Wolfram Alpha:

```
Bernoulli Principle
-------------------
The lowering of fluid pressure in regions where the flow velocity is increased.

Δl2
||
--------
/         A2, ρ2, h2, P2, v2
Δl1     /  -------
||     /  /
--------  /
----------
A1, ρ1, h1, P1, v1

Continuity Equation:

A1Δl1/t = A2Δl2/t
=>  A1v1 = A2v2 = volumetric flow (m3/s)

Bernoulli Equation:

U = Fd
= PAd since P = F/A
= PV
=> P = U/V ... energy per unit volume

KE per unit volume
/
P1 + (1/2)ρv12 + ρgh1 = P2 + (1/2)ρv22 + ρgh2

P + (1/2)ρv2 + ρgh = constant

It is a statement of the conservation of energy in a form useful for solving problems
involving fluids. For a non-viscous, incompressible fluid in steady flow, the sum of
pressure, potential and kinetic energies per unit volume is constant at any point.

Venturi:

^      ||           ||
| -----  ---        ||     ^
h1            \     ||     |   h2
|              -----  ---- |
v       . P1        .P2    v
----------
/
----------

P1 = h1ρg        P2 = h2ρg

H = h1 - h2 = (1/2)ρ(v22 - v12)

Geyser:
. .  v2 = 0
.      .
.   h?
.        .
.
-----  -------
||
|| d
||
----  ---- v1 ~ 0, P1 = dρsoilg
|          |
----------

dρsoilg - Patmos = (1/2)ρwater(0 - 0) + (h + d)ρwaterg

dρsoilg - Patmos = (h + d)ρwaterg

dρsoilg - dρwaterg - Patmos = hρwaterg

{dg(ρsoil - ρwater) - Patmos}/ρwaterg = h

Torricelli's Law
----------------

Water leaking from a tank.

Pa
|
v
|    |
|----|P1, v1, h1
|    |
|    |
|    |..> P2, v2, h2
|    |
----

P2 - P1 = (1/2)ρ(v22 - v12) + ρgh where h = h1 - h2

But P1 = P2 = Pa

Therefore, 0 = (1/2)ρ(v22 + ρgh if v1 ~ 0

=> v2 =√2gh```