Deeper Fluid Budget Scans

Bernoulli Speed Pressure Three-Row Scan

Speed 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

Slow section keeps high pressure

At height h=0 m, speed v=2 m/s has kinetic term 4 pascals, so pressure 96 pascals keeps the total at 100 pascals.

96+4+0=10096+4+0=100
Bernoulli speed-pressure scanPressure and speed labels close to one checked total.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=96 Paright v=2 m/sright h=0 mright K=4 Paright Z=0 Paright total=100 Pa

Faster section spends pressure on speed

At height h=0 m, speed v=4 m/s has kinetic term 16 pascals, so pressure 84 pascals keeps the total at 100 pascals.

84+16+0=10084+16+0=100
Bernoulli speed-pressure scanPressure and speed labels close to one checked total.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

Fastest section has the lowest pressure

At height h=0 m, speed v=6 m/s has kinetic term 36 pascals, so pressure 64 pascals keeps the total at 100 pascals.

64+36+0=10064+36+0=100
Bernoulli speed-pressure scanPressure and speed labels close to one checked total.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=6 m/sright h=0 mright K=36 Paright Z=0 Paright total=100 Pa