To find the new flow rate, we can use the equation for volumetric flow rate:
Q = πr^4ΔP / 8ηl
Where:
Q = volumetric flow rate
r = radius of the tube
ΔP = pressure difference
η = viscosity
l = length of the tube
Since the flow rate is directly proportional to the radius to the power of 4, we can use the following ratio:
(new flow rate) / (original flow rate) = (new radius)^4 / (original radius)^4
Given that the viscosity of blood plasma is 1.5 times that of glucose, we can say that the ratio of the viscosities is 1.5:
η_new = 1.5 * η_original
Assuming the radius remains the same, we can simplify the ratio formula to:
(new flow rate) / (original flow rate) = (1.5)^4
(new flow rate) = (1.5)^4 * (original flow rate) = 5.0625 * 3.0 cm^3/min = 15.19 cm^3/min
Therefore, the new flow rate when blood plasma is used instead of glucose solution is approximately 15.19 cm^3/min.