Final answer:
To calculate the viscosity of blood, we can use the formula n = (ΔP × V × r^2) / (4 × η × l), where ΔP is the pressure drop, V is the volume flow rate, r is the radius of the capillary, η is the viscosity of the fluid, and l is the length of the capillary. First, we need to convert the given values and then calculate the volume flow rate using the velocity of blood flow. Once we have all the values, we can substitute them into the viscosity formula to find the viscosity of blood.
Step-by-step explanation:
To calculate the viscosity, we can use the formula:
n = (ΔP × V × r2) / (4 × η × l)
Where:
n is the viscosity of blood
ΔP is the pressure drop (in Pascals)
V is the volume flow rate (in m3/s)
r is the radius of the capillary (in meters)
η is the viscosity of the fluid (in Pa·s or N·s/m2)
l is the length of the capillary (in meters)
First, we need to convert the given values:
Pressure drop: 2.65 kPa = 2.65 × 103 Pa
Length of the capillary: 2.00 mm = 2.00 × 10-3 m
Radius of the capillary: 5.00 µm = 5.00 × 10-6 m
Volume flow rate: Not given
Since the volume flow rate is not given, we need to calculate it using the formula:
V = (π × r2 × v)
Where:
r is the radius of the capillary
v is the velocity of blood flow
We can relate the velocity to the time it takes for blood to pass through the capillary using the formula:
v = l / t
Where:
l is the length of the capillary
t is the time taken for blood to pass through the capillary
We can substitute this back into the volume flow rate formula to get:
V = (π × r2 × (l / t))
Now, let's substitute all the values into the viscosity formula to calculate the viscosity of blood:
n = (2.65 × 103 × [(π × (5.00 × 10-6)2) × ((2.00 × 10-3) / 1.45)]) / (4 × η × (2.00 × 10-3))
By solving this equation, we can find the viscosity of blood.