Final answer:
When the glucose solution is replaced by whole blood with 2.50 times the viscosity, the new flow rate would be 1.60 cm³/min, calculated by dividing the original flow rate by the viscosity factor.
Step-by-step explanation:
The question involves calculating the flow rate of a solution through an IV (intravenous) tube. When the glucose solution with a flow rate of 4.00 cm³/min is replaced by whole blood, which has a viscosity 2.50 times that of the glucose solution, we have to determine the new flow rate of the blood under these conditions. According to Poiseuille's law, which describes the flow of fluids through a tube, the flow rate is inversely proportional to the viscosity, provided all other factors (pressure, tube dimensions) remain constant. Therefore, if the viscosity is increased by a factor of 2.50, the flow rate will decrease by the same factor, assuming a constant driving pressure and tube characteristics.Given the original flow rate (Q) of glucose as 4.00 cm³/min and the increase in viscosity (η) by a factor of 2.50 times, the new flow rate (Q') can be calculated as follows:Q' = Q / (Factor of increase in viscosity).
Thus, the new flow rate Q' for whole blood would be:Q' = 4.00 cm³/min / 2.50Q' = 1.60 cm³/minTo calculate the flow rate, we need to know the volume (in ml) and the time (in hours) that the solution needs to be administered. In this case, the doctor has ordered 500 ml of solution over 24 hours. The drop factor is given as 60 gtt/ml.To find the flow rate, we divide the volume by the time:Flow rate = Volume ÷ TimeFlow rate = 500 ml ÷ 24 hoursFlow rate = 20.83 ml/hourHowever, since the drop factor is given as 60 gtt/ml, we need to convert the flow rate to drops per minute. To do this, we multiply the flow rate by the drop factor:Flow rate (gtt/min) = Flow rate (ml/hour) * Drop factorFlow rate (gtt/min) = 20.83 ml/hour * 60 gtt/mlFlow rate (gtt/min) = 1249.80 gtt/minTherefore, the flow rate is approximately 1249.80 gtt/min.