I checked the uncertainty calculation formulae for sum and product of quantities. I want to know the overall uncertainty of measurement in case of sum of 2 equal quantities. Here I assume the uncertainty in one path of quantity x is say u(x) and I have two paths where x quantity flows to give a total of 2x quantity flow.

If I take the total quantity = 2x then the overall uncertainty would be the same as u(x) as 2 is a constant with no uncertainty of its own. However if I take the total quantity as sum i.e. x+x

then the standard uncertainty should be sqare root of [u(x) squared + u(x) squared] i.e. root 2 times x.

Which of the above is correct?

If I take the total quantity = 2x then the overall uncertainty would be the same as u(x) as 2 is a constant with no uncertainty of its own. However if I take the total quantity as sum i.e. x+x

then the standard uncertainty should be sqare root of [u(x) squared + u(x) squared] i.e. root 2 times x.

Which of the above is correct?

The reason, of course, is that you must understand whether the uncertainties and measurements are correlated or not. In the case of 2 measurements of exactly the same thing, in the absence of niose, the uncertainty is correlated then the uncertainty is 2x. For example, if you have two 10-dB pads, with the same s11 and s21, and you measure each and you get 10.1 for the first, and 10.1 for the second (and assume both pads are 10 dB) then each has an uncetainty of .1. But if you connect them together, the uncertainty is now .2, because you think they are 20.2 but actually they are 20.

Now if you connect them and measure them, they may measure differently becuase of other attributes (like linearity and match).

To understand the uncertainty in your case you have to break it down to each constituent piece and sum up from there.