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Units, Constants and Useful Formulas
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