VIPSolutionsGive step-by-step solution with explanation , calculation and final answer: An office room of size 9X15m is to be illuminated by 2x18W LED luminaire. The lamps are being mounted at a height of 3m from the work plane. The average illumination required is 240 lux. Calculate the number of lamps required to be fitted, assuming a CU of 0.75 and a LLF of 0.8. Assume the ceiling height of the room as 5m. Draw the layout of the luminaire arrangement. The lumen output of 2x18W LED may be taken as 4000 lumens.
Question:
Give step-by-step solution with explanation , calculation and final answer: An office room of size 9X15m is to be illuminated by 2x18W LED luminaire. The lamps are being mounted at a height of 3m from the work plane. The average illumination required is 240 lux. Calculate the number of lamps required to be fitted, assuming a CU of 0.75 and a LLF of 0.8. Assume the ceiling height of the room as 5m. Draw the layout of the luminaire arrangement. The lumen output of 2x18W LED may be taken as 4000 lumens.
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Asked by: mayank
Created at: 2025-09-18 02:28:56
Asked by: mayank
Created at: 2025-09-18 02:28:56
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# Step-by-Step Solution
## **1. Given Data**
- **Room size:** \(9 \text{m} \times 15\, \text{}\)
- **Area (\(A\)):** \(9 \times 15 = 135\, \text{m}^2\)
- **Illination required (\(E\)):** \(240\, \text{lux}\)
- **Luminaire:** 2 × 18W LED (each fitting)
- **Lumen output per luminaire (\(F\)):** 4000 lumens
- **Mounting height above work plane:** \(3\, \text{m}\)
- **Ceiling height:** \(5\, \text{m}\)
- **Coefficient of Utilization (CU):** 0.75
- **Light Loss Factor (LLF):** 0.8
---
## **2. Total Luminous Flux Required**
\[
\text{Total lumens required} = E \times A
\]
\[
= 240 \times 135 = 32,400 \text{ lumens}
\]
---
## **3. Effective Lumen Output Per Luminaire**
\[
\text{Effective lumens per luminaire} = F \times CU \times LLF
\]
\[
= 4000 \times 0.75 \times 0.8
\]
\[
= 4000 \times 0.6 = 2400 \text{ lumens}
\]
---
## **4. Number of Luminaires Required**
\[
\text{Number of luminaires} = \frac{\text{Total lumens required}}{\text{Effective lumens per luminaire}}
\]
\[
= \frac{32,400}{2400} = 13.5
\]
**Round up to the next whole number:**
\[
\boxed{14 \text{ luminaires}}
\]
---
## **5. Layout of Luminaire Arrangement**
- **Room dimensions:** \(9\, \text{m}\) (width) × \(15\, \text{m}\) (length)
- **Number of luminaires:** 14
**Suggested arrangement:**
- Try a rectangular grid that fits 14 fittings.
- Possible grid: 2 rows × 7 luminaires per row.
### **Top View Layout**
```
-------------------------------------------------
| O O O O O O O | ← 1st row
| |
| O O O O O O O | ← 2nd row
-------------------------------------------------
```
- **Rows:** 2 (along the width)
- **Luminaires per row:** 7 (along the length)
- **Spacing:**
- Lengthwise spacing ≈ \(15 / 8 \approx 1.88\, \text{m}\) (7 spaces between 8 points)
- Widthwise spacing ≈ \(9 / 3 \approx 3.0\, \text{m}\) (2 spaces between 3 points)
---
## **6. Final Answers**
- **Number of luminaires required:** \(\boxed{14}\)
- **Arrangement:** 2 rows × 7 luminaires per row, uniformly spaced.
---
### **Summary Table**
| Parameter | Value |
|--------------------------|----------------------|
| Room Area | 135 m² |
| Required Illumination | 240 lux |
| Lumen Output per Fitting | 4000 lumens |
| CU | 0.75 |
| LLF | 0.8 |
| Effective Output | 2400 lumens |
| Luminaires Needed | 14 |
---
**Note:**
Make sure the actual arrangement fits the room and avoids placing luminaires too close to walls. Adjust spacing as per architectural and lighting standards.
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