Honestly, clearly explaining Bernoulli’s equation has not been a strength in my instruction. I’ve done a better job each year making the connection to conservation of energy, and more and more students grasp the concept, but I have never done really well. Finally, I think I may have found a clear approach that demystifies Bernoulli’s equation through the use of LOL energy diagrams!
What set the stage for this insight was this excellent diagram in Knight’s College Physics text:
With this clearly defined system, I was able to focus on the volume of water on the left side of the system at time t1 “before” and the volume of water on the right side of the system at time t2 “after.” I treated the kinetic and potential energy of the middle region of the system as a different quantity (K + U) since it unchanged. I scanned my notes which includes the LOL diagram and the derivation of Bernoulli’s Equation from the LOL diagram: