66) Choose the correct option from the following listed formula. (Note: n_a is the % of air void, a_c is the air content & n is the soil’s porosity.)
a) n_a = n x a_c
b) n_a= n/(a_c )
c) n_a= n + a_c
d) n_a= n – a_c
Answer: a) n_a = n x a_c
The percentage of air voids is the ratio of the volume of air to the total volume. i.e. , n_a = (V_a )/V ……(i)
The air content is simply the ratio of the volume of air to the volume of the void.
i.e. , a_c = (V_a )/V_v ∴ V_a= a_c. V_v……(ii)
From the equation (i) & (ii),
We get, n_a = (a_c.V_v )/V
The ratio of the volume of the void to the total volume is nothing but the porosity. i.e. n = ( V_v )/V
∴ n_a = n x a_c
Therefore, the product of porosity & air content is nothing but a percentage of air voids.