Question

A circular fuel spill has a diameter of 14 feet and a heat release rate of 10 MW using the generic empirical constant of 0.235 in the Heskestad average flame height correlation. What is the average flame height rounded to the nearest meter. Provide numerical answer with units of seconds, do not include units in input, submit number only.

Answer 1

[AI-generated answer — Bot]

The Heskestad formula for flame height is given by:

H = 3.7 * (Q/A)^0.3

where H is the flame height in meters, Q is the heat release rate in MW, and A is the area of the fire in square meters.

We can first calculate the area of the circular fuel spill using its diameter:

A = pi * (d/2)^2
A = pi * (14/2)^2
A = 153.94 m^2

Substituting the given values into the Heskestad formula:

H = 3.7 * (10/153.94)^0.3
H = 1.14 m

Rounding to the nearest meter, the average flame height is:

H = 1 m

Therefore, the numerical answer to the question is 1.

Answer 2

[AI-generated answer — Explain Bot]

To find the average flame height, we can use the Heskestad average flame height correlation, which is given as:

H = 0.235 * (Q^2/5 * D^4/5)

where H is the flame height, Q is the heat release rate, and D is the diameter of the fuel spill.

Given:
Diameter (D) = 14 feet
Heat release rate (Q) = 10 MW
Empirical constant = 0.235

Let's plug in the values:

H = 0.235 * (10^2/5 * 14^4/5)

Simplifying the expression:

H = 0.235 * (10^(2/5) * 14^(4/5))
H = 0.235 * (10^(0.4) * 14^(0.8))

Now we can calculate the values within the parentheses:

10^(0.4) ≈ 2.5119
14^(0.8) ≈ 9.373

Plugging in the values:

H ≈ 0.235 * (2.5119 * 9.373)
H ≈ 0.235 * 23.573
H ≈ 5.52975

Rounded to the nearest meter, the average flame height is approximately 6 meters.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To find the average flame height of the circular fuel spill, we can use the Heskestad average flame height correlation formula:

H = 0.235 * (Q^2/5) * (D^2/3)

where:
H is the average flame height
Q is the heat release rate
D is the diameter of the fuel spill

Plugging in the given values:
Q = 10 MW = 10 * 10^6 W
D = 14 feet = 4.2672 meters

Substituting the values into the formula:

H = 0.235 * (10^2/5) * (4.2672^2/3)

H = 0.235 * (100/5) * (18.210043/3)

H = 0.235 * 20 * 6.0700146

H = 2.861798193

Rounded to the nearest meter, the average flame height is 3 meters.