When dealing with different unit systems in physics, engineering, and science, conversions between metric and imperial units are often necessary. One such conversion involves Exagram per Liter (Eg/L) and Slug per Cubic Inch (slug/in³). This guide will break down the process into easy steps so you can confidently convert 271.4 Exagram per Liter into Slug per Cubic Inch without confusion.
Understanding the Units
Before jumping into the conversion, let’s first define the two units involved:
- Exagram per Liter (Eg/L)
- Exagram (Eg): An Exagram is a unit of mass in the metric system equal to 10¹⁸ grams (or 10¹⁵ kilograms).
- Liter (L): A liter is a metric unit of volume equal to 0.001 cubic meters (m³).
- Therefore, Exagram per Liter (Eg/L) represents mass per unit volume, or density, in the metric system.
- Slug per Cubic Inch (slug/in³)
- Slug: A slug is a unit of mass in the Imperial (US Customary) system. 1 slug ≈ 14.5939 kilograms.
- Cubic Inch (in³): A cubic inch is a unit of volume, where 1 cubic inch = 0.000016387 cubic meters.
- Thus, Slug per Cubic Inch (slug/in³) represents density in the Imperial system.
Step-by-Step Conversion Process
To convert 271.4 Eg/L to slug/in³, we need to follow these steps:
Step 1: Convert Exagram to Kilogram
Since 1 Exagram (Eg) = 10¹⁵ kg, we convert 271.4 Eg into kilograms:271.4×1015 kg271.4 \times 10^{15} \text{ kg}271.4×1015 kg =2.714×1017 kg= 2.714 \times 10^{17} \text{ kg}=2.714×1017 kg
Step 2: Convert Liter to Cubic Meters
We know that 1 Liter = 0.001 m³, so the given density in kg/L can be converted to kg/m³ as follows:2.714×1017 kg/L×1000 L/m³2.714 \times 10^{17} \text{ kg/L} \times 1000 \text{ L/m³}2.714×1017 kg/L×1000 L/m³ =2.714×1020 kg/m³= 2.714 \times 10^{20} \text{ kg/m³}=2.714×1020 kg/m³
Step 3: Convert kg/m³ to Slug/m³
Since 1 slug = 14.5939 kg, we divide the kg/m³ value by this conversion factor:2.714×1020 kg/m³14.5939 kg/slug\frac{2.714 \times 10^{20} \text{ kg/m³}}{14.5939 \text{ kg/slug}}14.5939 kg/slug2.714×1020 kg/m³ =1.86×1019 slug/m³= 1.86 \times 10^{19} \text{ slug/m³}=1.86×1019 slug/m³
Step 4: Convert Slug per Cubic Meter to Slug per Cubic Inch
Since 1 m³ = 61,023.7441 in³, we divide by this factor:1.86×1019 slug/m³61023.7441\frac{1.86 \times 10^{19} \text{ slug/m³}}{61023.7441}61023.74411.86×1019 slug/m³ =3.05×1014 slug/in³= 3.05 \times 10^{14} \text{ slug/in³}=3.05×1014 slug/in³
Final Answer
Thus, 271.4 Exagram per Liter is approximately 3.05 × 10¹⁴ Slug per Cubic Inch.
Summary of the Steps
- Convert Exagram to Kilograms: 1Eg=1015kg1 Eg = 10^{15} kg1Eg=1015kg.
- Convert Liters to Cubic Meters: 1L=0.001m31 L = 0.001 m³1L=0.001m3.
- Convert kg/m³ to slug/m³: 1slug=14.5939kg1 slug = 14.5939 kg1slug=14.5939kg.
- Convert slug/m³ to slug/in³: 1m3=61,023.7441in31 m³ = 61,023.7441 in³1m3=61,023.7441in3.
- Perform the calculations step by step to find the final result.
Why is This Important?
Understanding these conversions is crucial in various scientific and engineering applications. Many fields, including aerospace, mechanical engineering, and fluid dynamics, require precise density conversions between different unit systems to ensure accurate calculations and measurements.