Final answer:
To find the new flow rate of whole blood assuming the same density but a viscosity 2.50 times that of the glucose solution, divide the original flow rate by the viscosity increase factor. The new flow rate will be 1.60 cm³/min.
Step-by-step explanation:
The student is asking how to calculate the new flow rate of whole blood through an intravenous (IV) system when it replaces a glucose solution that had been flowing at a rate of 4.00 cm³/min. The density of the whole blood is the same as the glucose solution, but the viscosity is 2.50 times greater. Given that all other factors remain constant, the Hagen-Poiseuille equation suggests that flow rate is inversely proportional to the viscosity. Therefore, the new flow rate will decrease by a factor equal to the increase in viscosity. This can be calculated as follows:
Initial flow rate of glucose solution = 4.00 cm³/min
Viscosity increase factor = 2.50
New flow rate = Initial flow rate / Viscosity increase factor
New flow rate = 4.00 cm³/min / 2.50
New flow rate = 1.60 cm³/min
Therefore, the new flow rate of whole blood would be 1.60 cm³/min.