Area [tex]A=30 m \times 12 m=360 m^2[/tex]
Depreciation Factor [tex]=1.3[/tex]
Utilisation Factor [tex]=0.5[/tex]
Assume mounting height [tex]=6 m[/tex]
Gross lumens required [tex]\phi=\frac{A \times E}{U F \times M F}[/tex]
[tex]\begin{array}{l}=\frac{A \times E \times D F}{U F} \\=\frac{360 \times 50 \times 13}{0.5}=46800 lcmen\end{array}[/tex]
If 100 watts are used, # of lamps required [tex]=\frac{46800}{1615}[/tex]
[tex]=29 lamps[/tex]
Answer (2)
To adequately light an area of 360 m², you will require approximately 29 lamps, each producing 1615 lumens, based on the calculated gross lumens required of 46800. This calculation takes into account the illumination level, depreciation, and utilization factors. Therefore, the number of lamps needed is 29.
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Calculate the gross lumens required using the formula: ϕ = U F A × E × D F = 0.5 360 × 50 × 1.3 = 46800 lumens.
Calculate the number of lamps required by dividing the gross lumens by the lumens per lamp: Number of lamps = 1615 46800 ≈ 28.98 .
Round the number of lamps to the nearest whole number since you can't have a fraction of a lamp.
The number of lamps required is 29 .
Explanation
Understanding the Problem We are given the area A = 30 m × 12 m = 360 m 2 , a depreciation factor of 1.3 , and a utilisation factor of 0.5 . We are also given that the illuminance E = 50 and the lumens per lamp is 1615 . The goal is to find the number of lamps required.
Calculating Gross Lumens First, we need to calculate the gross lumens required, denoted by ϕ . The formula for this is given by ϕ = U F A × E × D F where A is the area, E is the illuminance, D F is the depreciation factor, and U F is the utilisation factor.
Substituting Values Plugging in the given values, we have ϕ = 0.5 360 × 50 × 1.3 = 0.5 360 × 50 × 1.3 = 46800 lumens.
Calculating Number of Lamps Next, we need to find the number of lamps required. This is calculated by dividing the gross lumens required by the lumens per lamp. So, Number of lamps = 1615 ϕ = 1615 46800 ≈ 28.98 Since we can't have a fraction of a lamp, we round this up to the nearest whole number, which is 29.
Final Answer Therefore, the number of lamps required is 29.
Examples
Imagine you are designing the lighting for a warehouse. Knowing the area of the warehouse, the desired level of brightness (illuminance), and factors that reduce light output (depreciation and utilisation factors), you can calculate the total amount of light (lumens) needed. Then, knowing the light output of each lamp, you can determine how many lamps are required to adequately light the warehouse. This ensures that the warehouse is neither too dark (unsafe) nor too bright (wasteful).
