Internal pressures - Wind Loading of Structures - page 153

The fluctuating internal pressure coefficient, C pi (t), can be written as:
(6.1)
π 1 = A 3/2 / V 0 —where A is the area of the opening and V 0 is the internal volume;
—where p 0 is the atmospheric pressure;
π 3 = ρ a ŪA 1/2 /µ —where µ is the dynamic viscosity of air (Reynolds number);
π 4 = σ u /Ū —where σ u is the standard deviation of the longitudinal turbulence velocity
upstream;
π 5 = ℓ u /√A —where ℓ u is the length scale of turbulence (Section 3.3.4).
π 1 is a non-dimensional parameter related to the geometry of the opening and the
internal volume, π 3 is a Reynolds number (Section 4.2.4) based on a characteristic length
of the opening, π 5 is a ratio between characteristic length scales in the approaching flow
and of the opening. π 2 , the ratio of atmospheric pressure to the reference dynamic
pressure, is a parameter closely related to Mach number.
Amongst these parameters, π 1 and π 4 are the most important. This is fortunate when
wind-tunnel studies of internal pressures are carried out, as it is difficult or impossible to
maintain equality of the other three parameters between full scale and model scale.
6.2.2 Response time
If the inertial (i.e. mass times acceleration) effects are initially neglected, an expression
for the time taken for the internal pressure to become equal to a sudden increase in
pressure outside the opening such as that caused by a sudden window failure can be
derived (Euteneur, 1970).
For conservation of mass, the rate of mass flow-in through the opening must equal the
rate of mass increase inside the volume:
(6.2)
where ρ i denotes the air density within the internal volume.
For turbulent flow through an orifice, the following relationship between flow rate, Q,
and the pressure difference across the orifice, p e − p i , applies:
(6.3)
where k is an orifice constant, typically around 0.6.
Assuming an adiabatic law relating the internal pressure and density,
(6.4)