The cross-sectional area of the aorta is 3 cm^2, and the average velocity of blood leaving the h

step 1 All right, so this is just an application of continuity. We have that the flow in one portion is

The cross-sectional area of the aorta is 3 cm^2, and the...

The cross-sectional area of the aorta is $3 \mathrm{cm}^{2},$ and the average velocity of blood leaving the heart into the aorta is 30 $\mathrm{cm} / \mathrm{s}$ . If the combined effective cross sectional area of the body's capillaries is $600 \mathrm{cm}^{2},$ what is the average flow rate in a capillary? $$\begin{array}{l}{\text { A. } 1 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{B} .2 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{C} \cdot 0.01 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{D}, 0.15 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{E} .0 .2 \mathrm{cm} / \mathrm{s}}\end{array}$$

The cross-sectional area of the aorta is $3 \mathrm{cm}^{2},$ and the average
velocity of blood leaving the heart into the aorta is 30 $\mathrm{cm} / \mathrm{s}$ . If
the combined effective cross sectional area of the body's capillaries is $600 \mathrm{cm}^{2},$ what is the average flow rate in a capillary?
$$\begin{array}{l}{\text { A. } 1 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{B} .2 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{C} \cdot 0.01 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{D}, 0.15 \mathrm{cm} / \mathrm{s}} \\ {\mathrm{E} .0 .2 \mathrm{cm} / \mathrm{s}}\end{array}$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Continuity Equation

The continuity equation in fluid dynamics states that for an incompressible fluid, the product of cross-sectional area and velocity (A*v) remains constant along a streamline. This principle allows us to relate velocities in different parts of a flow system when the areas change, ensuring that the volumetric flow rate is conserved.

Cross-Sectional Area and Flow Rate

The volumetric flow rate of a fluid is determined by multiplying its cross-sectional area by its average velocity. When fluid moves from an area with a certain cross-section (like the aorta) to an area with a different total cross-section (like the capillary network), the conservation of flow rate implies that differences in area must be compensated by differences in velocity.

Conservation of Mass in Fluid Flow

Fundamental to the analysis of fluid motion is the principle of mass conservation, which ensures that the mass (or volume, for incompressible fluids) of fluid entering a system must equal the mass leaving it. This concept is critical in understanding how blood flow can slow down in the capillaries even though the total flow rate remains unchanged after leaving the heart.

Transcript

Please give Ace some feedback