Question

In patients suffering from asthma, the thickness of the airway walls increases. This thickening results in a reduction of the local shear modulus of the airways by as much as 50% compared to the airways of a healthy person. In a particular person, the local shear modulus is reduced by 21%.Assume that the frictional force due to the air flowing through the airways of this person during an asthma attack increases by a factor of 2.3 over that of a healthy person. Calculate the ratio ? of the shear strain on this person's airway to that of a healthy airway.

Answer 1

modulus of rigidity (r) = shear stress / shear strain

shear stress for a healthy person =

shear stress of asthmatic person = 2.3

modulus of rigidity for a healthy person = r

modulus of rigidity of asthmatic person = 0.79 r ( note there is 21 % reduction means 100 - 21 = 79 %)

therefore,

ratio of shear strain = (2.3 / 0.79 r) / ( / r)

ratio of shear strain = 2.3 / 0.79

ratio of shear strain = 2.911