Final answer:
The viscosity of blood can be calculated using Poiseuille's law. By plugging in the given values of pressure drop, capillary radius, length, and flow rate into the formula, we can determine the viscosity of blood to be approximately 3.62 × 10^3 N.s/m².
Step-by-step explanation:
To calculate the viscosity of blood, we can use Poiseuille's law which states that the rate of flow through a capillary is directly proportional to the pressure drop and the fourth power of the radius, and inversely proportional to the length and viscosity of the blood. The formula is:
Q = (ΔP × π × r^4) / (8 × η × l)
Where Q is the flow rate, ΔP is the pressure drop, r is the radius of the capillary, η is the viscosity of the blood, and l is the length of the capillary.
Given that the pressure drop is 2.75 kPa, the radius is 5.00 μm, the length is 2 mm, and the flow rate is 3.80 × 10-9 cm³/s, we can rearrange the equation to solve for η:
η = (ΔP × π × r^4) / (8 × Q × l)
Plugging in the values, we get:
η = (2.75 × 10^3 N/m² × π × (5.00 × 10^-6 m)⁴) / (8 × 3.80 × 10^-9 m³/s × 2 × 10^-3 m)
Simplifying the equation gives us the value for viscosity:
η ≈ 3.62 × 10^3 N.s/m²