A Bernoulli height-pressure scan varies height across three rows at fixed speed, showing how pressure falls as P + rho * g * h stays constant along the streamline. The arithmetic is exact only for the stated heights, pressures, densities, and rows in the ideal steady incompressible, inviscid model. Real flows add viscosity, turbulence, compressibility, pipe geometry, calibration, elevation reference, and measurement uncertainty.

Height rises only by spending pressure in a checked ideal budget. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Low outlet leaves pressure high

Speed stays v=4 m/s. Height h=0 m adds height term 0 pascals, leaving pressure 84 pascals.

84+16+0=10084+16+0=100
Bernoulli height-pressure scanThe height term is source-bound before totals match.PvPvrho=2 kg/m^3g=10 m/s^2left P=96 Paleft v=2 m/sleft h=0 mleft K=4 Paleft Z=0 Paleft total=100 Paright P=84 Paright v=4 m/sright h=0 mright K=16 Paright Z=0 Paright total=100 Pa

One metre of height costs twenty pascals

Speed stays v=4 m/s. Height h=1 m adds height term 20 pascals, leaving pressure 64 pascals.

64+16+20=10064+16+20=100
Bernoulli height-pressure scanThe height term is source-bound before totals match.PvPvrho=2 kg/m^3g=10 m/s^2left P=96 Paleft v=2 m/sleft h=0 mleft K=4 Paleft Z=0 Paleft total=100 Paright P=64 Paright v=4 m/sright h=1 mright K=16 Paright Z=20 Paright total=100 Pa

Three metres of height costs sixty pascals

Speed stays v=4 m/s. Height h=3 m adds height term 60 pascals, leaving pressure 24 pascals.

24+16+60=10024+16+60=100
Bernoulli height-pressure scanThe height term is source-bound before totals match.PvPvrho=2 kg/m^3g=10 m/s^2left P=96 Paleft v=2 m/sleft h=0 mleft K=4 Paleft Z=0 Paleft total=100 Paright P=24 Paright v=4 m/sright h=3 mright K=16 Paright Z=60 Paright total=100 Pa