Question

Some measurements on a blood sample at 37 ˚C (98.6 ˚F) indicate a shearing stress of 0.540 N/m2 for a corresponding rate of shearing strain of 198 s-1. Determine (a) the apparent viscosity of the blood and (b) its ratio to the viscosity of water at the same temperature.

Answer 1

`0.00273\ \text{Pa s}`

3.944

Step-by-step explanation:

`\tau` = Shearing stress =
`0.54\ \text{N/m}^2`

`\dot{\gamma}` = Rate of shearing strain =
`198\ \text{s}^(-1)`

(a) Viscosity is given by

`\mu_b=\frac{\tau}{\dot{\gamma}}\\\Rightarrow \mu_b=(0.54)/(198)\\\Rightarrow \mu_b=0.00273\ \text{Pa s}`

The apparent viscosity of the blood is
`0.00273\ \text{Pa s}`

(b) Viscosity of water at 37 ˚C = 0.0006922 Pa s =
`\mu_w`

The ratio is

`(\mu_b)/(\mu_w)=(0.00273)/(0.0006922)\\\Rightarrow (\mu_b)/(\mu_w)=3.944`

The required ratio is 3.944