Final answer:
The new flow rate when replacing a glucose IV solution with whole blood, which has 2.50 times the viscosity, while keeping all other factors constant, will be 1.60 cm³/min.
Step-by-step explanation:
Understanding Flow Rate in Free-Flow O₂ Administration
A glucose solution being administered via an IV has a flow rate of 4.00 cm³/min. The question asks what the new flow rate would be if this glucose is replaced with whole blood that has the same density but a viscosity that's 2.50 times that of the glucose. Assuming all other factors remain constant, the flow rate can be determined by considering Poiseuille's law, which states that flow rate is inversely proportional to the fluid's viscosity. Therefore, if the viscosity of the blood is 2.50 times greater than the glucose solution's viscosity, the flow rate would decrease by a factor of 2.50.
To find the new flow rate (Φ), we can use the inverse proportionality:
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- Φ₂ = Φ₁ / Viscosity Factor
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- Φ₂ = 4.00 cm³/min / 2.50
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- Φ₂ = 1.60 cm³/min
Therefore, the new flow rate when switching from glucose to whole blood in the IV would be 1.60 cm³/min.