土壤物理題庫
1. Prove the following relation of porosity to particle density and to bulk density:
ƒ=(ρs - ρb)/ρs = 1 - ρb/ρs
2. Prove the following relation between volume wetness, mass wetness, bulk density,
and water density (ρw = Mw/Vw):
θ = w ρb/ρw
3. A sample of moist soil having a wet mass of 1.0 kg and a volume of 0.64 liter
(6.4×10-4 m3) was dried in the oven and found to have a dry mass of 0.8 kg.
Assuming the typical value of particle density for a mineral soil (2650 kg/m 3),
calculate the bulk density ρb, porosity ƒ, void ratio e, mass wetness w, volume
wetness θ, water volume ratio νw, degree of saturation s, and air-filled porosity ƒa.
4. What is the equivalent depth of water contained in a soil profile 1 m deep if the
mass wetness of the upper 0.4 m is 15% and that of the lower 0.6 m is 25%?
Assume a bulk density of 1200 kg/m3 in the upper layer and 1400 in the lower
layer. How much water does the soil contain in cubic meters per hectare of land?
5. Give two bubble in a glass of carbonated water, one with a radius of 0.5 mm and
the other with a radius of 1.5 mm, what is the pressure difference between them?
Assume γ = 0.07 N/m.
6. Calculate the equilibrium capillary rise of water and mercury at 20℃ in glass
cylindrical capillary tubes of the following diameters: (a) 2 mm; (b) 0.5 mm; (c)
0.1 mm. Disregard density of atmosphere.
7. A capillary tube with an internal radius r = 0.25 mm is dipped into water of
surface tension 0.073 N/m. How high will the water rise in the tube if the contact
angle α = 0°, and how high if α = 45°?
8. The bottom of a capillary tube is immersed in a water reservoir. Water then rises
in the tube and comes to rest at a height of 50 mm above the free water surface.
The tube is then lifted slowly until the water in it begins to recede down the tube.
After the lifting is stopped, the meniscus inside the tube comes to rest at a height
of 57.5 mm. Assuming that the receding contact angle of water in the tube is 0°,
calculate: (a) the radius of the tube; (b) the advancing contact angle. Use a value
of 0.0705 N/m for the surface tension of water.
9. Using Stokes’s law, calculate the time needed for all sand particles (diameter > 50
μm) to settle out of a depth of 0.2 m in an aqueous suspension at 30℃. How long
for all silt particles to settle out? How long for “coarse” clay ( >1μm)?
10. Calculate the approximate specific surface of a sand composed of the following
array of particle size:
Average diameter:
1mm
0.5mm
0.2mm 0.1mm
Percent by mass:
40%
30%
20%
10%
11. Calculate the bulk density of a soil sample that has a wet weight of 15.2g, a dry weight of
14.5g, and a volume of 12.1cm3.
12. A soil sample has a bulk density of 1.12 Mg/m3 and a particle density of 2.62 Mg/m3.
Calculate the total porosity of the soil.
13. Calculate the aeration porosity of a soil sample that has a bulk density of 1.35 Mg/m3, a
particle density of 2.65 Mg/m3, and a gravimetric soil water content of 0.18 kg/kg
14. How many centimeters of a rainfall would be required to bring a soil from a water content
of 0.08kg/kg to 0.25 cm3/cm3 at a depth of 15 cm if the bulk density of the soil was 1.35
Mg/m3
15. Calculate the potential gradient between two points 20cm apart in vertical distance and
reading 20 b and 20 cm of Hg, respectively.
16. A tensiometer is buried in an unsaturated soil sample at a depth of 15cm below the soil
surface. The surface of the mercury reservoir is 10cm above the soil surface, and the
mercury-water interface in the tube connecting the tensiometer to the mercury is 20cm
above the soil surface. What is the matric potential of the soil sample in head
units(centimeters of water)?
17. A 10-cm-volume of soil sample weighs 15g before drying and 13g after drying. Calculate
(a) bulk density, (b) volumetric water content, (c) gravimetric water content, (d) total
porosity, (e) air-filled porosity of the sample. (Assume a particle density of 2.6g/cm3.)
18. A soil clod has a volume of 100cm3, gravimetric moisture content is 0.20, and bulk
density is 1.50 g/cm3. Calculate the degree of saturation and air-filled porosity？
19. Water is ponded on the surface of a saturated soil core to a constant depth of 10cm.
Assuming that the core has a cross-sectional area of 28.3cm2 and a height of 10cm, and
that 425cm3 of water is collected in the beaker in 4 hours , calculate the saturated
hydraulic conductivity and flux density of the soil. Place the reference level at the top of
the core.
20. A vacuum gage tensiometer，（full scale 0-100）
，reads 34. The distance from the gage to
the ceramic cup（vertical distance）is 100cm. Find the matric potential，ψm
21.The distance from the surface of the mercury reservoir to the center of the ceramic cup
（vertical distance）is 20cm and the value of mercury height is 14.2cm. Find the matric
potential，ψm？
22. Calculate the equivalent diameter of the pores filled with water that can be maintained at a
matric head of 100cm at equilibrium and a soil temperature of 20℃？ Surface tension of
water is 72dynes/cm at 20℃
23. How many centimeters (equivalent depth) of water are contained in a soil profile 1m deep
if the mass wetness of the upper 40cm is 15％, and that of the lower 60cm is 25％？ The
bulk density is 1.2 g/cm3 in the upper layer and 1.4g/cm3 in the deeper layer. How much
water does the soil contain in cubic meters per hectare of land？
24. Consider a soil core of equal diameter and length of 0.08m. Water is allowed to flow
vertically downward under a constant head of 0.04m. The constant rate of effluent
collected from bottom of core was 0.04m/s. Calculate the saturated hydraulic conductivity
of soil.
25. A soil in which the liquid water is in equilibrium with a water table at -70cm and the
reference level is chosen as -70cm. Find the values of ψp（pressure potential）
，ψm（matric
potential）
，ψ（gravitational
potential）
，ψ（hydraulic
potential）throughout the soil profile
g
h
to -110cm？
26. A soil in which water is flowing into a drain at -40cm. The reference level is the soil
surface. Find the values ofψ（
，ψm（matric potential）
，ψ（
p pressure potential）
g gravitational
potential）
，ψh（hydraulic potential） for the entire soil profile to -60cm. Estimates must
first be made of ψm？
27. Suppose you measured the following data for a soil. A horizon from 0 to 30cm with bulk
density=1.2 Mg/m3: θm(gravimetric water content)=28％ at -10kpa, 20％ at -100kpa, and
8％ at -1500kpa. Bt horizon 30 to 70cm with bulk density=1.4 Mg/m3: θm(gravimetric
water content)=30％ at -10kpa, 25％ at -100kpa, and 15％ at -1500kpa. Bx horizon
from 70 to 120cm with bulk density=1.95 Mg/m3: θm(gravimetric water content)=20％ at
-10kpa, 15％ at -100kpa, and 5％ at -1500kpa. Estimate the total available water holding
capacity of the soil？
28. A one hectare field contains 0.2 g g-1 of water to 10 m depth. Assuming a uniform soil
bulk density of 1.5 Mg/m3, calculate the total water content of soil in liters and equivalent
depth.
29. The 0-50 cm layer of a lakebed soil has a field capacity of 30% by weight, soil-water
content of 15% by weight, and bulk density of 1.2Mg m-3. A rainfall of 4 cm was received
of which 75% was lost as runoff. Calculate the following:
1. What is the volume of runoff from a test plot of 25m * 40m?
2. What is soil erosion (t/ha) if the runoff contained sediments of 25 g / liter?
30. A soil is sampled by a core measuring 7.6 cm in diameter and 7.6 am deep. The core
weighs 300 g. The total core plus wet soil weight is 1000 g. On oven drying at 1050C the
core plus dry soil weighed 860 g. Calculate wet and dry bulk densities and gravimetric
moisture contents.
31. One liter of dry soil sampled from a farm requires 300 g of water to completely saturate it.
Calculate: (a) its porosity and (b) volume of water required to saturate the plow layer (20
cm) of 1 hectare of the farmland.
32. A soil in the greenhouse container has a wet bulk density of 1.7 Mg/m3 and dry bulk
density of 1.4 Mg/m3. Calculate gravimetric and volumetric soil moisture contents, and
air-filled porosity.
33. Calculate particle density of a soil from the following data:
Weight of pycnometer= 50 g
Weight of the powder dry soil= 214 g
Mass of soil and deaerated water when pycnometer was filled to capacity + pycnometer
= 352 g
Temperature of water = 200C
Volume of pycnometer = 168 cm3
34. A sample of moist soil weighed 100 g and had an oven dry moisture content of 0.04. What
is the oven dry weight of the 100 g sample?
35. 10 mm of rain infiltrated a soil having aninitial moisture content by volume of 0.1 m3/m3.
If the soil absorbed enough of the rainfall to raise its moisture content to 0.2 m3/m3, how
many cm would the rainfall penetrate?
36. Compute soil moisture content of a 20 g of wet sample that registers an increase in
volume by 5 cm3. Assume particle density is 2.7 g/cm3.
37. The following soil data were obtained for an irrigation experiment with corn. Irrigation of
10 cm was applied on 6/10/88 after monitoring the soil moisture.
Soil moisture content
Bulk
Wilting
Field
Depth
density
point
capacity
(cm)
(g/cm3)
(w, g/g)
(w, g/g)
(g/g)
6/10/88
6/20/88
0-30
1.2
0.10
0.30
0.10
0.20
31-50
1.3
0.12
0.32
0.15
0.25
51-80
1.4
0.14
0.28
0.25
0.20
81-150
1.6
0.15
0.25
0.20
0.15
(a) Calculate depth of penetration of irrigation water
(b) Evaluate evaportranspiration of corn in mm/day
(c) Determine drainable porosity at field capacity assuming particle 2.65 g/cm
38. Net weight of a wet soil core 7.5 cm in diameter and 7.5 cm deep is
600 g. Calculate wet and dry density and equivalent depth of water
if the oven dry weight of the core is 500 g.
39. Point A is 10 cm above point B in a soil. At point A, ψg（gravitational potential）=15 cm.
What is ψg（gravitational potential） at point B？
40. If a tensiometer functions in the range of ψm（matric potential）from 0 to -800cm, what is
the largest effective pore radius of the ceramic material making up the tensiometer cup？