VIPSolutionsGive step-by-step solution with explanation and final answer: An office room of size 9 X 1 5 m is to be illuminated by 2 x 1 8 W LED luminaire. The lamps are being mounted at a height of 3 m from the work plane. The average illumination required is 2 4 0 lux. Calculate the number of lamps required to be fitted, assuming a CU of 0 . 7 5 and a LLF of 0 . 8 . Assume the ceiling height of the room as 5 m . Draw the layout of the luminaire arrangement. The lumen output of 2 x 1 8 W LED may be taken as 4 0 0 0 lumens.
Question:
Give step-by-step solution with explanation and final answer: An office room of size 9 X 1 5 m is to be illuminated by 2 x 1 8 W LED luminaire. The lamps are being mounted at a height of 3 m from the work plane. The average illumination required is 2 4 0 lux. Calculate the number of lamps required to be fitted, assuming a CU of 0 . 7 5 and a LLF of 0 . 8 . Assume the ceiling height of the room as 5 m . Draw the layout of the luminaire arrangement. The lumen output of 2 x 1 8 W LED may be taken as 4 0 0 0 lumens.
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Asked by: Abhishek
Created at: 2025-09-17 16:24:06
Asked by: Abhishek
Created at: 2025-09-17 16:24:06
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# Step-by-Step Solution
## **Given Data**
- Room size: \(9~\text{m} \times 15~\text{m}\)
- Mounting height above work plane: \(3~\text{m}\)
- Ceiling height: \(5~\text{m}\)
- Required illumination: \(240~\text{lux}\)
- Coefficient of Utilization (CU): \(0.75\)
- Light Loss Factor (LLF): \(0.8\)
- LED luminaire: \(2 \times 18~\text{W}\)
- Lumen output per luminaire: \(4000~\text{lumens}\)
---
## **1. Calculate the Area to Be Illuminated**
\[
\text{Area} = 9~\text{m} \times 15~\text{m} = 135~\text{m}^2
\]
---
## **2. Calculate Total Lumen Required**
\[
\text{Total lumens required} = \text{Illumination (lux)} \times \text{Area}
\]
\[
= 240~\text{lux} \times 135~\text{m}^2 = 32,400~\text{lumens}
\]
---
## **3. Adjust for CU and LLF**
The actual number of lumens needed from the luminaires must account for losses:
\[
\text{Effective lumens required} = \frac{\text{Total lumens required}}{\text{CU} \times \text{LLF}}
\]
\[
= \frac{32,400}{0.75 \times 0.8}
\]
\[
= \frac{32,400}{0.6}
\]
\[
= 54,000~\text{lumens}
\]
---
## **4. Calculate Number of Luminaires Needed**
Each luminaire provides \(4000~\text{lumens}\):
\[
\text{Number of luminaires} = \frac{\text{Effective lumens required}}{\text{Lumens per luminaire}}
\]
\[
= \frac{54,000}{4,000}
\]
\[
= 13.5
\]
Round up to the next whole number:
\[
\boxed{14~\text{luminaires}}
\]
---
## **5. Luminaire Layout**
**Room dimensions:** \(9~\text{m} \times 15~\text{m}\)
**Number of luminaires:** \(14\)
A possible rectangular grid arrangement:
- **Rows along 15 m side:** 2 rows
- **Luminaires per row:** 7 in each row
**Spacing:**
- Along 15 m: \(15~\text{m}/(7+1) \approx 1.88~\text{m}\) between luminaires
- Along 9 m: \(9~\text{m}/(2+1) \approx 3~\text{m}\) between rows
### **Simple Layout Sketch (Textual)**
```
-------------------------------------------------
| O O O O O O O | (row 1)
| |
| O O O O O O O | (row 2)
-------------------------------------------------
```
- \(O\) = Luminaire
---
## **Final Answers**
- **Number of luminaires required:** \(\boxed{14}\)
- **Layout:** 2 rows of 7 luminaires evenly spaced across the room
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