The blood flow rate through the aorta is typically 103 cm^3/s, and a typical adult has about 4.9 liters of blood.
(a) How long does it take for all your blood to pass through the aorta?
___________s
(b) If your aorta has a diameter of 2.1 cm, what is the speed of blood as it flows through the aorta?
___________cm/s
(a) 4.9 l / 103 cm
=4900 ml / 103 ml
= 47.6 s
(b) cross section area
A = π2.1²/4 = 3.46 cm²
Velocity = Volume/cross section area
= 103/3.46 cm/s
= 29.7 cm/s
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(a) To find the time it takes for all the blood to pass through the aorta, we need to use the equation:
Time = Volume / Flow Rate
We are given that the blood flow rate through the aorta is 103 cm^3/s, and the volume of blood in an adult is about 4.9 liters. We need to convert the volume to the same unit as the flow rate, which is cm^3.
1 liter = 1000 cm^3
Therefore, the volume of blood in cm^3 is:
4.9 liters * 1000 cm^3/liter = 4900 cm^3
Now we can substitute the values into the equation:
Time = 4900 cm^3 / 103 cm^3/s
Calculating this, we get:
Time = 47.57 seconds
Therefore, it takes about 47.57 seconds for all the blood to pass through the aorta.
(b) To find the speed of blood as it flows through the aorta, we need to use the equation:
Flow Rate = Cross-sectional Area * Speed
We are given that the flow rate is 103 cm^3/s and the diameter of the aorta is 2.1 cm. We need to calculate the cross-sectional area of the aorta.
The cross-sectional area of a circle can be calculated using the formula:
Area = π * (radius)^2
The radius of the aorta is half of its diameter:
Radius = 2.1 cm / 2 = 1.05 cm
Substituting the values into the formula:
Area = π * (1.05 cm)^2
Calculating this, we get:
Area = 3.46 cm^2
Now we can rearrange the equation to solve for speed:
Speed = Flow Rate / Cross-sectional Area
Substituting the values:
Speed = 103 cm^3/s / 3.46 cm^2
Calculating this, we get:
Speed ≈ 29.8 cm/s
Therefore, the speed of blood as it flows through the aorta is about 29.8 cm/s.