Practice problems: Porosity and bulk density

Bulk density is the weight per unit volume of a soil sample.

1. Calculate the bulk density of a 400 cm3 soil sample that weighs 575 g (oven dry weight).

r
_{b }= M_{s}/V_{s} = 575g/400cm^{3}= 1.44g/ cm^{3}

2. Calculate the bulk density of a 400 cm3 soil sample that weighs 600 g and that is 10% moisture.

Oven dry wt. = 600g/1.1 = 545.5g

r
_{b }= 545.5g/400cm^{3} = 1.36 g/cm^{3}

3. Calculate the volume of a soil sample that is 12% moisture, weighs 650 g and has a bulk density of 1.3 g/cm3.

Oven dry wt. = 650g/1.12 = 580.4g

1.3 g/cm^{3} = 580.4g/vol. vol. = 446.4cm^{3}

4. Calculate the bulk density of a rectangular soil sample with dimensions 12 cm by 6 cm by 4 cm, that is 15% moisture content and weighs 320 g.

Vol. of soil = 12cm x 6cm x 4cm = 288cm^{3}

Oven dry wt. = 320/1.15 = 272g

r
_{b }= 272/288 = 0.97g/cm^{3}

5. Calculate the oven dry weight of a 350 cm3 soil sample with a bulk density of 1.42 g/cm3.

1.42g/cm^{3} = M_{s}/350cm^{3} M_{s} = oven dry wt. = 497g

6. Calculate the porosity of a soil sample that has a bulk density of 1.35 g/cm3. Assume the particle density is 2.65 g/cm3.

Porosity = (1-(r
_{b}/r
_{d}) x 100 = (1-(1.35/2.65)) x 100 = 49%

7. Calculate the porosity (n) of a 250 cm3 clod that contains 140 cm3 water when saturated.

Porosity = V_{air} + V_{water}/V_{total} = 140cm^{3}/250cm^{3} = 56%

8. Calculate the bulk density of a soil sample that has a porosity of 45%.

i.e. for 1cm^{3} soil, assume r
_{d} of 2.65 g/cm^{3}

1cm^{3}-.45cm^{3} = .55 x 2.65g/cm^{3} = 1.46g/cm^{3}

9. Calculate the porosity of a 250 g sample that contains 65 g of water when 55% of the pores are full of water.

Oven dry wt. = 250g-65g = 185g soil

Vol. of soil solids = 185g/2.65g/cm^{3} = 69.8cm^{3} soil

Saturated water content = 65cm^{3}/0.55 = 118.2cm^{3} water

Total vol. of soil = 118.2cm^{3} + 69.8cm^{3} = 188cm^{3}

Porosity = V_{air} + V_{water}/V_{total} = 118.2cm^{3}/188cm^{3} x 100 = 63%

10. What is the particle density of a soil sample that has a bulk density of 1.55 g/cm3 and a porosity of 40%.

Porosity = (1-(r
_{b}/r
_{d}) x 100

40 = ((1-1.55/r
_{d}) x 100

1.55/r
_{d }= 0.6

r
_{d} = 2.58g/cm^{3}