Mass Flow Rate Uncertainty: A simple problem gone horribly, horribly wrong

[OUmecheng]

The Mass Flow Rate in a water flow system determined by collecting the discharge over a timed interval is 0.2 kg/s. The scales used can be read to the nearest 0.05kg and stop watch is accurate to 0.2 s. Estimate the precision with which the flow rate can be calculated for time intervals of a.) 10s and b.) 60s

Mdot= mass flow rate

Ok so I found the change in mass by using the flow-rate and given time: m = (Mdot)(change in time) so m = (0.2kg/s)(10s) = 2kg

Then i found the uncertainty in the time and mass:

Ut = 0.2s/10s = 0.02s
Um= 0.05kg/2kg

Then I took uncertainty of the mass flow rate, which came from a bunch of partials like this (d is delta):

UMdot = +/- {[(m/Mdot)(dMdot/delta m)(Um)^2 + (t/Mdot)(dMdot/dt)(Ut)^2]}^(1/2)

Then

UMdot = +/- {[((1)( +/- 0.025)^2 + ((-1)(0.02)^2]}^1/2

=0.032 = 3.2%

BUT the answer is exactly half of that, 1.6%

Where the hell did I go wrong?

I can figure out b.) no problem once I figure out why the initial problem isn't working.

 

[Filip Larsen]

If the scale can be read to nearest 0.05 kg, what is then the uncertainty in the mass? (hint: it is not ±0.05 kg as that would mean there had to be 0.1 kg between each mark). Same goes for your clock reading.

 

[OUmecheng]

If the scale can be read to nearest 0.05 kg, what is then the uncertainty in the mass? (hint: it is not ±0.05 kg as that would mean there had to be 0.1 kg between each mark). Same goes for your clock reading.

so half of the smallest increment? Making it ±0.025 kg.

 

[Filip Larsen]

so half of the smallest increment? Making it ±0.025 kg.

Indeed. The assumption is that when you read the weight off the scale you select the nearest mass mark and that means you will select a mark no further away from the true reading than half of the distance between the marks. Or, in other words, the true reading will (with some high probability) lie in the range ± 0.025 from the mark.

 

[rezeew]

As a scientist, it is important to always double check your calculations and make sure your assumptions and equations are correct. In this case, it seems like there may be an error in your equation for calculating the uncertainty in mass flow rate. It is also important to consider the precision and accuracy of your instruments when calculating uncertainties.

To troubleshoot this problem, I would suggest going back to the basics and rechecking all of your calculations and equations. It may also be helpful to consult with a colleague or mentor to see if they can spot any mistakes or offer any insights. Additionally, conducting a sensitivity analysis by varying the values of your inputs (such as time and mass) can help identify where the error may be coming from.

Once you have identified the error, you can apply the same methods to calculate the uncertainty for a time interval of 60 seconds. Remember to always be thorough and precise in your calculations, and to consider the limitations and uncertainties of your instruments.