Three question on error-propagation and flow measurements

[esc1729]

I’m calculating a discrete integral from distinct water-flow measurements. That means I have a few thousand data values in liter/second and I calculate from them the totally flown water in liter. The accuracy of the data is +/- 0.5 liter and I get one value every 5 seconds. The total time of measurement is about 3 hours. The water is coming in bunches of about 25 liters in a duration of 30 seconds to about 3 minutes. Between these flows there’s no water, so the accuracy is 100% then.

• First question: how will the error propagate?

I can read out the flow meter before and after the measurement in hi-res mode with 0.01 l accuracy, but not in-between. This is some restriction of the M-Bus interface to which the meter is connected. But I can read out the sum-value every 5 seconds together with the flow rates but only with 10 liter accuracy. Anyway, the moment of the switch to the next 10 liter value provides some information on at least one hidden decimal number, as it seems to me. So perhaps I can use something like ‘maximum likelihood’ approximation to get more accuracy?

• Second question: what’s the best way to analyze this data?

As I’ve found out meanwhile, the regime we are measuring in is just between home water technique and flow-rates seen in some processes in pharmaceutical and food industries. Normal home water meters are not built to this accuracy we would need (0.1 liter) or at least do not provide this accuracy remotely and those better flow-meters like perhaps HygienicMaster FEH300 from ABB probably cost a factor 20 to 100 more as the setup just now.

• Third question: should we change the meters?

Erich

 

[JaWiB]

First question: If you're simply summing values that have independent and random errors, then you add the uncertainties in quadrature; i.e., for N measurements:
$$\delta V = \sqrt{\sum_{i=1}^{N}{\delta V_{i}}^2$$