Final answer:
The new flow rate of an IV when replacing glucose with whole blood, with the latter having 2.50 times the viscosity, would be 1.60 cm³/min, given the original flow rate was 4.00 cm³/min and all other factors remained constant.
Step-by-step explanation:
The basic principles for calculating IV flow rate involve understanding fluid dynamics principles such as viscosity, density, and pressure differentials. However, when addressing a specific question about the change in flow rate given changes in viscosity but constant density, we can employ our knowledge of Poiseuille's law.
To calculate the new flow rate when replacing a glucose solution with whole blood, where the blood's viscosity is 2.50 times that of glucose, we can use the direct relationship between flow rate and viscosity as described by Poiseuille's law. This law states that flow rate (Q) is inversely proportional to the viscosity (η), when all other factors like pressure difference and tube dimensions are kept constant. Given that viscosity is the only factor changing and that it is increasing by 2.50 times, the new flow rate will decrease by the same factor assuming laminar flow and constant pressure conditions.
The original flow rate of the glucose solution is 4.00 cm³/min. With the increase in viscosity, the new flow rate for whole blood can be calculated as follows: New flow rate = Original flow rate / Increase in viscosity = 4.00 cm³/min / 2.50 = 1.60 cm³/min.