Final answer:
The new flow rate of the whole blood through the IV, which has the same density but a viscosity 2.50 times that of glucose, would be 1.60 cm³/min when all other factors remain constant.
Step-by-step explanation:
A glucose solution being administered with an IV has a flow rate of 4.00 cm³/min. The question asks us to determine the new flow rate if this solution is substituted with whole blood, which has the same density but a viscosity 2.50 times higher than that of glucose, assuming all other factors remain constant.
To calculate the new flow rate, one must understand the Hagen-Poiseuille equation, which describes the flow of a liquid through a pipe. This equation shows that the flow rate is inversely proportional to the viscosity of the fluid. Therefore, if the viscosity of blood is 2.50 times the viscosity of the glucose solution, the new flow rate will be 1/2.50 times the original flow rate.
Calculating this, we have:
New flow rate = Original flow rate / Viscosity factor
New flow rate = 4.00 cm³/min / 2.50
New flow rate = 1.60 cm³/min
Hence, the new flow rate of the whole blood through the IV will be 1.60 cm³/min.