Mass flow rate from a draining bottle with changing height

[JorgeM]

Hello there, I am going to implement a numerical method to solve how much Mass of a fluid has gone out of an opened bottle. I am going to get h(t) with some sensors but I am not sure if this expression for Mass gone out "M" is correct.
The area of the bottle at the up part. A1
The density of the fluid is D
The position Y of the fluid at the top is given by h(t)

What do you think?
Thanks a lot

 

[Chestermiller]

Hello there, I am going to implement a numerical method to solve how much Mass of a fluid has gone out of an opened bottle. I am going to get h(t) with some sensors but I am not sure if this expression for Mass gone out "M" is correct.
The area of the bottle at the up part. A1
The density of the fluid is D
The position Y of the fluid at the top is given by h(t)
View attachment 226013
What do you think?
Thanks a lot

Should’t It just be $DA_1(h(0)-h(t))$?