To estimate the total number of lamps required for a living room with an area of \(16 \, \text{m} \times 10 \, \text{m}\), you need to calculate the required illuminance (illumination level) and then determine how many lamps are necessary to achieve that level given their output.
### Steps for Calculation
1. **Determine the Room's Area:**
The area of the living room is:
\[
\text{Area} = 16 \, \text{m} \times 10 \, \text{m} = 160 \, \text{m}^2
\]
2. **Determine the Required Illuminance:**
Typical illuminance levels for a living room range from 200 to 300 lux. For this example, let's assume a target illuminance of 250 lux.
3. **Calculate the Total Luminous Output Required:**
The total luminous output required can be calculated using the formula:
\[
\text{Total Luminous Output Required} = \text{Illuminance} \times \text{Area}
\]
Substituting the values:
\[
\text{Total Luminous Output Required} = 250 \, \text{lux} \times 160 \, \text{m}^2 = 40{,}000 \, \text{lumens}
\]
4. **Apply the Utilization Factor and Maintenance Factor:**
The actual luminous output needs to account for both the utilization factor (how efficiently the light is used in the room) and the maintenance factor (to account for light loss over time). The effective luminous output required is:
\[
\text{Effective Luminous Output Required} = \frac{\text{Total Luminous Output Required}}{\text{Utilization Factor} \times \text{Maintenance Factor}}
\]
With a utilization factor of 0.8 and a maintenance factor of 0.8:
\[
\text{Effective Luminous Output Required} = \frac{40{,}000 \, \text{lumens}}{0.8 \times 0.8} = \frac{40{,}000 \, \text{lumens}}{0.64} = 62{,}500 \, \text{lumens}
\]
5. **Determine the Number of Lamps Needed:**
Each lamp has a luminous output of 1500 lumens. The number of lamps required is:
\[
\text{Number of Lamps} = \frac{\text{Effective Luminous Output Required}}{\text{Luminous Output per Lamp}}
\]
Substituting the values:
\[
\text{Number of Lamps} = \frac{62{,}500 \, \text{lumens}}{1500 \, \text{lumens per lamp}} \approx 41.67
\]
Since you can't have a fraction of a lamp, you will need to round up to the nearest whole number. Therefore, you will need:
\[
\text{Number of Lamps} = 42
\]
### Summary
To achieve an average illuminance of 250 lux in a living room with an area of 160 m², considering the utilization and maintenance factors, you would require approximately **42 lamps**, each providing 1500 lumens.