Biomedical Engineering Blood Pressure / Blood Flow

RUPRECHT-KARLS-
UNIVERSITY HEIDELBERG
Computer Assisted Clinical Medicine
Patrick Heiler
11/25/2011 | Page 7 Static Pressure
p stat = F/A;
F
A
V
H
Fx
⎛ ∂p
⎞ ∂p
∂p
∂p
= p ⋅dydz
− ⎜ p + dx⎟dydz
= − dV Fy
= − dV , Fz
= − dV
⎝ ∂x
⎠ ∂x
∂y
∂z
r
F = −grad
p ⋅dV
RUPRECHT-KARLS-
UNIVERSITY HEIDELBERG
Computer Assisted Clinical Medicine
Patrick Heiler
11/25/2011 | Page 8 Hydrostatic Pressure
Force of Gravity of volume element dV:
pressure on ground element da:
hydrostatic pressure distribution:
dF = ρ ⋅ g ⋅dV
, ⇒ dp = ρ ⋅ g ⋅ dz
p
p
atm
atm
H
(0) = ∫ ρ ⋅ g ⋅dz
= ρ ⋅ g ⋅ H
0
H
( h)
= ∫ ρ ⋅ g ⋅ dz = ρ ⋅ g(
H − h)
h
F
A
V
H
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