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I have two columns of water at different (but constant) temperatures. If I calibrate a pressure transducer using the first column at differing heights, when I measure the second column how do I account for the change in temperature (and water density)?

I want to measure pressure in megapascals (MPa) so for the calibration I currently plot pressure transducer mV output at different column heights against the calculated megapascal for the corresponding height and temperature of water using the equation:

pressure = height (m) x water density (kg/m3) x gravitational constant (m/s2)

But the density of the second column is different so this value needs to be adjusted.

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  • $\begingroup$ can you measure the weight and volume of the water in both columns (e.g. by placing the columns on a scale)? that would give you the average densities. The different densities account for the different temperatures, i.e. at 1 bar, water at 5 dCelsius is 1000 kg/m3 while at 95 dCelsius is 960 kg/m3. source $\endgroup$ – nluigi Dec 8 '15 at 9:33
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You can either compensate for it in your measurement or neglect it and lump it in with the other error.

First though, you need to decide if the error would even be worth correcting. At 4 °C, the density of water is 1000 kg/m^3 and 958 kg/m^3 at 100 °C. That's a maximum of 4.2% at those temp extremes. Over small variations in temperature, correcting for it is like picking the fly poop out of the pepper... it's insignificant and pales in comparison to the other sources of error like your instrumentation. The real question is: Can your application tolerate that error?

If you do decide to compensate for it, you need to measure temperature (and that has it's own errors) and in your equation make density a function of temperature.

$ p = h_{col} * \rho (T_{water}) * g $

My guess though, based on experience is that once you look into it, the variation in density due to expected water temperature changes is going to be negligible compared to things like manually reading a height scale unless you're doing some crazy stuff.

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  • $\begingroup$ Thank you - yes, the application can tolerate that error. Much appreciated! $\endgroup$ – lufin Dec 8 '15 at 22:29
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The pressure will be the same regardless of the temperature. So, the two columns will have the correct pressure recording. However, the height of the column will vary.

i.e. - Say you have your pressure transmitter reading for calibration a 10C column (999.7 kg/m^3). The results are:

0.5m - 4.9 kPa - 7 mV; 1m - 9.8 kPa - 10 mV; 2m - 19.6 kPa - 13 mV;

Then you measure the second column at 70C (977.8 kg/m^3), and it reads 7mV. Then the column will still be 4.9kPa at the base, but the new height will be 51.1 cm, not the original 50 cm. The pressure will still be 4.9kPa though.

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you can olso put temperature gauge for each column vessel with Instrument calibrated accepted because ; 1# the volume of column vessel & level of water are not the same in between this is normal condition (ambient) event not pressurized yet, temperature and pressure of each vessel not the same due to gravity same case Hydrostatic test for under water pipe line offshore to Onshore. due to sea water temperature are not stabile, I agree with the 1st answer

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