Answer :
Calculating minute ventilation, this formula should be used:
- Minute ventilation = tidal volume x respiratory rate (normal is 4-6 L/min) Tidal volume = alveolar space + dead space.
What is minute ventilation?
Minute ventilation is the tidal volume times the respiratory rate, usually, 500 mL × 12 breaths/min = 6000 mL/min.
Therefore, the 5mm tube will be calculated as:
500 x 15= 7,500 mL/min.
And the 3mm tube will be calculated as:
65 x 15= 975mL/min
The effect decreasing the tube radius will have on increased resistance and minute ventilation is that there will be a decrease in the tube minute ventilation.
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Decreasing the tube radius increases the resistance significantly, which drastically reduces the minute ventilation. In a specific example, reducing the radius from 5 mm to 3 mm decreases the flow rate to roughly 13% of its original value while increasing the resistance to approximately 694.4% of the original value.
To calculate the minute ventilation, we use the formula:
Minute Ventilation (MV) = Tidal Volume (TV) x Respiratory Rate (RR)
However, the exact tidal volume and respiratory rate are not provided. Instead, we can focus on understanding the impact of tube radius on minute ventilation. According to Poiseuille's law, the flow rate (Q) in a tube is proportional to the fourth power of the radius (r) of the tube:
Q ∝ r^4
Thus, even a small change in the radius will have a significant impact on the flow rate.
Example Calculation
If the radius decreases from 5 mm to 3 mm:
Original radius r1 = 5 mm, New radius r2 = 3 mm
The ratio of the new flow rate (Q2) to the original flow rate (Q1) can be calculated as:
Q2 / Q1 = (r2 / r1)^4 = (3 / 5)^4 = 0.1296
This calculation shows that the diameter reduction significantly decreases the flow rate to approximately 13% of the original flow rate.
Impact on Resistance
According to Poiseuille's law, resistance (R) is inversely proportional to the fourth power of the radius:
R ∝ 1 / r^4
Thus, by decreasing the radius, the resistance increases dramatically. Using the same radii (from 5 mm to 3 mm):
R2 / R1 = (r1 / r2)^4 = (5 / 3)^4 = 6.944
This means that the resistance increases to approximately 694.4% of the original resistance.
In summary, decreasing the tube radius significantly increases the resistance, which in turn reduces the minute ventilation.
