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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 = Ms/Vs = 575g/400cm3= 1.44g/ cm3
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
rb = 545.5g/400cm3 = 1.36 g/cm3
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/cm3 = 580.4g/vol. vol. = 446.4cm3
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 = 288cm3
Oven dry wt. = 320/1.15 = 272g
rb = 272/288 = 0.97g/cm3
5. Calculate the oven dry weight of a 350 cm3 soil sample with a bulk density of 1.42 g/cm3.
1.42g/cm3 = Ms/350cm3 Ms = 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 = Vair + Vwater/Vtotal = 140cm3/250cm3 = 56%
8. Calculate the bulk density of a soil sample that has a porosity of 45%.
i.e. for 1cm3 soil, assume r d of 2.65 g/cm3
1cm3-.45cm3 = .55 x 2.65g/cm3 = 1.46g/cm3
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/cm3 = 69.8cm3 soil
Saturated water content = 65cm3/0.55 = 118.2cm3 water
Total vol. of soil = 118.2cm3 + 69.8cm3 = 188cm3
Porosity = Vair + Vwater/Vtotal = 118.2cm3/188cm3 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/cm3