Continuity and Ideal Flow Budgets

Bernoulli Budget Trades Pressure Speed Height

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+3684+16=64+36
Level Bernoulli budgetEach pressure and kinetic term is source-bound.rho=2 kg/m^3g=10 m/s^2left P=84 Paleft v=4 m/sleft h=0 mleft K=16 Paleft Z=0 Paleft total=100 Paright P=64 Paright v=6 m/sright h=0 mright K=36 Paright Z=0 Paright total=100 Pa

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+6064+16+20=24+16+60
Height Bernoulli budgetBoth sides close to the same total.rho=2 kg/m^3g=10 m/s^2left P=64 Paleft v=4 m/sleft h=1 mleft K=16 Paleft Z=20 Paleft total=100 Paright P=24 Paright v=4 m/sright h=3 mright K=16 Paright Z=60 Paright total=100 Pa

Both ideal budgets close to the same total

Each displayed Bernoulli side totals 100 pascals; hidden losses are outside this model.

total=100 Pa\mathrm{total}=100\ \mathrm{Pa}
Ideal flow budgetsThe capstone keeps one exact table visible.rho=2 kg/m^3g=10 m/s^2left P=64 Paleft v=4 m/sleft h=1 mleft K=16 Paleft Z=20 Paleft total=100 Paright P=24 Paright v=4 m/sright h=3 mright K=16 Paright Z=60 Paright total=100 Pa