# Fluid Statics

Matter exists in three states solid, liquid and gas. Any state of matter that can flow is a fluid. Liquids and gases are therefore, referred to as fluids.

### Density :

Density of a substance is the mass per unit volume. Homogenous bodies have uniform density:
ρ = M/V

The unit of density is kg/m3 in S.I. system. Dimension of density is given by [ρ] = = [M] [L-3].

#### Relative Density or Specific Gravity :

Relative density of a substance is the ratio of the density of the substance to the density of pure water (ρw = 1000 kg/m3) at 4°C.

ρr = ρ/ρw.

Relative density is dimensionless

Illustration 1: A hollow metallic sphere has inner and outer radii respectively as 5 cm and 10 cm. If the mass of the sphere is 2.5 kg, find (a) density of the material (b) relative density of the material of the sphere.

Solution: The volume of the material of the sphere is

V = 4/3 π(r23 – r13) = (4/3)x 3.14 x 0.000875 m3
= 0.00367 m3

(a) Therefore, density of the material of the sphere is
ρ= M/V = 2.5/0.00367 kg/m3

= 681.2 kg/m3

(b) ρr = 681.2/1000 = 0.6812

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