A 2 foot diameter pool fire kerosene 1 meter deep is burning in a confined area. What is the largest mass flux for the pool fire with a 95% confidence? Round to the nearest thousands decimal point with units of kg/(m2 s).
To determine the mass flux for the pool fire, we can use the equation for mass burning rate:
m' = ρ * h * D * B
where m' is the mass flux (kg/(m^2 s)), ρ is the fuel density (0.820 kg/L for kerosene), h is the depth of the pool (1 meter), and D is the diameter (2 feet, or 0.6096 meters).
The value B is the burning rate coefficient, which is a function of the type of fuel and wind conditions. For kerosene, B is about 8.27 x 10^-7 (m^2/s) under low wind conditions.
First, convert the fuel density from kg/L to kg/m^3:
ρ = 0.820 kg/L * 1000 L/m^3 = 820 kg/m^3
Now, plug in the values given:
m' = ρ * h * D * B
m' = (820 kg/m^3) * (1 m) * (0.6096 m) * (8.27 x 10^-7 m^2/s)
m' = 0.00041429 kg/(m^2 s)
Since we want the largest mass flux with a 95% confidence, we need to perform a statistical analysis on this value. If we assume that the burning rate coefficient (B) has some uncertainty, we can find the value for B that corresponds to the largest mass flux with 95% confidence.
In this case, let's assume a normal distribution for B with a mean of 8.27 x 10^-7 m^2/s and a standard deviation of 10^-7 m^2/s. To calculate the value of B with 95% confidence, we can use the formula:
B_95 = mean(B) + 1.96 * std(B)
B_95 = [8.27 x 10^-7 m^2/s] + [1.96 * 10^-7 m^2/s]
B_95 = 10.11 x 10^-7 m^2/s
Now, we can calculate the largest mass flux with a 95% confidence:
m'_95 = ρ * h * D * B_95
m'_95 = (820 kg/m^3) * (1 m) * (0.6096 m) * (10.11 x 10^-7 m^2/s)
m'_95 = 0.00050534 kg/(m^2 s)
Rounding to the nearest thousands decimal point, the largest mass flux for the pool fire with a 95% confidence is 0.000 kg/(m^2 s).