimetric Prover. The prover is simply a scale mounted tank suitable for capturing a discrete volume of product to be measured.

Gravimetric Proving (proving by weight) is commonly used for testing and calibrating meters used on LPG (propane) and NH3 (Anhydrous Ammonia). These provers may be quite large but are most commonly used for smaller meters due to their unwieldy sizes. The scale mounted tank will be mounted either on a truck or a trailer. It is plumbed to allow product to be pumped into the tank and then back out to storage. If the meter is calibrated in units of volume some method of determining the products density at the test temperature must be available so that the weights may be converted back to volume. Although there are several methods available, the most reliable one is a clear pressure jar in which floats a hydrometer (and a thermometer - required for hydrometer corrections).

300 litre mass prover
Hydrometer Pressure Jar

The 300 litre mass prover in operation testing a small retail LPG dispenser (not seen in picture). Note the dispenser nozzle is connected to the hose reel inlet to circulate product and stabilize temperature before testing. The red weights on the side of the prover are to test the scale before using the prover to test the dispenser.

The calculations required to use a Gravimetric Prover for testing volumetric meters are quite involved but consist of the following basic steps.

Correct the Register/Meter reading to standard conditions:

  1. A sample of the product is taken and density is determined. This is often done in a pressure jar with a hydrometer and thermometer.
  2. The density determined above is corrected to a standard density at 15 °C using ASTM-IP Table 53.
  3. A test run of product is pumped into a scale borne tank and weighed.
  4. Product Temperature and Pressure are recorded during the filling of the tank.
  5. The non-compensated or Gross Register reading is recorded.
  6. The Volume Reduction Factor (VRF) at 15 °C is determined using ASTM-IP Table 54.
  7. The Vapour Pressure (Vp) for the product is determined using the average meter Temperature and the Corrected Density.
  8. The Pressure Correction Factor (PCF) is determined using the difference between the actual Pressure and the Vapour Pressure. Pressure = Observed Pressure - Vapour Pressure. A factor of 1.002 may be used if actual pressure is unknown.
  9. A corrected gross reading is determined. Corrected Gross = Gross Register x VFR x PCF.

Calculate the known volume in the prover:

  1. Read Net weight of product in tank on scale in kilograms.
  2. Divide Net weight of product by Corrected Density of Propane at 15 °C in kg/litre.
  3. Subtract the Known Volume in the prover from the Corrected Gross Reading determined previously to find the error.

Test the Automatic Temperature Compensation (ATC) if equipped:

  1. Record both the Gross and Net meter readings from the meter being tested.
  2. Divide the Net meter reading by the Gross meter reading to find the actual Volume Reduction Factor (VRF).
  3. Using the VRF Table (ASTM-IP Table 54), determine if the actual VRF is within the acceptable VRF range (usually +/- 1 °C)

The author can provide worksheets to complete these calculations. Please contact APLJaK Ventures for more information.

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Vapour Displacement Provers

This section will be expanded upon shortly. Please stay tuned....

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Proving Methods (Dynamic)

Pipe prover    Compact prover

Dynamic meter proving utilizes pipe provers, piston provers, compact provers or master meters. These prover types are known as closed systems and are acceptable for use on both high and low Vp products. Closed system provers will generally require correction factors for pressure and temperature differences between the prover and the meter under test (DUT).

Master Meters are seldom used due to the fact that they have the same inherent problems as the meters that they are being used to prove and because they themselves require proving before they may be used.

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Pipe Provers

skid mounted pipe prover static pipe prover

Pipe prover is a generic name given to a family of closed circuit provers used to "prove" meter performance. They are generally composed of a section of pipe of constant size in which a piston or sphere is moved along by the flowing liquid to be measured. The piston or sphere passes a start and a stop detector. The pulses received from the meter under test (DUT) are counted while the displacer moves between the start and stop detectors. As the volume between these two detectors is known (determined by water draw), the pulses per litre of product can be deduced.

Pipe provers may be referred to as uni-directional or bi-directional spheroid provers or bi-directional piston provers. The API requires that a minimum of 10 000 meter pulses be obtained to ensure an accurate picture of meter performance. This value is based upon the assumption that there may be an error of 1 pulse each time a detector is passed. Therefore, there may be a 2 pulse error in any one run. 2 parts in 10 000 is equal to a possible error of 0.02%. A lower number of total pulses would mean a potentially larger, and therefore unacceptable, error being introduced by the detectors. There is another type of "pipe prover", generally referred to as a Small Volume, Compact or Piston Prover. These use pulse interpolation to obtain comparable results using less pulses.

The prover must be sized appropriately for the meter to be tested. In addition to the requirement of 10 000 minimum pulses, the displacer velocity must be calculated.

Vd = 0.212 * [Fl / Dia2]

Vd = The velocity of the displacer in m/s
Fl = the meters flow rate in litres/min
Dia = the inside diameter of the prover in cm

The velocity should fall within the following ranges:
Uni-Directional Pipe Prover = 0.1 m/s < 1.5 m/s
Bi-Directional Pipe Prover (ball type) = 0.1 m/s < 3.0 m/s
Bi-Directional Pipe Prover (piston type) = 0.1 m/s < 1.0 m/s

Determination of Meter Performance with a Pipe Prover
Correction Factors for Temperature and Pressure Effects
on Prover Volume
Cts The correction factor for the effect of temperature on steel
Cts = 1 + (Tp-15)Em

Tp = temperature of the prover shell in degrees Celsius. (This is the same as the temperature of the liquid in the prover.)
Em = Coefficient of Cubical Expansion/degree Celsius of the material of which the prover shell is constructed.

Cps The correction factor for the effect of pressure on steel
Cps = (1 + [(P * D)/(E * t)])

P = Internal Pressure in KPa(gauge).
d = Internal diameter of the prover in cm.
E = Modulus of Elasticity of material used in construction of the prover shell.
t = Wall thickness of prover in cm.

Correction Factors for Temperature and Pressure Effects on Liquid Volume
Ctl The correction factor for the effect of temperature on the liquid
Ctl = looked up in API Tables (54)

Note: corrections are made using the products density at 15 degrees Celsius and either 101.325 KPa or equilibrium Vapour Pressure (only if Vp > 101.325 KPa @ 15 degrees Celsius)

Cpl The correction factor for the effect of pressure on the liquid
Cpl = (1 / [1 - (P - Pe) * F])

P = Internal Pressure in KPa(gauge).
Pe = Equilibrium Vapour Pressure in KPa. (Note: most VP charts are in terms of absolute pressure. To use these, 101.325 KPa must be subtracted from the readings.) F = compressibility factor for hydrocarbons from API Chapter 11.2.2M

Combined Correction Factors
CPV Corrected Prover Volume
CPV = Cts * Cps * Ctl * Cpl * Actual Prover Volume

CMV Corrected Meter Volume
CMV = Average Pulses * [(Ctl * Cpl) / Kp]

Kp = Number of Pulses / Gross Displayed Volume

MF New Meter Factor

Meter Error (% Registration) = (Old Meter Factor - New Meter Factor) * 100%

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Compact Provers

Compact or Piston (sometimes referred to as small volume) provers are similar to standard pipe provers with the noticeable difference that the displacer is not free, it is in fact a piston connected to a piston rod. The rod extends outside the barrel of the prover and is usually fitted with an indicator either of the micrometer type, or fully electronic using a displacement transducer and flags/proximity switches.

Due to the relatively small volume of product displaced by the pistons travel or stroke, a means had to be found to ensure compliance with the API's recommended standard minimum of 10 000 pulses per run. The means employed was pulse interpolation.

There are several methods of employing pulse interpolation, but by far the most used is the dual chromometry (double clock) method (see API Chapter 6. Proving Systems - Pulse Interpolation). Essentially this method involves the use of two timers (T1 & T2) both driven by the same hi speed clock (>1 Megahertz) oscillator. The sequence employed is:

  1. Start Timer 1 (T1) when first detector switch is activated.
  2. Start Timer 2 (T2) at the leading edge of the next flow meter pulse following T1 start. (This is also where the pulse counter will start counting)
  3. Stop Timer 1 (T1) when the final detector switch is activated.
  4. Stop Timer 2 (T2) at the leading edge of the next flow meter pulse following T1 stop. (This is also where the pulse counter stops counting)
double chronometry pulse counting

the formula to determine the number of full & partial pulses is then:

actual pulses = pulses counted [n+1] * T1/T2


double chronometry formula

K = proving K factor
T1 = time elapsed for Timer 1 over duration of run
T2 = time elapsed for Timer 2 over duration of run
n+1 = number of pulses counted during T1 timing
Vol = base volume of the prover

The other correction factors for Ctl, Cps & Cpl are made as for pipe provers above. However, the factor for Cts (Correction for Temperature Effects on the Steel) are made differently. The value for Em (cubical coefficient of expansion for prover material) must be changed to reflect the square coefficient of expansion for prover material (CCE/3 * 2) and a new variable for the linear coefficient of expansion of the prover rod must be added. Most prover rods are made of a nickel alloy called Invar. The linear coefficient of expansion of Invar is very low (4.32 x 10-6 / °C) which means that the length of the rod changes little with temperature changes.

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Last modified: 25 August 2012 16:13:58