Final answer:
The estimated total length of capillaries in the human body is approximately 1.992 million meters. The number of capillaries in the body is approximately 1.992 billion capillaries.
Step-by-step explanation:
To estimate the total length of capillaries in the human body, we can make use of the information given. We know that approximately 2% of the 5 liters of blood in the body is resident in the systemic capillaries at any given time. Using this information, we can calculate that there are about 0.1 liters of blood in the systemic capillaries (5 liters x 2%).
Next, we need to find the volume per unit length of the capillaries. The volume per unit length can be calculated using the formula:
Volume per unit length = π × (radius)²
Since the diameter of the capillaries is given as 8 µm, the radius will be half of that, which is 4 µm (convert to meters = 4 x 10⁻⁶ m).
Plugging in the values, we have:
Volume per unit length = π × (4 x 10⁻⁶)² = 5.027 x 10⁻¹² m³/m
To find the total length of the capillaries, we divide the volume of blood in the capillaries by the volume per unit length:
Total length = (0.1 liters x (1 x 10⁻³ m³/L)) / (5.027 x 10⁻¹² m³/m)
Total length = 1.992 x 10⁶ m
So, the estimated total length of capillaries in the human body (excluding the lungs) is approximately 1.992 million meters.
To calculate the number of capillaries in the body, we can assume an average capillary length of 1 mm (convert to meters = 1 x 10⁻³ m). The number of capillaries can be found by dividing the total length of capillaries by the average length:
Number of capillaries = total length / average length
Number of capillaries = 1.992 x 10⁶ m / (1 x 10⁻³ m)
Number of capillaries = 1.992 x 10⁹ capillaries