Final answer:
To calculate the viscosity of blood, we must rearrange Poiseuille's equation and convert all given data to SI units, such as converting the length of the capillary to meters and the diameter to radius. We then find the flow rate and subsequently the viscosity.
Step-by-step explanation:
The question is asking to calculate the viscosity of blood, given the time it takes for blood to travel through a capillary, the length and diameter of the capillary, and the pressure drop. To find the viscosity, we use Poiseuille's law which relates the volume flow rate (Q) to the viscosity (η), assuming laminar flow in a cylindrical tube:
V = πr4ΔP / (8ηL)
Where V is the volume flow rate, r is the radius of the capillary, ΔP is the pressure drop, η is the viscosity, and L is the length of the capillary. We need to rearrange the equation to solve for η. Additionally, we need to convert our units to standard SI units for consistency. Let's use the given values to calculate η.
Step-by-Step Solution:
- Convert the length of the capillary from mm to m: L = 2 mm = 2 x 10-3 m
- Convert the diameter of the capillary to radius in m: r = Diameter/2 = (5 x 10-6 m)/2
- Calculate the flow rate V: V = π x (Radius)4 x (Pressure drop) / (8 x η x Length). From the given data, we have to find the volume flow rate given the time and cross-sectional area (A = πr2)
- Compute the viscosity η by rearranging the equation and solve for η using the calculated flow rate.
The computed value of η will give us the viscosity of blood in (N.s)/m2.