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A glucose solution being administered with an IV has a flow rate of 4.0 cm3/min. What will the new flow rate be if the glucose is replaced by whole blood having the, same density, but a viscosity of 2.5 times that of glucose? All other factors remain constant. 4−0 cm

2
/min

User Rfernandes
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Final answer:

The new flow rate when whole blood replaces glucose solution with 2.5 times the viscosity will be 10.00 cm³/min.

Step-by-step explanation:

The formula for calculating the flow rate of a fluid through a tube is Q = (πr^4ΔP)/8ηL, where ΔP represents the pressure differential, η stands for fluid viscosity, and L is the tube's length. The density factor is null because the density of whole blood and glucose solution are the same. The viscosity, which is 2.5 times that of glucose, is the only variable that varies. Consequently, Q' = Q × (η'/η), where η' is the blood viscosity and η is the glucose viscosity, will be the new flow rate.

In this case, η' = 2.5η, so the new flow rate is Q' = Q × (2.5η/η) = 2.5Q. Since the original flow rate is 4.00 cm³/min, the new flow rate will be Q' = 2.5 × 4.00 cm³/min = 10.00 cm³/min.

User Fzf
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