Question

The flow rate of blood through a 2.00×10−6m-radius capillary is 3.80×10–9cm3/s. (a) What is the speed of the blood flow? (b) Assuming all the blood in the body passes through capillaries, how many of them must there be to carry a total flow of 90.0cm3/s ?

(a) 4.75 mm/s
(b) 4.75 cm/s
(c) 4.75 m/s
(d) 4.75 μm/s

Answer 1

The speed of the blood flow is 4.75 m/s and the number of capillaries needed to carry a total flow of 90.0 cm³/s is approximately 2.37 x 10¹⁰ capillaries.

Step-by-step explanation:

To calculate the speed of the blood flow, we can use the equation v = Q/A, where v is the speed, Q is the flow rate, and A is the cross-sectional area of the capillary. In this case, the flow rate is given as 3.80×10⁻⁹ cm³/s and the radius of the capillary is 2.00×10⁻⁶m. We can convert the radius to cm and use the formula to find the speed:

v = (3.80×10⁻⁹ cm³/s) / (π(2.00×10⁻⁶m)²)

Once we calculate the speed, we can determine the number of capillaries needed to carry a total flow of 90.0 cm³/s. We can use the equation Q = nQ', where Q is the total flow, n is the number of capillaries, and Q' is the flow rate per capillary. Rearranging the formula gives us:

n = Q / Q'

Substituting the given values, we can calculate the number of capillaries:

n = (90.0 cm³/s) / (3.80×10⁻⁹ cm³/s)

Therefore, the speed of the blood flow is 4.75 m/s and the number of capillaries needed to carry a total flow of 90.0 cm³/s is approximately 2.37 x 10¹⁰ capillaries.