Vital systems such as firefighting and water utilities rely on access to water at any time. Buffer tanks are important components in these systems and serve as local water reservoirs, ensuring that the required amount of water is present when required.
The water tank is often a ‘black box’, and it might be difficult to determine how much water is available at a given time. Therefore, the water tank is typically equipped with some kind of level measurement device, which can provide precise measurement of the water volume.
This article explores different methods of level measurement with a special focus on the use of pressure sensors as a precise and reliable solution.
Let’s say that one of our customers needs a solution for level measurement in the open cooling water container in their new plant. The water container has a Ø of 890 mm and a height of 2500 mm. The normal water level will be 1500 mm and the minimum water level will be 500 mm. At 1700 mm max water level, an alarm signal is needed to alert employees to cut the water supply in the tank so that it does not overflow.
The ambient temp will be between 8 °C and 35 °C. The Medium temperature will be 10 °C to 25 °C. The medium is water.
The customer requests a sensor with a 4 to 20 mA output and accuracy better than 2% on the measuring range of the sensor. The process connection and other parameters (electrical plug) are flexible.
The sensor will be installed in the bottom of the tank to measure the water column.
The first step is to select all the mentioned data and calculate the max pressure of the media in the mentioned application:
container type:
open (vented tank) ambient pressure influence
p1 ambient pressure= 1000,3 hPa ~= 1 bar
p2 Hydrostatic Pressure =?
h height of the tank= 2500 mm=2,5m
ρ water density at 10°C = 999,70 kg/m³
hmax water column= 1700 mm =1,7 m
hnorm water column= 1500 mm =1,5 m
hmin water column= 500 mm =0,5 m
Ø container= 890 mm = 0,89 m
V container volume=(π*d²)/4 h = (3,14*0,89m²)/4*1,7m=1,19m³
A container surface=π*d*H =3,14*0,89m*2,5m=6,98m²
With the tank volume value, we know that the max level of water in the tank will be 1,19 m³ or 1190 l. We also know that water has a density of 999,70 kg/m³ or ≈1kg /l .
That means that the max weight of the water in the container will be approximately 1190 kg.
To calculate the pressure in the bottom of the container, we need only the ρ (water density), g gravity, and max height of the water column. The container surface and volume are not so relevant.
Calculation:
P2= ρ⋅g⋅hmax=999,70kg/m^3 *9,81m/s^2 *1,70m=16672kg/m*S²16.672 kg/m*S² or Pa (pascal) (16672 Pa =167 mbar)
With this knowledge we can select an additional sensor for the application.
For a closed container, the important parameters are the same as for an open container. The only difference is that most of the closed containers are pressurized and don’t have a vented connection to the ambient pressure. To compensate for this value, it makes sense to install another sensor at the top of the container.
If the container is vented, we must considerate the influence of the ambient pressure in the calculation.
Application example:
If we have in a closed container (no ventilation) with a medium that evaporates, such as gasoline, we will get an overpressure above the liquid. This overpressure will sit in the top of the tank and can be changed without influencing the medium level. This overpressure must be measured by another pressure sensor, as the gas trapped above the liquid causes a higher hydrostatic pressure, which must be compensated for to avoid false values on the level measurement.
container type:
closed (no vented tank) overpressure influence
p1 overpressure= 80 hPa ~= 80 mbar
p2 hydrostatic Pressure=150 hPa = 150 mbar
htank height of the tank= 2500 mm
ρ Gasoline = 750 kg/m³
We want to know the real medium level on the container. For this calculation, we can use the following formula:
h medium column=((p2-p1) )/((p*g))= ((150 mbar-80mbar))/((750kg/m^3 *9,81ms/s^2 ))=70mbar/(7357,5 kg/m*S²)=70mbar/73,5mbar=0,95m
If we decide to make the same calculation with estimated medium values based on the typical prevailing gas pressure, you will get a miscalculation of the filling level. This could lead to a critical error in the application process.
Another typical sensor application in an open or closed container is to define the unknown or alternate media density using differential pressure. This can be realized if we mount two sensors at two different points in the medium column of the container. It is important to know the exact distance between the sensors to accurately calculate the media density.
container type:
open
p1 overpressure= 6864,93 kg/m*S²=6864,93 Pa
p2 pressure=16672kg/m*S²=16672 Pa
ρ density = ?
g gravity = 9,81 ms/s²
hmax medium column= 1700 mm =1,7 m
hdif difference between 2 sensors=1m
Ƥ=((p2-p1))/((hdif*g))=((16672 kg/m*S2-6864,93 kg/m*S^2))/((1m*9,81 m/S²))=(9807,07 kg/m*S²)/(9,81 m/S²)=999,70 kg/m³
We can say now that the medium in the container has a density of 999,70 kg/m³. This is equal to the water density at 21°C.
If density change is caused by temperature, a temperature sensor can be installed.
