Final answer:
The new flow rate of whole blood, with a viscosity 2.50 times greater than the glucose solution, will be 1.60 cm³/min, calculated by dividing the original flow rate (4.00 cm³/min) by the viscosity factor (2.50).
Step-by-step explanation:
The student's question involves calculating the new flow rate of a liquid through an intravenous (IV) drip when the viscosity changes. Given that the flow rate of glucose is 4.00 cm³/min, and the viscosity of blood is 2.50 times that of glucose, we must determine the new flow rate when the glucose is replaced by whole blood, assuming all other factors, including density, remain constant.
According to the principle of fluid dynamics, specifically the Hagen-Poiseuille equation, the flow rate (Q) is inversely proportional to the viscosity (η) when the pressure difference (ΔP), the length of the tube (L), and the radius of the tube (r) are constant. So, if the viscosity increases by a factor of 2.50, the new flow rate Q' can be calculated using the relationship,
Q' = Q / 2.50,
where Q is the original flow rate of the glucose solution. Substituting the given Q value, we get,
Q' = 4.00 cm³/min / 2.50 = 1.60 cm³/min.
Therefore, the new flow rate of whole blood through the IV will be 1.60 cm³/min.