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285 lines
12 KiB
Markdown
285 lines
12 KiB
Markdown
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[](https://github.com/marketplace/actions/arduino_ci)
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[](https://github.com/RobTillaart/WaterMix/actions/workflows/arduino-lint.yml)
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[](https://github.com/RobTillaart/WaterMix/actions/workflows/jsoncheck.yml)
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[](https://github.com/RobTillaart/WaterMix/issues)
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[](https://github.com/RobTillaart/WaterMix/blob/master/LICENSE)
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[](https://github.com/RobTillaart/WaterMix/releases)
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[](https://registry.platformio.org/libraries/robtillaart/WaterMix)
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# WaterMix
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Arduino library for mixing water with different temperatures.
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## Description
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**Warning: Experimental**
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Experimental library for elementary math of mixing certain amounts of water or other
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(same) liquids with different temperatures.
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The library provides math **add()** for mixing a volume of a liquid with temperature T1
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with another volume of the same liquid with temperature T2.
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The **WaterMix** class of the library has **water specific** functions.
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The library does not support mixing different liquids as that would need the density
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function for every liquid involved. Furthermore not all liquids mix well with each other.
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The **add()** function can be called multiple times, e.g. to mix more than two amounts
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of liquids. One can also mix an other LiquidMix object (same liquids).
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Besides the **add()** the library supports:
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- **div()** to "split the liquid in equal amounts" and a
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- **mul()** to multiply it (magically) and
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- **sub()** to remove part of the liquid.
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This library is meant to be useful e.g. by doing "water math" for aquaria or cooking.
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Also the library is well suited for basic educational purposes.
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Since version 0.1.2, the library has a base class, named **LiquidMix** which can do
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the basic math. The extended math like in **WaterMix** needs a **density()** function
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and cannot be done as the liquid is unknown.
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For now the library is experimental and refactoring is expected.
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If you have requests, questions or ideas, let me know by opening an issue.
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By adding the LiquidMix base class the library allows easy derived classes
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like the WaterMix.
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#### Limitations
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The **LiquidMix** uses a generic volume parameter instead of gallons or liters as
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this way any user selected unit can be used.
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However you must use the chosen units consistently as the library cannot handle
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different units simultaneously.
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To use different units for volume you can convert them with the library named
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**VolumeConverter**.
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For the **LiquidMix** the temperature unit can also be chosen by the user and
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can be Kelvin, Celsius, Fahrenheit or other.
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However you must use the chosen units consistently as the library cannot handle
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different units simultaneously. Check **Temperature** library below for conversion.
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The **WaterMix** class must use the **Celsius** scale as the **density()** function
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used is defined in degrees Celsius.
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#### Accuracy
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The working range for temperature is not tested e.g. with real water.
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It is expected to work quite well for water with a range from 5°C to 80°C.
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In the basic math the **add()** function assumes there is no expansion so
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the density is identical for both volumes of waters.
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Of course this assumption is incorrect, therefore there will be a difference
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between the theoretical values and doing the mixing in practice.
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However these delta's are expected to be small, less than 1% in many cases.
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Given the accuracy of volume measurement and temperature measurement, this
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delta of 1% will often be acceptable.
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If one wants a more exact answer, one could use **WaterMix** class.
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This class supports the **addExact()** function which compensates for
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the density of the water at a given temperature.
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This function is much slower but will provide a more exact answer.
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#### Related
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- https://github.com/RobTillaart/Temperature
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- https://github.com/RobTillaart/VolumeConverter
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- https://github.com/RobTillaart/weight
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## Interface
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```cpp
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#include "WaterMix.h"
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```
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#### LiquidMix (base class)
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To be used with any liquid.
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- **LiquidMix()** constructor, starts with no liquid of 0°
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- **void begin(float volume = 0, float temperature = 0)**
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sets initial values, default no liquid of 0°.
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- **void add(float volume, float temperature)** add an amount of liquid
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with temperature to the "LiquidMix".
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- **void sub(float volume)** subtract a volume from the "LiquidMix".
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Temperature won't change.
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- **void div(float nr)** divide the amount of liquid, same temperature.
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- **void mul(float nr)** multiply the amount of liquid, same temperature.
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- **float volume()** get the current volume.
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- **float temperature()** get the current temperature.
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#### WaterMix
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WaterMix is specific for water and has the following additional functions:
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- **WaterMix()** constructor, starts with no water of 0°
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- **void addExact(float volume, float temperature)**
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add an amount of water with temperature to the "WaterMix".
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The math uses the **density** of the water at the given temperature.
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This is slower as **add()** but more exact.
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Note the temperature must be in °C.
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- **float mass()** get the mass of the current volume. Water only!
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- **float volume2mass(float volume, float temperature)** idem, Water only!
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Use volume == 1 to get the density of water at the given temperature.
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Assumption is no pressure.
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- **float mass2volume(float mass, float temperature)** idem, Water only!
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## Performance
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Most functions are minimal and fast, the ones that do the core math
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are **add()** and **addExact()**.
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The WaterMix_exact.ino sketch provides performance figures shown here.
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Note that the **addExact()** differs in runtime as it uses a linear lookup
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for the density so the numbers below are indicative.
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Tested on UNO, 16 MHz.
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| Version | Function | time (us) | Notes |
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|:-----------:|:------------:|:-----------:|:--------|
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| 0.1.1 | add() | 72 |
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| 0.1.1 | addExact() | 576 | most accurate |
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Note it is possible to improve the performance of the lookup of the density
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by reducing the amount of interpolation points in the tables (at your own risk).
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This will reduce the accuracy however still be better than the faster **add()**.
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Performance of **addExact()** can be improved by caching the mass of the water.
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As this is needed for every next **addExact()**. As the volume can be manipulated
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by **div()** et al, there must be additional code and/or a "dirty" flag.
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To be investigated.
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Finally the lookup can be improved by a binary search, however previous experience
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indicate that this only improves above a certain number of elements (~20).
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## Volumetric Coefficient of Expansion
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The VCE is related to density and not supported in the library.
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Math needs to be understood / investigated.
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(0.1.1 supports an **addExact()** for water only, temperature in °C)
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The VCE is useful as background information as the theoretical volumes
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calculated in this library will differ from reality due to the VCE effect.
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This difference depends on the liquid used and the delta temperature.
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#### Water
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The VCE of water depends on the temperature.
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Source: - https://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html
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| Temp °C | density | % wrt 4°C | V.C.E (\*10<sup>-4</sup>) | Notes |
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|:---------:|:------------|:----------:|:---------------------------|:--------|
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| 0.1 | 0,9998495 | 0,0125 | -0.68 | note negative value
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| 1 | 0,9999017 | 0,0073 | -0.50 | note negative value
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| 4 | 0,9999749 | 0,0000 | 0.003 |
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| 10 | 0,9997000 | 0,0275 | 0.88 |
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| 15 | 0,9991026 | 0,0873 | 1.51 |
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| 20 | 0,9982067 | 0,1771 | 2.07 |
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| 25 | 0,9970470 | 0,2937 | 2.57 |
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| 30 | 0,9956488 | 0,4345 | 3.03 |
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| 35 | 0,9940326 | 0,5978 | 3.45 |
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| 40 | 0,9922152 | 0,7821 | 3.84 |
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| 45 | 0,9902100 | 0,9861 | 4.20 |
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| 50 | 0,9880400 | 1,2079 | 4.54 |
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| 55 | 0,9856900 | 1,4492 | 4.86 |
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| 60 | 0,9832000 | 1,7062 | 5.16 |
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| 65 | 0,9805500 | 1,9810 | 5.44 |
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| 70 | 0,9777600 | 2,2720 | 5.71 |
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| 75 | 0,9748400 | 2,5784 | 5.97 |
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| 80 | 0,9717900 | 2,9003 | 6.21 |
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| 85 | 0,9686100 | 3,2381 | 6.44 |
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| 90 | 0,9653100 | 3,5911 | 6.66 |
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| 95 | 0,9618900 | 3,9594 | 6.87 |
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| 100 | 0,9583500 | 4,3434 | 7.03 |
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#### Other liquids
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Unknown if these liquids are expanding linear or not.
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Source: - https://www.engineeringtoolbox.com/cubical-expansion-coefficients-d_1262.html
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(extended table)
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| Liquid | V.C.E. per °C | V.C.E. per °F |
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|:--------------------------------------|:----------------|:----------------|
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| Acetone | 0.00143 | 0.00794 |
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| Alcohol, ethyl (ethanol) | 0.00109 | 0.000606 |
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| Alcohol, methyl (methanol,CH3OH) | 0.00149 | 0.000828 |
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| Calcium Chloride, 5.8% | 0.00025 | 0.00014 |
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| Engine oil | 0.0007 | 0.00039 |
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| Ethylene glycol | 0.00057 | 0.000312 |
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| Gasoline | 0.00095 | 0.000528 |
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| Glycerine (glycerol) | 0.00050 | 0.000278 |
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| Oil (unused engine oil) | 0.00070 | 0.000389 |
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| Olive oil | 0.00070 | 0.000389 |
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| Paraffin oil | 0.000764 | 0.000424 |
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| Petroleum | 0.0010 | 0.00056 |
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| Potassium chloride, 24.3% | 0.00035 | 0.000194 |
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| Sodium | 0.00027 | 0.00015 |
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| Sodium chloride, 20.6% | 0.00041 | 0.000228 |
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## Future
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#### Must
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- update documentation
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- library can be used for water and salinity and other linear related things.
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#### Should
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- investigate linear expansion
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- VCE as parameter.
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- do not make the library too complex (see could below).
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- extend unit tests
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#### Could
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- add **void cool(time)** == depends on many factors
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- need to configure curve constant (only option).
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- must use defined liquid and temp scale.
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- **void AddEnergy(float joule)** to raise temperature (joule)
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- must use defined liquid and temp scale.
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- specific heat needed. (WaterMix only?)
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- replace div and mul with operators \* and \/
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- investigate injection of density function to make LiquidMix generic?
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#### Wont (or on special request)
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- add "unit string" + Printable interface?
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-idem Temp scale?
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- energy functions to calculate how hot an amount of water
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should be to reach a certain temperature.
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- Think Aquaria or cooking.
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- investigate how to mix different liquids?
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- gives too much params
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- use double instead of float?
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- weight and temperature are not that accurate (assumption)
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- investigate the caching of the mass of the water.
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- **addExact()** only, 4 bytes only for WaterMix class
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- it is so far no performance issue.
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- catch temperature below zero?
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- must use defined liquid and temp scale.
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- user responsibility for now.
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## Support
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If you appreciate my libraries, you can support the development and maintenance.
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Improve the quality of the libraries by providing issues and Pull Requests, or
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donate through PayPal or GitHub sponsors.
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Thank you,
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