I'm not feeling confident in making the argument that the g*delta_z term in the energy equation can be neglected. Unfortunately, we did not measure the height difference between the pressure measurements in lab. However, if 4 inches is a good estimate, that term adds about 1 J/kg to the energy rise. My energy rise values range from about 20 to 1500, so this term feels not quite negligible at the low end, and it's an easy constant to add in.