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shareFluid Flow
Discussion
All things are flowing — Heraclitus ca. 500 BCE
continuity equation
For incompressible fluid flow …
| φ = | V | = Av = constant | ⇒ | A1v1 = A2v2 |
| t |
If the fluid is compressible, then …
| I = | m | = ρAv = constant | ⇒ | ρ1A1v1 = ρ2A2v2 |
| t |
Notes from The Economist
A sverdrup (named for the Norwegian oceanographer and meteorologist Harald Sverdrup) the unit in which ocean currents are measured, is one million cubic metres of water per second. The Gulf Stream, the northern part of a circulation system known as the North Atlantic Gyre, reaches 150 Sverdrups at its peak. On average, it flows at around 100 Sverdrups.
bernoulli's equation
Bernoulli's equation is based on the law of conservation of energy; the increased kinetic energy of a fluid is offset by a reduction of the "static energy" associated with pressure. The fluid is assumed incompressible and inviscid (that is, the fluid does not generate drag).
Something like this is probably right.
| W | = | ΔE | ||||
| − PΔV | = | ΔU | + | ΔK | ||
| P1V1 | − | P2V2 | = | U2 − U1 | + | K2 − K1 |
Rearrange
| P1V1 | + | U1 | + | K1 | = | P2V2 | + | U2 | + | K2 |
| P1V1 | + | mgh1 | + | ½ mv12 | = | P2V2 | + | mgh2 | + | ½ mv12 |
| P1V1 | + | mgh1 | + | ½ mv12 | = | P2V2 | + | mgh2 | + | ½ mv12 |
| V1 | V1 | V1 | V2 | V2 | V2 | |||||
| P1 | + | ρgh1 | + | ½ ρv12 | = | P2 | + | ρgh2 | + | ½ ρv12 |
The conclusion is most certainly right
P1 + ρgh1 + ½ ρv12 = P2 + ρgh2 + ½ ρv12
The third term in this equation is the dynamic pressure (q).
q = ½ ρv12
The space shuttle and "Max. Q".