So I've found several instances in which Bernoulli and Conservation of momentum (in Reynolds transport theorem form) give different answers for the study of an inviscid fluid. Let's consider a simple situation as described in my diagram attached. Basically a tap/faucet is releasing fluid, which is known to be inviscid. We want to find the velocity at the bottom just before it hits the ground. My solution does it out with both Bernoulli and conservation of momentum, but the factor of 2 that comes from the kinetic energy in Bernoulli doesn't appear in the final expression from conservation of momentum. This is only a simple example and I've come across this discrepancy about the '2' several times. I'm not sure what is going on here and any help would be much appreciated!