As indicated in the figure below, as blood flows through capillaries, the blood pressure decreases (43 mmHg at inlet to 15 mmHg at outlet). Let's assume that this decrease in pressure is a linear function of length (x) and can be described by the following equation: Pc(x) = (43 - 28x) mmHg We can assume that the other hydrostatic and osmotic pressures do not change along the length of the capillary. Specifically, oncotic pressure in the capillary is 28 mmHg. In the interstitial fluid surrounding our capillaries, hydrostatic pressure in the interstitial fluid surrounding the capillaries is about -2.0 mmHg, and osmotic pressure of about 1.0 mmHg. At what length value of x does flow switch from going out of the capillaries into the surrounding tissue to into the capillaries from the surrounding tissue? Don't worry about the units of x. We can think of x as a fraction representing how far down the capillary we are relative to total length. For example, x of 0.5 would be halfway down the total length. Assume a Staverman reflection coefficient of 0.9. Please show your derivation.
As indicated in the figure below, as blood flows through capillaries, the blood pressure decreases (43 mmHg at inlet to 15 mmHg at outlet). Let's assume that this decrease in pressure is a linear function of length (x) and can be described by the following equation: Pc(x) = (43 - 28x) mmHg We can assume that the other hydrostatic and osmotic pressures do not change along the length of the capillary. Specifically, oncotic pressure in the capillary is 28 mmHg. In the interstitial fluid surrounding our capillaries, hydrostatic pressure in the interstitial fluid surrounding the capillaries is about -2.0 mmHg, and osmotic pressure of about 1.0 mmHg. At what length value of x does flow switch from going out of the capillaries into the surrounding tissue to into the capillaries from the surrounding tissue? Don't worry about the units of x. We can think of x as a fraction representing how far down the capillary we are relative to total length. For example, x of 0.5 would be halfway down the total length. Assume a Staverman reflection coefficient of 0.9. Please show your derivation.
Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
Section: Chapter Questions
Problem 1RQ: The correct sequence of levels forming the structural hierarchy is A. (a) organ, organ system,...
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Transcribed Image Text:decreases (43
As indicated in the figure below, as blood flows through capillaries, the blood
mmHg at inlet to 15 mmHg at outlet). Let's assume that this decrease in pressure is a linear
function of length (x) and can be described by the following equation:
pressure
Pc(x) = (43 – 28x) mmHg
We can assume that the other hydrostatic and osmotic pressures do not change along the length of
the capillary. Specifically, oncotic pressure in the capillary is 28 mmHg.
In the interstitial fluid surrounding our capillaries, hydrostatic pressure in the interstitial fluid
surrounding the capillaries is about –2.0 mmHg, and osmotic pressure of about 1.0 mmHg.
At what length value of x does flow switch from going out of the capillaries into the
surrounding tissue to into the capillaries from the surrounding tissue? Don't worry about the
units of x. We can think of x as a fraction representing how far down the capillary we are relative to
total length. For example, x of 0.5 would be halfway down the total length. Assume a Staverman
reflection coefficient of 0.9. Please show your derivation.
inlet
outlet
X = 0
X = 1
Po(x) = (43 – 28x) mmHg
Po(x=0)
T = 28 mmHg
Po(x=1) = 15 mmHg
TT = 28 mmHg
= 43 mmHg
capillary
p = -2.0 mmHg
N = 1.0 mmHg
interstitial fluid
Lymph fluid to lymph nodes
then return to venous blood.
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