Abstract
The hydraulic model is a set of closed-form, deterministic equations used to predict average crowd speeds and movement times of evacuees exiting a building. The standard SFPE hydraulic model assumes that crowd speed is only influenced by crowd congestion and type of terrain, when in fact, it is also affected heavily influenced by smoke, which not only causes evacuees to slow down due to poorer visibility but may also force them to switch a different movement mode: crawling. This paper gathers and refines empirical data from various published experiments involving individuals and groups moving through smoke by walking upright and crawling, to establish two new variants of the hydraulic model describing the movement of crowds through smoke by the two movement modes.
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Notes
The walking height was calculated at 1.78 m, which is the eye height of the 95th percentile adult male based on anthropometric US data [18]
Similarly, the crawling height was determined to be 0.76 m [18]
The walking height was calculated at 1.78 m, which is the eye height of the 95th percentile adult male based on anthropometric US data [18]
Similarly, the crawling height was determined to be 0.76 m [18]
Abbreviations
- BHM:
-
Basic Hydraulic Model
- SMHM:
-
Smoke-Modified Hydraulic Model
- CMHM:
-
Crawl-Modified Hydraulic Model
- \(S\) :
-
Average crowd velocity, [m/s]
- \(D\) :
-
Average crowd density, [persons/m2]
- \({F}_{C}\) :
-
The flow rate of a pedestrian stream, [persons/s]
- \({W}_{p}\) :
-
Physical width of a passageway, [m]
- \(BL\) :
-
One-sided boundary layer width of a passageway, [m]
- \({W}_{e}\) :
-
Effective width of a passageway, [m]
- \({F}_{s}\) :
-
Specific flowrate, i.e., flowrate per unit of effective width [persons/(m s)]
- \({F}_{sm}\) :
-
The maximum specific flowrate of a crowd, [persons/s/m effective width]
- \(k\) :
-
Structural speed modifier for speed calculation, to account for the type of passageway, e.g., ramp, corridor, stairway, etc. [dimensionless]
- \({C}_{s}\) :
-
The extinction coefficient [m−1 or dB/m], a measure of smoke density
- VA :
-
Visual acuity [dimensionless]
- \({R}_{{v}_{smoke}}\) :
-
Mobility: a speed reduction factor that accounts for lower visibility in smoke, [dimensionless]
- \(IWS\) :
-
Average Walking speed of an individual unimpeded by congestion or smoke [m/s]
- \(I{WS}_{i}\) :
-
Initial Walking speed of an individual unimpeded by congestion or smoke [m/s]
- \(I{WS}_{max}\) :
-
Maximum Walking speed of an individual, unimpeded by congestion or smoke [m/s]
- \({D}_{u}\) :
-
Maximum safe crowd density above which there is a risk of a crowd crush, [persons per m2]
- \({D}_{l}\) :
-
Maximum crowd density, [persons per m2], below which the crowd would have the same speed as an unimpeded individual, \(IWS\)
- \({S}_{c}\) :
-
Projected crawling speed of a crowd [m/s]
- \({S}_{s}\) :
-
Projected speed of a crowd in smoke, while walking upright (m/s)
- \({k}_{c}\) :
-
Structural speed modifier for crawling though a 90° turn
- \({n}_{90(uv)}\) :
-
Number of 90° turns along the path of a crawling crowd from the source till arc \((u,v)\)
- DLP :
-
Distance between the transmitter and the receiver in a visual smoke density measurement device, [m]
- \(I\) :
-
Luminous intensity of the transmitted light after it has passed through a smoke layer, [cd]
- \({I}_{o}\) :
-
Luminous intensity of the incident light, [cd]
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Funding
This work was supported by the American University of Sharjah Graduate Teaching Assistant scholarship.
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Abougharib, A., Ndiaye, M. Modified Hydraulic Models for Thin Smoke and Crowd Crawling Phenomena. Fire Technol 58, 2123–2142 (2022). https://doi.org/10.1007/s10694-022-01244-z
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DOI: https://doi.org/10.1007/s10694-022-01244-z