Explanation of equations pi = RTCsolite used to calculate the osmotic pressure

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Explanation of equations

pi = RTCsolite

used to calculate the osmotic pressure. it is Van'T Hoff's LAw

Csolute is the concentration of the solute in moles per liter

if the solution contains N solutes you sum them

Raoult's Law - valid for many highly dilute solutions

Above is an example problem

J is the volumetric fluid transfer rate across the capillary membrane directly proportional to the effective pressure drop DELTA P

Lp is hydraulic conductance: a measure of the efficency of bulk flow through a material. Lp is a constanct that is inversely related to the flow resistance of the capillary membrane (m^2s/kg)

S: the total circumferential surface area of the capillary membrane

the difference between the hydrodynamic pressure of the capillary (PC) and the interstitial fluid (PIF)

(+) fluid will leave the capillary

(-) fluid will flow from the interstitial fluid into the capilary

The differnce in the osmotic pressure between the capillary (piC) and the intersitial fluid (piIF)

(+) osmotic flow of water from the interstitial fluid into the capillary

(-) osmotic flow of water out of the capilary

Poiseuille's Equation: A relationship between flow (Q) and the pressure drop (P0 - PL) in a cylindrical tube ( a culindrical pore)

u is the viscosity ( a measure of the flow resistance of the fluid)

R is the radius of the cylindrical tube or pore

L is the length of the tube or pore

Lp is hydraulic conductance

delta P is effective pressure drop

tm is thickness of capillary wall

the curved T is the tortuosity: a correction factor

total cross -sectional area of the pores (Ap) = NpiR^2

Nerst Equation is used for calculating equilibrium membrane potential for a particular ion

Problem 1:

b)

Consider a composite membrane that is being used to filter plasma from blood. Plasma has a viscosity of 1.2 cP. The composite membrane consists of a microporous spongy-like material that provides structural support. This membrane is 25 μm thick and has pores that are 2 μm in diameter. These pores are also tortuous and have a tortuosity (i.e., τ) of 1.67. The porosity of this membrane (i.e., AP/S) is also equal to 0.60. Attached to this microporous membrane is a thin permselective skin, 3.23 μm thick, that has an NMWCO of 1000. The pores in this membrane skin are therefore about 0.0015 μm in diameter. The tortuosity of the pores in the membrane skin is also equal to 1.67, and the porosity of the membrane skin is equal to 0.60. Use the formula found in Problem 13 to predict the overall hydraulic conductance for this composite membrane. Find the total filtration flow rate (milliliters per hour) across this composite membrane assuming that the total surface area of the membrane is 1 m2 and that the overall effective pressure drop across the composite membrane is 160 mmHg.

All Equations! π = RT ? C π= solute i-1 ?! At a physiological temperature of 37 C The osmotic pressure in mmHg Solute concentration: milliosmolar LpS