Page 403 - Color_Atlas_of_Physiology_5th_Ed._-_A._Despopoulos_2003

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U osm = osmolality of urine [Osm · L ] b. Elliptical hollow body, considering wall
P X, P PAH, P In = plasma concentration of sub- thickness:
stance X, para-aminohippuric acid, and in- 1 1
dicator (e.g., inulin, endogenous crea- P tm = S · w ( r 1 + r 2 ) [Pa];
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tinine) [mol · L ] or [g · L ] c. Spherical hollow body (r 1 = r 2 = r):
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P osm = osmolality of plasma [Osm · L ] T S · w
HCT = hematocrit [L of blood cells/L of P tm = 2 r [Pa] or P tm = 2 r [Pa];
blood]
d. Cylindrical hollow body
9. Equations for filtration (r 2 ! ', therefore 1/r 2 = 0):
(see also pp. 152, 208) P tm = T [Pa] or P tm = S · w [Pa]
a. Effective filtration pressure at capillaries r r
(P eff) P tm = transmural pressure [Pa]
P eff = P cap –P int – π cap + π int [mmHg] T = wall tension [N · m ]
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-2
S = wall tension [N · m ]
b. Effective filtration pressure at capillaries w = wall thickness [m]
of renal glomerulus:
P eff = P cap –P Bow – π cap [mmHg] 11. Equations for cardiovascular function
Appendix c. Filtration rate (Q at glomerulus = GFR) (see also items 2, 5b, 6c, and 9 as well as
.
.
Q = P eff · F · k [m · s
]
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3
p. 186ff.)
a. Cardiac output (CO):
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(interstitium) [mm Hg]
13 P cap (P int) = hydrostatic pressure in capillaries CO = f · SV [l · min ]
π cap (π int) = oncotic pressure in capillaries b. Hagen–Poiseuille equation
(interstitium) [mm Hg] 8 · l · η
P eff = mean effective filtration pressure [mm Hg] R = π · r 4 ;
2
A = area of filtration (m ) f = heart rate [min ]
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k = permeability to water (hydraulic conduc- SV = stroke volume [L]
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3
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tance) [m · s · mm Hg ] R = flow resistance in a tube [Pa · s · m ] of
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known length l [m] and inner radius r [m]
10. Law of Laplace η = viscosity [Pa · s]
(see also pp. 118, 188, and 210)
a. Elliptical hollow body (with radii r 1 and r 2)
1 1
P tm = T ( + ) [Pa];
r 1 r 2

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Despopoulos, Color Atlas of Physiology © 2003 Thieme
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