### Introduction

The High Brix Measurement by Dilution Calculator determines the specific gravity of a liquid from a specific gravity measurement after it has been diluted with a given volume of water. This calculation is useful for determining the specific gravity of high-Brix liquids such as honey or concentrates with specific gravities that are outside of the range of standard hydrometers or refractometers.

The calculator will adjust the hydrometer reading for temperature if the measurement temperature and the hydrometer calibration temperature are provided. If the entered SG value is already corrected for temperature, or if temperature corrections are not desired, simply enter 20°C (68°F) in both of the temperature fields and no corrections will be made. Details of the hydrometer temperature correction calculations can be found here. The temperature correction is applied only to the hydrometer reading and not to the liquid volumes. The temperatures of the original liquid and the added water should be about the same so that the correct dilution ratio is used in the calculation.

The accuracy of this calculation is highly dependent on how thoroughly the diluted sample is mixed. If the diluted sample is not mixed well, the measured SG might not be representative of the mixture, which would result in an inaccurate SG estimate for the original liquid.

### Input Field Definitions

Measurement Type – Select from hydrometer or refractometer. Hydrometer measurements will be temperature corrected if desired.

Sample Volume – The original volume of the sample to be diluted.

Water Added – The volume of water added to dilute the sample.

Refractometer Reading – The refractometer reading for the diluted sample. Required only if refractometer was selected as the measurement type. Range: 0° to 100°Brix

Hydrometer SG Reading – The hydrometer SG reading for the diluted sample. Required only if hydrometer was selected as the measurement type. Range: 0.77193 to 1.55454

SG Reading Temperature – The temperature of the diluted sample at the time of the SG reading. Required only if hydrometer was selected as the measurement type. Range: 0°C (32°F) to 40°C (104°F)

Calibration Temperature – The hydrometer calibration temperature of the hydrometer used to take SG reading. Required only if hydrometer was selected as the measurement type. Range: 0°C (32°F) to 40°C (104°F)

### Output Field Definitions

Corrected SG (20°C/20°C) – The temperature-corrected SG value. Reported only if hydrometer was selected as the measurement type.

Calculated Sample SG – The calculated SG of the original sample prior to dilution.

Diluted Volume – The calculated volume of the diluted sample, which is not simply the sum of the sample and water volumes because of solution effects.

### Calculation Details

We can calculate the specific gravity of the original sample using the previously developed mass balance equations (2-12) and (2-13), repeated here for completeness:

v = _{f}sg_{f}ρ_{w}B_{f}v + _{i}sg_{i}ρ_{w}B_{i}m_{sa}B_{s} |
(2-12) |

v = _{f}sg_{f}ρ_{w}v + _{i}sg_{i}ρ_{w}m + _{sa}v_{wa}ρ_{w} |
(2-13) |

where:

*v _{i}* = initial must volume, liters

*v _{f}* = final volume, liters

*sg _{i}* = initial specific gravity

*sg _{f}* = final specific gravity

*B _{i}* = initial Brix

*B _{f}* = final Brix

*B _{s}* = sugar Brix

*ρ _{w}* = density of water = 0.9982 kg/liter at 20ºC

*m _{sa}* = mass of sugar added, kg

*v _{wa}* = volume of water added, liters

In this case the known values are *v _{i}*,

*sg*,

_{f}*B*, and

_{f}*m*. Given that we are adding only water and no sugar, we can re-arrange equation (2-13) to solve for the final (diluted) volume

_{wa}*v*to get:

_{f}v = (_{f}v + _{i}sg_{i}v) / _{wa}sg_{f} |
(2-27) |

Then we can solve equation (2-12) for the original Brix of the sample *B _{i}* to get:

B = (_{i}v) / (_{f}sg_{f}B_{f}v)_{i}sg_{i} |
(2-28) |

Since *sg _{i}* and

*B*are interdependent, the solution must be obtained iteratively.

_{i}