Relation Between Dry unit Weight, Bulk unit Weight & Water Content

Relation Between Dry unit Weight, Bulk unit Weight & Water Content

4th March 2020 0 By Malay Sautya

Relation Between Dry unit Weight, Bulk unit Weight & Water Content

In this article,We will make the formula/relation between the dry unit weight( \gamma_{d} ), bulk unit weight( \gamma ) and water content(w).

[Note: Bulk unit weight means bulk density, and dry unit weight means dry density. So, be careful if the question is like that; derive the relation between bulk density, dry density and water content, therefore, the answer will be same.]

Let,

  • W = Total weight of given soil mass.
  • V = Total volume of the given soil mass.
  •  W_{d} = Weight of soil solid in a given soil mass.
  •  W_{w} = Weight of water present in the given soil mass.
  • w = Moisture content or Water content.

From the definition of water content, we can write,

 w = \frac{W_{w}}{W_{d}}
[Add 1 in both sides]
So,  1 + w = 1 + \frac{W_{w}}{W_{d}}
Or,  1 + w = \frac{W_{w} + W_{d}}{W_{d}}
[ We know, Total weight = Weight of water + Weight of soil solid. So,  W = W_{w} + W_{d} ]
Or,  1 + w = \frac{W}{W_{d}}
Or,  W_{d} = W/(1+w)

Again from the definition of dry unit weight, We have,

\gamma_{d} = \frac{W_{d}}{V}
[Now, put the value of  W_{d} , which we have got from the above equation]
Hence, \gamma_{d} = \frac{W}{V(1+w)}
[We know,  \gamma = \frac{W}{V} ]
Or,  \gamma_{d} = \frac{\gamma }{(1+w)}

So, the final relation or formula is  \gamma_{d} = \frac{\gamma }{(1+w)}

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