Question

A workshop measures 10m × 25m. The shop is illuminated by 24 lamps of 200 watts each. The lumen efficiency of each lamp is 15 lumens per watt. Depreciation factor is assumed to be 0.8 and a coefficient of utilization 0.5. Determine the illumination on the working plane.

Answer 1

To determine the illumination on the working plane, we need to calculate the illuminance in lux (lm/m²) provided by the lamps. Here's a step-by-step approach to solving this problem:

### Given Data
- Dimensions of the workshop: \( 10 \, \text{m} \times 25 \, \text{m} \)
- Number of lamps: 24
- Power rating of each lamp: 200 watts
- Lumen efficiency of each lamp: 15 lumens per watt
- Depreciation factor: 0.8
- Coefficient of utilization: 0.5

### Step-by-Step Calculation

1. **Calculate the Total Luminous Output of All Lamps:**

   Each lamp produces:
   \[
   \text{Luminous Output per Lamp} = \text{Power} \times \text{Lumen Efficiency}
   \]
   \[
   = 200 \, \text{watts} \times 15 \, \text{lumens/watt}
   \]
   \[
   = 3000 \, \text{lumens}
   \]

   Total luminous output from 24 lamps:
   \[
   \text{Total Luminous Output} = 24 \times 3000
   \]
   \[
   = 72{,}000 \, \text{lumens}
   \]

2. **Apply the Depreciation Factor:**

   The depreciation factor accounts for the reduction in lighting effectiveness over time.
   \[
   \text{Effective Luminous Output} = \text{Total Luminous Output} \times \text{Depreciation Factor}
   \]
   \[
   = 72{,}000 \times 0.8
   \]
   \[
   = 57{,}600 \, \text{lumens}
   \]

3. **Apply the Coefficient of Utilization:**

   The coefficient of utilization accounts for the effectiveness of light distribution.
   \[
   \text{Utilized Luminous Output} = \text{Effective Luminous Output} \times \text{Coefficient of Utilization}
   \]
   \[
   = 57{,}600 \times 0.5
   \]
   \[
   = 28{,}800 \, \text{lumens}
   \]

4. **Calculate the Area of the Workshop:**

   \[
   \text{Area} = 10 \, \text{m} \times 25 \, \text{m}
   \]
   \[
   = 250 \, \text{m}^2
   \]

5. **Determine the Illuminance (Lux):**

   \[
   \text{Illuminance} = \frac{\text{Utilized Luminous Output}}{\text{Area}}
   \]
   \[
   = \frac{28{,}800}{250}
   \]
   \[
   = 115.2 \, \text{lux}
   \]

### Conclusion

The illumination on the working plane of the workshop is **115.2 lux**.

Answer 2

To determine the illumination on the working plane, we'll calculate the average illumination (or illuminance) in lux, which is the amount of luminous flux received per unit area. Here's the step-by-step process:

### 1. Calculate the Total Luminous Flux

**Luminous Flux** (Φ) is given by the product of the lumen output per lamp and the number of lamps.

Each lamp has a luminous efficiency of 15 lumens per watt. For a lamp of 200 watts, the total luminous output is:
\[ \text{Luminous output per lamp} = 200 \, \text{watts} \times 15 \, \text{lumens/watt} = 3000 \, \text{lumens} \]

With 24 lamps:
\[ \text{Total Luminous Flux} = 24 \, \text{lamps} \times 3000 \, \text{lumens/lamp} = 72000 \, \text{lumens} \]

### 2. Apply the Depreciation Factor

The depreciation factor accounts for losses over time (e.g., lamp aging, dirt). The given factor is 0.8:
\[ \text{Effective Luminous Flux} = 72000 \, \text{lumens} \times 0.8 = 57600 \, \text{lumens} \]

### 3. Apply the Coefficient of Utilization (CU)

The coefficient of utilization adjusts for the efficiency of light distribution in the space. The given CU is 0.5:
\[ \text{Utilized Luminous Flux} = 57600 \, \text{lumens} \times 0.5 = 28800 \, \text{lumens} \]

### 4. Calculate the Area of the Working Plane

The area of the workshop is:
\[ \text{Area} = 10 \, \text{m} \times 25 \, \text{m} = 250 \, \text{m}^2 \]

### 5. Determine the Illumination (Lux)

Illuminance (E) is the total luminous flux divided by the area:
\[ \text{Illuminance (E)} = \frac{\text{Utilized Luminous Flux}}{\text{Area}} \]
\[ \text{Illuminance (E)} = \frac{28800 \, \text{lumens}}{250 \, \text{m}^2} = 115.2 \, \text{lux} \]

### Summary

The illumination on the working plane is **115.2 lux**.