The aorta in an average adult has a cross-sectional area of 2.0 cm^2 a. Calculate the flow rate

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The aorta in an average adult has a cross-sectional area of...

The aorta in an average adult has a cross-sectional area of $2.0 \mathrm{cm}^{2}$ a. Calculate the flow rate (in grams per second) of blood $\left(\rho=1.0 \mathrm{g} / \mathrm{cm}^{3}\right)$ in the aorta if the flow speed is $42 \mathrm{cm} / \mathrm{s}$ b. Assume that the aorta branches to form a large number of capillaries with a combined cross-sectional area of $3.0 \times 10^{3} \mathrm{cm}^{2}$. What is the flow speed in the capillaries?

The aorta in an average adult has a cross-sectional area of $2.0 \mathrm{cm}^{2}$
a. Calculate the flow rate (in grams per second) of blood $\left(\rho=1.0 \mathrm{g} / \mathrm{cm}^{3}\right)$ in the aorta if the flow speed is $42 \mathrm{cm} / \mathrm{s}$
b. Assume that the aorta branches to form a large number of capillaries with a combined cross-sectional area of $3.0 \times 10^{3} \mathrm{cm}^{2}$. What is the flow speed in the capillaries?

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Key Concepts

Flow Rate

Flow rate is the volume of fluid that passes through a given cross-sectional area per unit time. It is typically calculated as the product of the cross-sectional area and the flow speed, which is a central concept in both fluid dynamics and physiology.

Continuity Equation

The continuity equation expresses the conservation of mass in fluid flow. For an incompressible fluid, it states that the product of the cross-sectional area and the fluid speed remains constant along a streamline, even when the area changes. This principle is essential for understanding how fluid speeds adjust when moving from larger to smaller vessels or vice versa.

Density and Mass Flow Rate

Density is a measure of mass per unit volume. When calculating the mass flow rate of a fluid, its density is multiplied by the volumetric flow rate. This conversion is important in situations where it is necessary to know the mass of the fluid being transported, as seen in many applications of fluid mechanics and physiology.

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