Converting a flow rate from pounds per second (lb/s) to cubic meters per minute (m³/min) involves several steps. This process requires understanding unit conversions for mass, volume, time, and the density of the material being measured. Below is a detailed explanation of the stepwise conversion process.
Step 1: Units Involved
Before performing the conversion, it is essential to clarify the units:
- Pound per second (lb/s): A measure of mass flow rate, indicating how many pounds of a substance pass through a point per second.
- Cubic meter per minute (m³/min): A measure of volumetric flow rate, indicating how many cubic meters of a substance flow per minute.
Step 2: Obtain the Substance’s Density
The relationship between mass and volume is determined by the density of the substance. Density is typically expressed in units such as pounds per cubic foot (lb/ft³) or kilograms per cubic meter (kg/m³). For this example, let’s assume the density of the substance is provided as 62.4 lb/ft³, which corresponds to the approximate density of water at standard conditions.
Step 3: Convert Pounds to Kilograms
The metric system uses kilograms (kg) for mass. To convert from pounds to kilograms, use the conversion factor:
1 lb=0.453592 kg1 \, \text{lb} = 0.453592 \, \text{kg}1lb=0.453592kg
Multiply the mass flow rate by this factor:
0.38 lb/s×0.453592 kg/lb=0.17236496 kg/s0.38 \, \text{lb/s} \times 0.453592 \, \text{kg/lb} = 0.17236496 \, \text{kg/s}0.38lb/s×0.453592kg/lb=0.17236496kg/s
Step 4: Convert Cubic Feet to Cubic Meters
Density in metric units is often given as kilograms per cubic meter (kg/m³). First, convert the density from pounds per cubic foot to kilograms per cubic meter. Use the conversion factor:
1 ft3=0.0283168 m31 \, \text{ft}^3 = 0.0283168 \, \text{m}^31ft3=0.0283168m3
Thus,
62.4 lb/ft3×0.453592 kg/lb÷0.0283168 m3/ft3=999.972 kg/m362.4 \, \text{lb/ft}^3 \times 0.453592 \, \text{kg/lb} \div 0.0283168 \, \text{m}^3/\text{ft}^3 = 999.972 \, \text{kg/m}^362.4lb/ft3×0.453592kg/lb÷0.0283168m3/ft3=999.972kg/m3
This value confirms the density of water in metric units.
Step 5: Calculate Volumetric Flow Rate in Cubic Meters per Second
The volumetric flow rate is calculated by dividing the mass flow rate by the density of the substance:
Volumetric Flow Rate (m3/s)=Mass Flow Rate (kg/s)Density (kg/m3)\text{Volumetric Flow Rate (m}^3/\text{s)} = \frac{\text{Mass Flow Rate (kg/s)}}{\text{Density (kg/m}^3)}Volumetric Flow Rate (m3/s)=Density (kg/m3)Mass Flow Rate (kg/s)
Substitute the values:
Volumetric Flow Rate (m3/s)=0.17236496 kg/s999.972 kg/m3≈0.00017237 m3/s\text{Volumetric Flow Rate (m}^3/\text{s)} = \frac{0.17236496 \, \text{kg/s}}{999.972 \, \text{kg/m}^3} \approx 0.00017237 \, \text{m}^3/\text{s}Volumetric Flow Rate (m3/s)=999.972kg/m30.17236496kg/s≈0.00017237m3/s
Step 6: Convert Seconds to Minutes
To express the flow rate in cubic meters per minute (m³/min), multiply the result by the number of seconds in a minute:
0.00017237 m3/s×60 s/min=0.0103422 m3/min0.00017237 \, \text{m}^3/\text{s} \times 60 \, \text{s/min} = 0.0103422 \, \text{m}^3/\text{min}0.00017237m3/s×60s/min=0.0103422m3/min
Final Result
The flow rate of 0.38 pounds per second is equivalent to approximately 0.01034 cubic meters per minute, assuming a density of 62.4 lb/ft³.
Key Points to Remember
- Always ensure the density of the substance is known and correctly converted to the desired units.
- Use standard conversion factors for pounds to kilograms, cubic feet to cubic meters, and seconds to minutes.
- Perform calculations step by step to minimize errors, especially when dealing with multiple unit conversions.
This stepwise approach ensures accuracy and clarity in converting flow rates between different units.