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

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