### Solution of Unit Weight and Its Conversion from Metric Units to SI and US Units.

Articles > Solution of Unit Weight and Its Conversion from Metric Units to SI and US Units.

### Question:

A cohesive soil sample was taken from an SPT and returned to the laboratory in a glass jar. It was found to weigh 140.5 grams. The sample was then placed in a container of V = 500 cm3 and 423 cm3 of water were added to fill the container. From these data, what was the unit weight of the soil in kN/m3 and pcf?

### Solution:

For formulas of soil phase relationships read Soil Phase Relationships article.

Notice that the 140.5 grams is a mass. Therefore, the ratio of mass to volume is the density rho

$\rho = m/v = 140.5/(500-423)=1.82g/cm^3$

$\gamma = \rho g = 1.82g/cm^3*(1kg/1000g)*(9.806m/sec^2)*(1kN/1000N)*(1000cm/1m)^3=17.9kN/m^3$

for conversion from SI units to US units:

$\gamma = 17.9kN/m^3*(1000N/1kN)*(0.2248lbs/1N)*(1m^3/35.3ft^3)=114pcf$