If dry density, water density and specific gravity of solids of a given soil sample are 1.6 g/cc, 1.84 g/cc and 2.56 respectively, the porosity of the soil sample, is

Dry density = 1.6 g/cc
Density of water=1.84 g/cc
Specific Gravity of solids=2.56
The porosity of the Soil sample =?

We know that,
Dry density = (specific gravity * density of water )/(1+e).
1.6 = (2.56*1.84)/(1+e).
=>1.6=4.7104/(1+e).
=> (4.7104-1.6) = 1.6e.
=> e= 3.1104/1.6
so e = 1.944
Now,
n= e/(1+e).
or, n= 1.944/(1+1.944).
n = 0.66 .

As per the given problem, the Porosity of the given solid is 0.66.

Usually, we take the density of water as 1g/cc or 1000kg/m^3
Let’s input density of water is equal to 1 g/cc then,
Dry density = (specific gravity *density of water )/(1+e)
1.6=(2.56*1)/(1+e)
=> 1.6=2.56/(1+e)
=> 2.56-1.6=1.6e
=> 0.96=1.6e
e= 0.96/1.6.
It gives the value of void ratio e= 0.6.
Now, the value of the porosity of solids will be
n = e/(1+e)
n = 0.6/(1+0.6)
n = 0.6/1.6
n = 0.375.