Blood takes about 1.50 s to pass through a 2.0-mm-long capillary. If the radius of the capillary is

5.00 u�m and the pressure drop is 2.60 kPa, calculate the viscosity of blood

To calculate the viscosity of blood, we can use Poiseuille's law, which relates the pressure drop across a cylindrical tube to the flow rate and the physical properties of the fluid and the tube.

Poiseuille's law can be written as:

ΔP = (8ηLQ) / (πr^4)

Where:
ΔP = pressure drop across the tube (in Pascals)
η = viscosity of the fluid (in Pa s or N s/m^2)
L = length of the tube (in meters)
Q = flow rate of the fluid (in m^3/s)
r = radius of the tube (in meters)

We have the following values in the problem:
L = 2.0 mm = 0.002 m
ΔP = 2.60 kPa = 2600 Pa
r = 5.00 μm = 5.00 × 10^(-6) m

To calculate the flow rate (Q), we can use the formula:
Q = V / t

Where:
V = volume of blood passing through the capillary (in m^3)
t = time taken to pass through the capillary (in seconds)

We need to calculate V first. The volume of a cylinder can be calculated using the formula:
V = πr^2L

Substituting the given values:
V = π(5.00 × 10^(-6))^2 × 0.002 = 7.85 × 10^(-11) m^3

Now, we can calculate the flow rate:
Q = (7.85 × 10^(-11)) / 1.50 = 5.23 × 10^(-11) m^3/s

Now, we can rearrange Poiseuille's law to solve for η:
η = (ΔP × πr^4) / (8LQ)

Substituting the given values:
η = (2600 × (5.00 × 10^(-6))^4 × π) / (8 × 0.002 × 5.23 × 10^(-11))

Simplifying the equation, we get:
η = 146 × 10^(-3) Pa s

Therefore, the viscosity of blood is approximately 0.146 Pa s.