The resistances of two splits A and Bare 0.35 Ns²m^-8 and 0.05 Ns²m^-8 respectively. The combined resistance of the shafts and trunk airways is 0.4 Ns²m^-8. A booster fan is planned to be installed in split A to increase the quantity flowing through it. Assuming that the surface fan continues to operate at a constant pressure of 1000 Pa, the critical pressure of the booster fan in Pa is

Solution(By Examveda Team)

To find the critical pressure of the booster fan, we can use the equation:
Combined Resistance = Surface Fan Pressure + (Booster Fan Pressure / Flow Quantity)

Given:
Resistance of Split A = 0.35 Ns²m^-8
Resistance of Split B = 0.05 Ns²m^-8
Combined Resistance = 0.4 Ns²m^-8
Surface Fan Pressure = 1000 Pa (constant)
Flow Quantity through Split A (without booster fan) = Resistance of Split A / Surface Fan Pressure
Flow Quantity through Split A = 0.35 Ns²m^-8 / 1000 Pa = 0.00035 m³/s
Flow Quantity through Split B = Resistance of Split B / Surface Fan Pressure
Flow Quantity through Split B = 0.05 Ns²m^-8 / 1000 Pa = 0.00005 m³/s

Now, using the combined resistance equation, we can calculate the critical pressure of the booster fan (let's denote it as Pb):
Combined Resistance = Surface Fan Pressure + (Pb / Flow Quantity through Split A)

0.4 Ns2m-8 = 1000 Pa + (Pb / 0.00035 m3/s)

Now, solve for Pb:
Pb = 0.4 Ns2m-8 - 1000 Pa * (1 / 0.00035 m3/s)
Pb = 0.4 Ns2m-8 - 2857.14 Pa
Pb = 875 Pa

Therefore, the critical pressure of the booster fan is 875 Pa