A drawing hall 30 meters by 15 meters with a ceiling height of 5 meters is to be provided with a general illumination of 120 lumens per meter square; taking a coefficient of utilization of 0.5 and depreciation factor of 1.4. Determine the number of fluorescent tubes required, their spacing, mounting height, and total wattage. Take luminous efficiency of fluorescent tube as 40 lumens per watt for 80-watt tubes.
2 Answers
To determine the number of fluorescent tubes required for the drawing hall, along with their spacing, mounting height, and total wattage, follow these steps:
### 1. **Calculate the Total Luminous Output Required**
**1.1. Area of the Hall**
The area of the drawing hall is:
\[ \text{Area} = \text{Length} \times \text{Width} \]
\[ \text{Area} = 30 \, \text{m} \times 15 \, \text{m} = 450 \, \text{m}^2 \]
**1.2. Total Luminous Output Needed**
The general illumination required is 120 lumens per square meter. Therefore:
\[ \text{Total Luminous Output Required} = \text{Area} \times \text{Illumination Level} \]
\[ \text{Total Luminous Output Required} = 450 \, \text{m}^2 \times 120 \, \text{lumens/m}^2 = 54{,}000 \, \text{lumens} \]
**1.3. Adjust for Coefficient of Utilization and Depreciation Factor**
The coefficient of utilization (CU) is 0.5, and the depreciation factor (DF) is 1.4. Therefore:
\[ \text{Adjusted Luminous Output} = \text{Total Luminous Output Required} \times \text{CU} \times \text{DF} \]
\[ \text{Adjusted Luminous Output} = 54{,}000 \, \text{lumens} \times 0.5 \times 1.4 = 37{,}800 \, \text{lumens} \]
### 2. **Determine the Number of Fluorescent Tubes Required**
**2.1. Luminous Output per Tube**
For an 80-watt fluorescent tube with a luminous efficiency of 40 lumens per watt:
\[ \text{Luminous Output per Tube} = \text{Wattage} \times \text{Luminous Efficiency} \]
\[ \text{Luminous Output per Tube} = 80 \, \text{watts} \times 40 \, \text{lumens/watt} = 3{,}200 \, \text{lumens} \]
**2.2. Number of Tubes Required**
The number of tubes needed is:
\[ \text{Number of Tubes} = \frac{\text{Adjusted Luminous Output}}{\text{Luminous Output per Tube}} \]
\[ \text{Number of Tubes} = \frac{37{,}800 \, \text{lumens}}{3{,}200 \, \text{lumens/tube}} = 11.8125 \]
Since we can’t have a fraction of a tube, round up to the nearest whole number:
\[ \text{Number of Tubes} = 12 \]
### 3. **Determine the Total Wattage**
**3.1. Total Wattage**
The total wattage required is:
\[ \text{Total Wattage} = \text{Number of Tubes} \times \text{Wattage per Tube} \]
\[ \text{Total Wattage} = 12 \times 80 \, \text{watts} = 960 \, \text{watts} \]
### 4. **Spacing and Mounting Height**
**4.1. Spacing of Tubes**
The spacing of the tubes will depend on the layout, but to ensure uniform distribution:
- **Lengthwise Spacing**: The hall is 30 meters long. If placing tubes along the length, you need to determine the spacing such that the total length covered is approximately 30 meters.
- **Widthwise Spacing**: The hall is 15 meters wide. Ensure the tubes are evenly distributed along this width.
If you use a standard layout with tubes mounted in rows, you might consider a grid spacing based on the length and width of the hall. For simplicity, let’s assume you’ll place the tubes in a grid pattern:
- Place 3 rows of 4 tubes each (3 rows x 4 tubes = 12 tubes).
- **Spacing Between Tubes in Each Row**: For 30 meters length, with 4 tubes, place them approximately every 7.5 meters apart.
- **Spacing Between Rows**: For 15 meters width, with 3 rows, place them approximately every 5 meters apart.
**4.2. Mounting Height**
Mount the tubes at the ceiling height, which is 5 meters from the floor.
### Summary
- **Number of Fluorescent Tubes Required**: 12
- **Total Wattage**: 960 watts
- **Spacing of Tubes**:
- Lengthwise (30 meters): Approximately every 7.5 meters apart.
- Widthwise (15 meters): Approximately every 5 meters apart.
- **Mounting Height**: 5 meters
This setup will ensure that the drawing hall achieves the desired level of illumination uniformly.
### 1. **Calculate the Total Luminous Output Required**
**1.1. Area of the Hall**
The area of the drawing hall is:
\[ \text{Area} = \text{Length} \times \text{Width} \]
\[ \text{Area} = 30 \, \text{m} \times 15 \, \text{m} = 450 \, \text{m}^2 \]
**1.2. Total Luminous Output Needed**
The general illumination required is 120 lumens per square meter. Therefore:
\[ \text{Total Luminous Output Required} = \text{Area} \times \text{Illumination Level} \]
\[ \text{Total Luminous Output Required} = 450 \, \text{m}^2 \times 120 \, \text{lumens/m}^2 = 54{,}000 \, \text{lumens} \]
**1.3. Adjust for Coefficient of Utilization and Depreciation Factor**
The coefficient of utilization (CU) is 0.5, and the depreciation factor (DF) is 1.4. Therefore:
\[ \text{Adjusted Luminous Output} = \text{Total Luminous Output Required} \times \text{CU} \times \text{DF} \]
\[ \text{Adjusted Luminous Output} = 54{,}000 \, \text{lumens} \times 0.5 \times 1.4 = 37{,}800 \, \text{lumens} \]
### 2. **Determine the Number of Fluorescent Tubes Required**
**2.1. Luminous Output per Tube**
For an 80-watt fluorescent tube with a luminous efficiency of 40 lumens per watt:
\[ \text{Luminous Output per Tube} = \text{Wattage} \times \text{Luminous Efficiency} \]
\[ \text{Luminous Output per Tube} = 80 \, \text{watts} \times 40 \, \text{lumens/watt} = 3{,}200 \, \text{lumens} \]
**2.2. Number of Tubes Required**
The number of tubes needed is:
\[ \text{Number of Tubes} = \frac{\text{Adjusted Luminous Output}}{\text{Luminous Output per Tube}} \]
\[ \text{Number of Tubes} = \frac{37{,}800 \, \text{lumens}}{3{,}200 \, \text{lumens/tube}} = 11.8125 \]
Since we can’t have a fraction of a tube, round up to the nearest whole number:
\[ \text{Number of Tubes} = 12 \]
### 3. **Determine the Total Wattage**
**3.1. Total Wattage**
The total wattage required is:
\[ \text{Total Wattage} = \text{Number of Tubes} \times \text{Wattage per Tube} \]
\[ \text{Total Wattage} = 12 \times 80 \, \text{watts} = 960 \, \text{watts} \]
### 4. **Spacing and Mounting Height**
**4.1. Spacing of Tubes**
The spacing of the tubes will depend on the layout, but to ensure uniform distribution:
- **Lengthwise Spacing**: The hall is 30 meters long. If placing tubes along the length, you need to determine the spacing such that the total length covered is approximately 30 meters.
- **Widthwise Spacing**: The hall is 15 meters wide. Ensure the tubes are evenly distributed along this width.
If you use a standard layout with tubes mounted in rows, you might consider a grid spacing based on the length and width of the hall. For simplicity, let’s assume you’ll place the tubes in a grid pattern:
- Place 3 rows of 4 tubes each (3 rows x 4 tubes = 12 tubes).
- **Spacing Between Tubes in Each Row**: For 30 meters length, with 4 tubes, place them approximately every 7.5 meters apart.
- **Spacing Between Rows**: For 15 meters width, with 3 rows, place them approximately every 5 meters apart.
**4.2. Mounting Height**
Mount the tubes at the ceiling height, which is 5 meters from the floor.
### Summary
- **Number of Fluorescent Tubes Required**: 12
- **Total Wattage**: 960 watts
- **Spacing of Tubes**:
- Lengthwise (30 meters): Approximately every 7.5 meters apart.
- Widthwise (15 meters): Approximately every 5 meters apart.
- **Mounting Height**: 5 meters
This setup will ensure that the drawing hall achieves the desired level of illumination uniformly.
To determine the number of fluorescent tubes required for the drawing hall, we need to calculate the total luminous output required and then figure out how many fluorescent tubes are needed to achieve this output. Here’s a step-by-step approach:
### 1. Calculate the Total Illuminance Required
The drawing hall dimensions are:
- Length = 30 meters
- Width = 15 meters
- Area = \( 30 \times 15 = 450 \) square meters
The required illuminance (general illumination) is 120 lumens per square meter.
So, the total luminous output required is:
\[ \text{Total luminous output required} = \text{Area} \times \text{Illuminance} \]
\[ \text{Total luminous output required} = 450 \, \text{m}^2 \times 120 \, \text{lm/m}^2 \]
\[ \text{Total luminous output required} = 54{,}000 \, \text{lumens} \]
### 2. Adjust for Coefficient of Utilization and Depreciation Factor
The coefficient of utilization (CU) is 0.5 and the depreciation factor (DF) is 1.4. Therefore, the total luminous output required should be adjusted as follows:
\[ \text{Adjusted luminous output} = \text{Total luminous output required} \times \text{CU} \times \text{DF} \]
\[ \text{Adjusted luminous output} = 54{,}000 \, \text{lumens} \times 0.5 \times 1.4 \]
\[ \text{Adjusted luminous output} = 54{,}000 \times 0.7 \]
\[ \text{Adjusted luminous output} = 37{,}800 \, \text{lumens} \]
### 3. Determine the Number of Fluorescent Tubes Required
Given:
- Luminous efficiency of fluorescent tube = 40 lumens per watt
- Wattage of each fluorescent tube = 80 watts
First, calculate the luminous output of one tube:
\[ \text{Luminous output per tube} = \text{Luminous efficiency} \times \text{Wattage} \]
\[ \text{Luminous output per tube} = 40 \, \text{lm/W} \times 80 \, \text{W} \]
\[ \text{Luminous output per tube} = 3{,}200 \, \text{lumens} \]
Now, calculate the number of tubes required:
\[ \text{Number of tubes} = \frac{\text{Adjusted luminous output}}{\text{Luminous output per tube}} \]
\[ \text{Number of tubes} = \frac{37{,}800}{3{,}200} \]
\[ \text{Number of tubes} = 11.8125 \]
Since you cannot have a fraction of a tube, you’ll need 12 fluorescent tubes to meet the illumination requirement.
### 4. Calculate Total Wattage
The total wattage required is:
\[ \text{Total wattage} = \text{Number of tubes} \times \text{Wattage per tube} \]
\[ \text{Total wattage} = 12 \times 80 \]
\[ \text{Total wattage} = 960 \, \text{watts} \]
### 5. Spacing and Mounting Height
**Spacing:**
To ensure even illumination, the spacing between the tubes should be determined based on the layout and arrangement of the tubes. A common practice is to arrange tubes in a grid pattern with equal spacing, but for precise spacing, you should follow standard lighting design guidelines or software for layout planning.
**Mounting Height:**
The mounting height is typically the same as the ceiling height unless there are specific design requirements. In this case, it’s 5 meters.
### Summary
- **Number of fluorescent tubes required:** 12
- **Total wattage:** 960 watts
- **Spacing and mounting height:** Arrange the tubes in a grid pattern, and mount them at the ceiling height of 5 meters.
Ensure to adjust the layout to avoid shadows and achieve uniform lighting distribution.
### 1. Calculate the Total Illuminance Required
The drawing hall dimensions are:
- Length = 30 meters
- Width = 15 meters
- Area = \( 30 \times 15 = 450 \) square meters
The required illuminance (general illumination) is 120 lumens per square meter.
So, the total luminous output required is:
\[ \text{Total luminous output required} = \text{Area} \times \text{Illuminance} \]
\[ \text{Total luminous output required} = 450 \, \text{m}^2 \times 120 \, \text{lm/m}^2 \]
\[ \text{Total luminous output required} = 54{,}000 \, \text{lumens} \]
### 2. Adjust for Coefficient of Utilization and Depreciation Factor
The coefficient of utilization (CU) is 0.5 and the depreciation factor (DF) is 1.4. Therefore, the total luminous output required should be adjusted as follows:
\[ \text{Adjusted luminous output} = \text{Total luminous output required} \times \text{CU} \times \text{DF} \]
\[ \text{Adjusted luminous output} = 54{,}000 \, \text{lumens} \times 0.5 \times 1.4 \]
\[ \text{Adjusted luminous output} = 54{,}000 \times 0.7 \]
\[ \text{Adjusted luminous output} = 37{,}800 \, \text{lumens} \]
### 3. Determine the Number of Fluorescent Tubes Required
Given:
- Luminous efficiency of fluorescent tube = 40 lumens per watt
- Wattage of each fluorescent tube = 80 watts
First, calculate the luminous output of one tube:
\[ \text{Luminous output per tube} = \text{Luminous efficiency} \times \text{Wattage} \]
\[ \text{Luminous output per tube} = 40 \, \text{lm/W} \times 80 \, \text{W} \]
\[ \text{Luminous output per tube} = 3{,}200 \, \text{lumens} \]
Now, calculate the number of tubes required:
\[ \text{Number of tubes} = \frac{\text{Adjusted luminous output}}{\text{Luminous output per tube}} \]
\[ \text{Number of tubes} = \frac{37{,}800}{3{,}200} \]
\[ \text{Number of tubes} = 11.8125 \]
Since you cannot have a fraction of a tube, you’ll need 12 fluorescent tubes to meet the illumination requirement.
### 4. Calculate Total Wattage
The total wattage required is:
\[ \text{Total wattage} = \text{Number of tubes} \times \text{Wattage per tube} \]
\[ \text{Total wattage} = 12 \times 80 \]
\[ \text{Total wattage} = 960 \, \text{watts} \]
### 5. Spacing and Mounting Height
**Spacing:**
To ensure even illumination, the spacing between the tubes should be determined based on the layout and arrangement of the tubes. A common practice is to arrange tubes in a grid pattern with equal spacing, but for precise spacing, you should follow standard lighting design guidelines or software for layout planning.
**Mounting Height:**
The mounting height is typically the same as the ceiling height unless there are specific design requirements. In this case, it’s 5 meters.
### Summary
- **Number of fluorescent tubes required:** 12
- **Total wattage:** 960 watts
- **Spacing and mounting height:** Arrange the tubes in a grid pattern, and mount them at the ceiling height of 5 meters.
Ensure to adjust the layout to avoid shadows and achieve uniform lighting distribution.