Flow rate = volume of fluid that moves past a given point per unit time (L/min)
Radius & Resistance
Poiseuille’s Equation: Q = P π r4 / 8 L ή
Resistance is inversely proportional to radius to the forth power.
Small changes in radius result in large changes in resistance.
Controlling Flow
Vasoconstriction:
r
R
Q
Vasodilation:
r
R
Q
Small changes in r result in large changes in resistance and flow.
Total Flow
Law of conservation of mass: The flow through each segment of the circulatory system must be equal.
Total flow is constant across all parts of the circulatory system.
Total Flow
Total Flow
Series : ◦ RT = R1 + R2 + R3
Parallel : ◦ 1/RT = 1/R1 + 1/R2 +1/R3
Circulatory systems have both series and parallel arrangements of blood vessels.
Total Flow
Velocity of Flow
Velocity of blood flow in a given blood vessel is inversely related to the crosssectional area of the blood vessel.
Blood velocity = Q/A A= summed cross-sectional area of channels.
Velocity of Flow
Regions of the circulatory system that are involved in the exchange of materials have very high total crosssectional areas, so they have very low velocities, which aids diffusion.
Pressure & Blood Vessels
Pressure within walled chambers exerts a force on those walls.
Blood pressure within walled chambers (heart or blood vessels) exerts a force.
Force can be quantified using the law of LaPlace.
Pressure & Blood Vessels
Law of LaPlace:
T = aPr
Pressure & Blood Vessels
Taking into account wall thickness: σ = Pr/w
thickness
stress on wall
Pressure & Blood Vessels
Organisms are reasonably build
As thickness increases, stress in the wall decreases, therefore: ◦ BVs such as the aorta, which must withstand very high pressures, are thicker and stronger. ◦ Arterioles which are subject to lower pressure are thinner.
Circulatory Systems
Vertebrate circulatory systems contain one or more pumps in a series:
Single-Circuit Circulatory System: ◦ Water breathing fish
Double-Circuit Circulatory System: ◦ Mammals and birds
