## Sunday, December 4, 2011

### Fluid Expansion in Vertical Cylindrical Tank

For large tanks over 100,000 liters, vertical cylindrical tanks are typically used. Expansion of liquid in a large tank will be visually apparent, especially when the change from night to day and from day to night, when the temperature difference of about 10 degrees Celcius or 18 degrees Fahrenheit can occur.

This is sometimes confusing for those who do not understand. If the temperature is very hot during the day, then rain in the afternoon, then diesel fuel stock is checked at night, the difference can be seen and the stock is very much reduced. This can lead to misunderstanding, as though there are a number of diesel fuel were stolen.

For example:
A diesel fuel has volumetric expansion coefficient of 0.00095 , with the volume of fuel about 113 cubic meters or 113,000 liters, or about 113 tons, and stored in a vertical cylindrical tank 6 meters in diameter or radius of 3 meters, the fuel level in the tank is 4 meters. If there is an increase of 10 degrees Celsius ambient temperature which can occur at dawn till the morning, there will be expansion which reached 1.07m3 or 1,070 liters, and reading at glass sight or dipstick rise as high as 3.8 cm. And vice versa, fuel level can be lower if ambient temperature is lower.

The following table provides an overview of the expansion of some liquid in a vertical cylindrical tank. Given examples of two types of tanks, including Low-Profile or low height tanks with large diameter, while the other is an High-Profile tank with high wall and small diameter. Calculations do not include the expansion of tank material, the increase in fluid temperature is considered equal to the increase in ambient temperature. Excel workbook can be downloaded.

 LOW PROFILE TANK Radius Height Volume Expansion Fluid Height Rise Volumetric Coefficient of Expansion (1/K, 1/oC) m m m3 m3 m cm Water 0.00021 3 4 113.14 0.24 0.009 0.86 Engine Oil 0.00070 3 4 113.14 0.79 0.028 2.80 Diesel Fuel 0.00095 3 4 113.14 1.07 0.038 3.80 Temperature change 10 oC HIGH PROFILE TANK Radius Height Volume Expansion Fluid Height Rise Volumetric Coefficient of Expansion (1/K, 1/oC) m m m3 m3 m cm Water 0.00021 2 9 113.14 0.24 0.019 1.93 Engine Oil 0.00070 2 9 113.14 0.79 0.063 6.30 Diesel Fuel 0.00095 2 9 113.14 1.07 0.086 8.55 Temperature change 10 oC