Additionally, assume an ambient room temperature of 22C. Use gravity, specific heat, density of air and...

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Additionally, assume an ambient room temperature of 22C. Use gravity, specific heat, density of air and other constant values as provided in NFPA 72 Table B.7. Base calculations on a worst case scenario where a fire is centered between four detectors. Remember to account for ceiling height where necessary. The fire scenario for this problem will involve a chair with burning characteristics similar to that of chair F26 under test number 25 in Table B.2.3.2.6.2(e) of NFPA 72. Use FM's time constant (to) for the given listed 15 ft spacing to determine the sprinkler RTI (Table B.3.2.5 NFPA 72). a) Determine the heat detector activation times using Alpert's correlations and the steady-state approach (assume a steady HRR of 800 kW). b) Assuming t fire growth and a convective heat release fraction of 70%, determine heat detector activation times using the following approaches: i. Quasi-steady state with an initial time step At=5s. Perform a sensitivity analysis with at least two other time steps. Plot and compare the HRR and detector temperatures for all three time steps. For each iteration, use the midpoint HRR value for the given time step. For example: First step (t=0 to t=5): HRR = a(At/2) = a(5/2) Second step (t-5 to t=10): HRR = a(t1 +At/2)= a(5+ 5/2) ii. Method developed by Heskestad, Delichatsios and Beyler (NFPA 72 Figure B.3.3.4.4 provides a helpful methodology). c) Plot and compare the HRR, gas and detector temperatures as a function of time for both methods used in (b). For the quasi-steady method, only use the results for At=5s. d) Identify the limitations and assumptions inherent to each approach taken in (a) & (b) for calculating heat detection times. Additionally, assume an ambient room temperature of 22C. Use gravity, specific heat, density of air and other constant values as provided in NFPA 72 Table B.7. Base calculations on a worst case scenario where a fire is centered between four detectors. Remember to account for ceiling height where necessary. The fire scenario for this problem will involve a chair with burning characteristics similar to that of chair F26 under test number 25 in Table B.2.3.2.6.2(e) of NFPA 72. Use FM's time constant (to) for the given listed 15 ft spacing to determine the sprinkler RTI (Table B.3.2.5 NFPA 72). a) Determine the heat detector activation times using Alpert's correlations and the steady-state approach (assume a steady HRR of 800 kW). b) Assuming t fire growth and a convective heat release fraction of 70%, determine heat detector activation times using the following approaches: i. Quasi-steady state with an initial time step At=5s. Perform a sensitivity analysis with at least two other time steps. Plot and compare the HRR and detector temperatures for all three time steps. For each iteration, use the midpoint HRR value for the given time step. For example: First step (t=0 to t=5): HRR = a(At/2) = a(5/2) Second step (t-5 to t=10): HRR = a(t1 +At/2)= a(5+ 5/2) ii. Method developed by Heskestad, Delichatsios and Beyler (NFPA 72 Figure B.3.3.4.4 provides a helpful methodology). c) Plot and compare the HRR, gas and detector temperatures as a function of time for both methods used in (b). For the quasi-steady method, only use the results for At=5s. d) Identify the limitations and assumptions inherent to each approach taken in (a) & (b) for calculating heat detection times.