Suppose that blood flows through the aorta with a speed of 0.35 m/s. The cross-sectional area of the aorta is 2.0x10-4 m2. (a) Find the volume flow rate of the blood (b) The aorta branches into tens of thousands of capillaries whose total cross-sectional area is about 0.28 m2 .What is the average blood speed through them ?
rate (m^3/s) = speed (m/s) * area (m^2)
= 0.35 * 2.0*10^-4
= 0.70 * 10^-4
= 7.0 * 10^-5
= .0000070 m^3/s
7.0*10^-5 = v * .28
v = 25 * 10^-5
= 2.5 * 10^-4 m/s
Thank you very much ^__^
To find the volume flow rate of the blood in the aorta, we can use the equation:
Volume Flow Rate = Speed x Cross-sectional Area
(a) Volume Flow Rate of blood in the aorta:
Given:
Speed (v) = 0.35 m/s
Cross-sectional Area (A) = 2.0 * 10^(-4) m^2
Using the equation, we have:
Volume Flow Rate = 0.35 m/s * 2.0 * 10^(-4) m^2
Volume Flow Rate = 7.0 * 10^(-5) m^3/s
Therefore, the volume flow rate of blood in the aorta is 7.0 * 10^(-5) m^3/s.
(b) To find the average blood speed through the capillaries, we can use the principle of continuity, which states that the volume flow rate remains constant throughout a closed system.
The volume flow rate of blood in the aorta is the same as the volume flow rate of blood in the capillaries, so we can use the same value for the volume flow rate.
Volume Flow Rate (capillaries) = 7.0 * 10^(-5) m^3/s
Given:
Total cross-sectional area of the capillaries (A_capillaries) = 0.28 m^2
Using the equation, we can find the average blood speed through the capillaries:
Speed (capillaries) = Volume Flow Rate (capillaries) / Total Cross-sectional Area (capillaries)
Speed (capillaries) = (7.0 * 10^(-5) m^3/s) / (0.28 m^2)
Speed (capillaries) ≈ 2.5 * 10^(-4) m/s
Therefore, the average blood speed through the capillaries is approximately 2.5 * 10^(-4) m/s.
To find the volume flow rate of blood, we need to multiply the speed of blood flow with the cross-sectional area of the blood vessel.
(a) The volume flow rate (Q) is given by the equation:
Q = A * V
Where:
Q = Volume Flow Rate
A = Cross-sectional Area
V = Speed of blood flow
Given:
V = 0.35 m/s
A = 2.0x10^(-4) m^2
Substituting the values into the equation, we can calculate the volume flow rate:
Q = (2.0x10^(-4) m^2) * (0.35 m/s)
Q = 7.0x10^(-5) m^3/s
Therefore, the volume flow rate of blood is 7.0x10^(-5) m^3/s.
(b) To find the average blood speed through the capillaries, we can use the principle of continuity. According to the principle of continuity, the volume flow rate of a fluid remains constant as it passes through different parts of a continuous flow system.
Thus, we can set the volume flow rate of blood through the aorta equal to the volume flow rate through the capillaries:
Q_aorta = Q_capillaries
Since the capillaries have a total cross-sectional area of 0.28 m^2, we need to calculate the average blood speed through them.
Using the equation Q = A * V, we can rearrange it to solve for V:
V = Q / A
Given:
Q = 7.0x10^(-5) m^3/s (calculated in part a)
A = 0.28 m^2
Substituting the values into the equation, we can calculate the average blood speed:
V = (7.0x10^(-5) m^3/s) / (0.28 m^2)
V = 2.5x10^(-4) m/s
Therefore, the average blood speed through the capillaries is 2.5x10^(-4) m/s.