Question

A glucose solution being administered with an IV has a flow rate of 1.86 cm3/min. What will the new flow rate be if the glucose is replaced by whole blood having the same density but a viscosity 2.70 times that of the glucose? All other factors remain constant.

Answer 1

Answer:

Q' = 0.688 cm³/min

Explanation:

Given that initial flow rate

Q= 1.86 cm³/min

Lets final flow rate is Q' cm³/min

From Poiseuilles law for

$Q=\dfrac{\Delta P\pi r^4}{8\eta L}$       -------1

Where

ΔP=Pressure difference

L= Length

η=viscosity

r= Radius

Given that all other factor is same only viscosity become 2.7 η.

New viscosity, η'= 2.7  η

New discharge Q'

$Q'=\dfrac{\Delta P\pi r^4}{8\eta' L}$   ----2

Q' η' = Q  η

Form 1 and 2 equation

Q' x  2.7  η = 1.86 x  η

Q' = 0.688 cm³/min