Bernoulli's equation is an energy ledger, P + 0.5 * rho * v^2 + rho * g * h = constant, trading pressure, speed, and height along a streamline. The budget is exact only for stated pressure, speed, height, and density in the steady incompressible, inviscid flow model. Real fluids add viscosity, turbulence, compressibility, pipe losses, geometry tolerance, calibration, and measurement uncertainty.
A constrained ideal Bernoulli budget binds pressure, speed, and height terms. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Speed and pressure trade in the level budget
With density 2, speeds 4 and 6 give kinetic terms 16 and 36 pascals.
84+16=64+36
Height can trade with pressure too
At shared speed 4, heights 1 and 3 make height terms 20 and 60 pascals.
64+16+20=24+16+60
Both ideal budgets close to the same total
Each displayed Bernoulli side totals 100 pascals; hidden losses are outside this model.