# How to convert bars to meters head?

I am trying to convert 1 bar to meters to come up with a conversion factor. Thus,

1 bar = x meters head


What is x?

From my computations I got something like this:

1 bar = 100000 Pascal
1 psi = 100000 psi * 0.45359237 kg * 9.80665 (m/s^2) / (10 * 2.54mm * 2.54mm) =
= 6894.75729316 Pascal


then assuming that

1 psi = 2.31 feet
1 foot = 0.3048 meters


converting from bars to meters I get

1 bar = (100000 / 6894.75729316) * 2.31 * 0.3048 = 10.2119330683 meters


Wolfram for "1 bar to meter of water" gets

10.19716 meters of water column


which is not the same as my value.

1 bar = 10.199773339984 m


These numbers are all different ...

Is there a more authoritative way to come up with a conversion value for 1 bar to meters?

• You can't convert bar to meters. A bar is 1 bar ≡ 100,000 Pa ≡ 100,000 $Newton/meter^2$. "Meters of head" refers to some sort of pressure measuring device using a liquid where the difference in liquid levels gives a pressure. So it depends on what you are using for the liquid. – MaxW Jun 25 '18 at 15:41
• @MaxW I think Dennis is well aware that he cannot convert bar to meters. If you take the time to actually read his question you will find that he can make the conversion from bars to meters head himself. The problem comes when he compares his answer with online calculators. He is asking about the most rigorous or "correct" way to make this conversion. – user3408085 Jun 25 '18 at 16:33
• More of less agree but the website to which the OP posted doesn't give units. Trying to guess what liquid at what temperature and what ... and what ... just leaves you chasing your tail. – MaxW Jun 25 '18 at 16:52
• @Dennis - Temperature differences could definitely be it. The density of water changes by a few percent between 0˚ and 100 ˚C whereas the height difference between the two values you stated is only about a 0.1% difference. – Samuel Weir Jun 25 '18 at 17:32
• 2.31 ft/psi only applies to water. Other liquids will produce a different value because of their different density. Also, why worry about 12 digits past the decimal point? You will probably not find any measuring devices that can give you such precision, so reporting that many digits is not only useless, it obscures any information regarding what device you used to take your measurements. Your three reported conversions of 1 bar to meters are within 0.1% of each other, which means that for all practical purposes, they are the same number. – David White Jan 24 at 6:11

## 1 Answer

Head is the elevation you can raise a column of water of density 1000 kg/m^3 with a prescribed pressure. So you have the equation $$\rho g h=1\ bar=10^5\ Pa$$. So $$h=\frac{10^5}{1000\times9.80655}=10.197\ meters$$

• mm I find that interesting. The equations I had were worked out from definitions, but went in a more round-a-bout way to get to the value compared to your more straightforward method. perhaps there is an assumption in my method that threw the value off. – Dennis Jun 26 '18 at 15:12
• I'm sure it was just roundoff error. – Chet Miller Jun 26 '18 at 15:23
• I used wolfram for computation, can't be round-off error! :) I do suspect that 1 psi is not 2.31 feet. At least Wolfram says it's 2.306659 feet ... So I'm suspecting that to be an incorrect assumption – Dennis Jun 26 '18 at 15:41
• That’s exactly what I mean by roundoff. – Chet Miller Jun 26 '18 at 16:16