# Fluid Density Properties

## Fluid Density

Fluid Density is the mass per unit volume and is denoted by the Greek letter ρ (rho).

The dimensions of density are mass per length cubed or M / L³

The old English system of units uses the slug for the unit of mass and feet for the unit of length. Dimensions commonly used in connection with this system are force, F, length, L, and time, T.

In the Systeme International (SI), the common dimensions are mass, M, length, L, and time, T. By using the LFT dimension the slug can be obtained by relating mass to force with acceleration due to gravity.

i.e. F(force) = M(mass) x g(acceleration due to gravity)

Since the units of acceleration are ft³/sec²

the units of density in the english system are Slug/ft³ or lb•sec²/ft^4

The units of density in the SI system are kg/m³ or N•sec²/m^4

It is possible to convert between the English system and the SI system by substituting the equivalent of each dimension with the appropriate value.

1 Slug/ft³ = 515.363 kg/m³

The density of water is 1.94 slug/ft³ or 1000 kg/m³ (1 gr/cm³);

## Specific Weight

Specific weight, sometimes referred to as unit weight, is simply the weight of fluid per unit volume. It is usually denoted by the Greek letter γ (gamma) and has dimensions of force per unit volume.

Its units in the English system and the SI system are lb/ft³ and N/m³ or kg/m²•sec²

The specific weight and the fluid density are related by the acceleration due to gravity, or

γ = gρ

In the U.S., density is often given as pounds per cubic foot, lb/ft³

Since g = 32.2 ft/sec² (9.81 m/sec²), the specific weight of water is

γ = 32.2 x 1.94 slugs = 62.4 lb/ft³

γ = 9.81 x 1000 kg/m³ = 9810 N/m³ (SI)