Sunday, October 18, 2020

HP 42S/DM42: Height of a Fire, Time to Clear a Corridor

 HP 42S/DM42:  Height of a Fire, Time to Clear a Corridor


HP 42S/DM42/Free42 Program:  FIREHGT


The program FHGT approximates the height of a fire in three scenarios:


* A relatively large fire

* A fire with a base area of approximately 0.5 meter

* A fire set in a corner


The general equation is:


H = factor * Q^0.4


H = height of a fire in meters, including the tip

factor = constant depending on the scenario the fire is set in

Q = energy release rate in kilowatts


00  {119-Byte Prgm}

01 LBL "FIREHGT"

02 "ENERGY? (kW)"

03 PROMPT

04 STO 01

05 LBL 00

06 "TYPE?"

07 AVIEW

08 "LARGE"

09 KEY 1 GTO 01

10 "0.5 M"

11 KEY 2 GTO 02

12 "CORNER"

13 KEY 3 GTO 03

14 MENU

15 LBL 10

16 STOP 

17 GTO 10

18 LBL 01

19 0.23

20 GTO 04

21 LBL 02

22 0.21 

23 GTO 04

24 LBL 03

25 0.075

26 GTO 04

27 LBL 04

28 CLMENU

29 EXITALL

30 RCL 01

31 0.4

32 Y↑X

33 ×

34 "HEIGHT=" 

35 ARCL ST X

36 AVIEW

37 END


Example:


Q = 2650 kW


large fire:  H = 5.38302238231 m

0.5 m fire:  H = 4.9149334795 m

corner fire:  H = 1.7553338554 m


HP 42S/DM42/Free42 Program:  SMOKE


The program SMOKE estimates:


*  The front velocity of the smoke, or how quickly the smoke fills a corridor

*  The time it takes for front velocity to fill the corridor.


Equations used:


V ≈ 0.5 * √(g * (1 - Ta/T) * H)

tf = L / Vf


g = acceleration of gravity, for Earth, g = 9.80665 m/s

Ta = ambient temperature

T = gas temperature  (Ta ≤ T)

H = height of the corridor in meters

L = length of the corridor in meters 


Note 1 - Ta/T = (Da - Dc) / Da

Da = density of the corridor of the ambient air

Dc = density of the fire fluid


00 {99-Byte Prgm}

01 LBL "SMOKE"

02 1

03 "AMB. TEMP?"

04 PROMPT

05 "GAS TEMP?"

06 PROMPT

07 ÷

08 -

09 9.80665

10 ×

11 "HEIGHT? (M)"

12 PROMPT

13 ×

14 SQRT

15 2

16 ÷

17 ENTER

18 "VEL= "

19 ARCL ST X

20 AVIEW 

21 STOP 

22 R↓

23 1/X

24 "LENGTH? (M)"

25 PROMPT

26 ×

27 "TIME="

28 ARCL ST X

29 AVIEW

30 END


Example:


Amb. Temp:  78 °F = 25.555555556 °C

Gas Temp:  103 °F = 39.44444444 °C

Height:  3.048 m

Length:  3.6576 m


Results:


Velocity:  1.622103844 m/s

Time:  2.254849474 s


Source:


Lawson, J.R. and Quintiere, J.G..   "Slide Rule Estimates of Fire Growth". Fire Technology, Vol. 21., No. 4, November 1985, pg. 267



Eddie


All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


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