##### Question

In: Civil Engineering

# compare the apparent specific gravity of the glass to its unit weight. Which is greater? and...

compare the apparent specific gravity of the glass to its unit weight. Which is greater? and why

## Solutions

##### Expert Solution

Unit weight

Unit weight is also known as specific weight, is the weight of substance in a single volume unit.

it can be calculate by using the formula.

................(equation 1)

is the specific weight or unit weight of the material (weight per unit volume,N/m3 )

is the density of the material (mass per unit volume, kg/m3)

is acceleration due to gravity (rate of change of velocity, given in m/s2, and on Earth = 9.81 m/s2)

where the density of the material can be find out as

where is the mass, and is the volume of the material

apply this in equation 1

so unit weight is .....................(equation 3)

Apparent specific gravity

specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance.The reference substance is taken as water at its densest point (at 4 °C or 39.2 °F) which is 1000 kg/m3 or 1g/cm3

specific gravity =ρmaterial / ρwater

if we take water as reference material ρwater is  1g/cm3

specific gravity =ρmaterial /1 = ρmaterial

Specific gravity=ρmaterial=

but it may contain water-permeable voids.so apparent specific gravity is calculated  on the basis of the net volume of material , that is the volume excluding water-permeable voids

Apparent specific gravity = ......................(equation 3)

is the dry mass of the material and $}{v_n$ is the the net volume of the material excluding volume of absorbed matter

so unit weight of material is    from equation 1

and apparent specific gravity is from equation 3

(dry mass of the material) and (net volume of the material excluding volume of absorbed matter) is differ by a small amount so it is nearly equal to which is density of the material from equation 1.

So the unit weight of the material =specific gravity* ≈ apparent specific gravity*

It is clear that for any material unit weight of the material is greater than specific gravity by (acceleration due to gravity)

For glass material the density is 2500 Kg/m3 or 2.5 g/cm3 density of water is 1000 Kg/m3 or 1 g/cm3

Apparent specific gravity=ρglass / ρwater == 2.5 (unitless)

and unit weight = specific gravity* =2.5 *9.81=24.525 kN/m3

From these it is clear that the unit weight of the glass is higher than specific weight by a value of g (9.81m/s2) .It is because unit weight of any material is specific gravity times acceleration due to gravity.

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