Glycerine at 20°C has a specific gravity of 1.263. Compute its density and specific weight.
The correct answer and explanation is:
Let’s solve the problem step-by-step:
Given:
- Specific gravity (SG) of glycerine at 20°C = 1.263
- Temperature = 20°C (important because density depends on temperature)
What to find:
- Density (ρ) of glycerine (in kg/m³ or g/cm³)
- Specific weight (γ) of glycerine (in N/m³)
Step 1: Understanding specific gravity
- Specific gravity (SG) is the ratio of the density of a substance to the density of water at a specified temperature (usually 4°C for water since it is the max density point).
- The density of water at 4°C = 1000 kg/m³ (or 1 g/cm³)
- So:
SG=ρsubstanceρwaterSG = \frac{\rho_{\text{substance}}}{\rho_{\text{water}}}
Step 2: Calculate density of glycerine
ρglycerine=SG×ρwater=1.263×1000=1263 kg/m3\rho_{\text{glycerine}} = SG \times \rho_{\text{water}} = 1.263 \times 1000 = 1263 \text{ kg/m}^3
So, the density of glycerine at 20°C is 1263 kg/m³.
Step 3: Calculate specific weight
- Specific weight (γ) is the weight per unit volume.
- It is related to density by:
γ=ρ×g\gamma = \rho \times g
where gg = acceleration due to gravity ≈ 9.81 m/s². γ=1263×9.81=12394.03 N/m3\gamma = 1263 \times 9.81 = 12394.03 \text{ N/m}^3
So, the specific weight of glycerine is approximately 12,394 N/m³.
Summary:
- Density of glycerine at 20°C = 1263 kg/m³
- Specific weight of glycerine at 20°C = 12,394 N/m³
Explanation (300 words):
Specific gravity is a dimensionless quantity that compares the density of a substance to the density of a reference substance, usually water at 4°C. Because the density of water at this temperature is 1000 kg/m³, the specific gravity numerically equals the density of the substance in kg/m³ divided by 1000.
In this problem, glycerine’s specific gravity is 1.263, meaning glycerine is 1.263 times denser than water. To find the actual density, multiply this ratio by the density of water, which results in 1263 kg/m³. This tells us that one cubic meter of glycerine weighs more than one cubic meter of water due to its higher molecular mass and packing density.
Specific weight, on the other hand, represents the force per unit volume due to gravity. It is computed by multiplying the density by gravitational acceleration (9.81 m/s² on Earth). Specific weight is useful in fluid mechanics and engineering because it directly relates to the weight force exerted by the fluid volume, important for calculating pressure, buoyancy, and flow characteristics.
Here, multiplying 1263 kg/m³ by 9.81 m/s² gives about 12,394 N/m³, meaning that each cubic meter of glycerine weighs approximately 12,394 newtons (about 1263 kilograms-force).
Both values are essential for practical applications such as designing equipment that handles glycerine, estimating fluid flow in pipes, or calculating forces on submerged structures. Temperature is crucial because fluid density changes with temperature; here, the value is specifically for 20°C, which is standard room temperature.
In summary, knowing specific gravity allows quick density calculation by comparison to water, and specific weight connects that density to gravitational force, both key properties in fluid dynamics and engineering design.