Lessons · Engineering · density and specific weight
Density and specific weight: how heavy a volume is
Density ρ is mass per volume, in kg/m³. Specific weight γ = ρ × g is weight per volume, in N/m³.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
The tank drawing gives dimensions, not a mass. Whether the slab under it is thick enough depends on the weight of the water in it, and that comes only from density, volume and g.
How to think about it
Get the volume in cubic metres first, since that is where the unit mistakes hide. Then mass is density times volume, and weight is that times g, or specific weight times volume in one step.
Worked example
ρ = m / VDensity. Rearranged, m = ρ × V.
Aluminium ρ = 2700 kg/m³; a bar 1.0 m × 0.05 m × 0.05 m = 0.0025 m³Volume first, in m³.
m = 2700 × 0.0025 = 6.75 kgThe mass of the bar.
γ = ρ g = 2700 × 9.81 = 26,487 N/m³; W = 26,487 × 0.0025 = 66.2 NSpecific weight, then the weight of the same bar. Same answer as 6.75 × 9.81, by a different road.
Your turn
Water, 1000 kg/m³, g = 9.81 m/s². Write its specific weight.
γ = 1000 × 9.81 = N/m³
Solve one, graded on the server
The trap
Mixing cm³ and m³. A cubic metre is a million cubic centimetres, so steel at 7.85 g/cm³ is 7850 kg/m³, not 7.85. Off by a thousand, and the tank slab is designed for a bathtub.