Final answer:
When the viscosity is increased by a factor of 2.5 without changing other factors, the new flow rate of the fluid in the IV will be 1.60 cm³/min, which is found by dividing the original flow rate (4.00 cm³/min) by the increase in viscosity (2.5).
Step-by-step explanation:
To calculate the flow rate of the solution in the IV, we first need to understand that the rate at which fluids flow through a system is affected by several factors, including the viscosity of the fluid. When the viscosity of the fluid is increased, the flow rate generally decreases because the fluid resists motion more. In this case, the viscosity of whole blood is 2.50 times that of glucose, which implies that the flow rate will decrease proportionally.
However, since the density remains constant and no other factors change, we can simplify the relationship by focusing solely on the change in viscosity. If glucose has a flow rate of 4.00 cm³/min and the whole blood is 2.50 times more viscous, the new flow rate can be found by dividing the original flow rate by the increase in viscosity.
Mathematically:
Original Flow Rate / Increase in Viscosity = New Flow Rate
4.00 cm³/min / 2.5 = 1.60 cm³/min
Therefore, the new flow rate would be 1.60 cm³/min.