First, I took measurements with the LSM9DS0 taking measurements as quickly as it could.  That is, ~100 Hz.

Here is the water tap open a bit.

Here is the tap fully open.

The detection algorithm is pretty simple: Once you have a reading greater than 6050, look for a reading less than 2500.  Once you get less than 2500, look for a reading above 6050.  Once you get past 6050, increment a counter by 1, and start looking for <2500 again, and so on.  From each peak to peak (i.e., 1 count) is approximately 0.0657 L of water.  Pretty fine granularity!