Staircase pressurization fan , what is the equation to calculate the air flow and static pressure for fan ?

It depends on the volume of staircase and area of leakage or normally its in cfm/m3

or you can use the following equation

Q = 0.827 A (ΔP)1/2

Q = Air Flow rate (m3/s).A = Flow area / leakage area (m2).ΔP = Pressure difference (Pa). normally50 Pa is used.

static can be calculated by adding all friction losses in the duct if applicable + the air outlet which has been taken into the consideration + the pressure which is needed to be maintained + if any dampers or specific filters are taken into the system

Hope this will work

For stairwell pressurization, refer to the below information:

Q (Total) = Q (Leakage) + Q (open doors)

Q (Leakage) =0.827 x A (Leakage) x (ΔP)1/2

Q (open doors) = sum [ A (open door) x V]

Where,

Q, Flow in m3/s.

A, Area in m2.

ΔP, Pressure difference between staircase and adjacent spaces in Pa.

A (leakage), Area of gaps arround door varies from0.01 to0.06 depending on the door type.

A (open door), area of the open door.

V, Air velocity across the open door.

BS5588:

ΔP =50 Pa.

1 open door on fire floor with V =2 m/s and2 open doors with V =0.75 m/s.

NFPA:

ΔP =45~133 Pa.

No mention for the number of open doors; Q (Total) = Q (Leakage).

In addition to what M. Arsalan has mentinoned which is the situation where all the doors of stairwell are closed, you have to consider the following:

1. Air flow through internally open doors (Doors which are opened inside the building).

2. Air flow through externally open doors (Doors which are opened to outside). 

For how to calculate the above2 You have to see ASHRAE Applications Fire and smoke management.

It depends on the volume of staircase and area of leakage or normally its in cfm/m3

or you can use the following equation

Q = 0.827 A (ΔP)1/2

Q = Air Flow rate (m3/s).A = Flow area / leakage area (m2).ΔP = Pressure difference (Pa). normally50 Pa is used.