Physics Exam

physics_1.pdf

Home >Physics homework help >Physics Exam

Exam 1 Test questions- At least 90% of the points on your exam will be a selection of these questions. Problems involving calculations will have altered numbers. 1) Define or describe the following;

a) Reference state for soil water potential b) Diffuse double layer c) Soil bulk density d) Soil water potential equilibrium

e) Cohesion f) Soil water hysteresis

g) Porosity h) Matric potential i) Total soil water potential j) Specific surface k) Contact angle l) Air entry matric potential m) Volumetric water content n) Time Domain Reflectometry o) Gravimetric water content p) Shrink-swell

q) Adhesion r) Solute potential s) Head units t) Isomorphous substitution u) Water characteristic function

2) Short answer- a. If water exist in soil as films only (that is, water is only coating particle surfaces), explain why you would expect more water in a clay soil than in a sand. b. As a soil drains, is it true that small diameter pores drain before larger diameter pores? Explain. c. For a given soil, is the bulk density a constant? Explain. d. Explain why soil water would move from a drier to a wetter soil. Or could it? e. Does water drip from unsaturated soil? Explain based on interfacial curvature. f. It is often said that water always flow downhill. Is this true? Explain. g. Why do we need a reference state for the soil water potential? List the properties of the reference state. h. Can an unsaturated sand pull water from an unsaturated clay? Briefly explain. i. Why does free water move against gravity into narrow diameter pores?

3) Concise essay

a. Briefly describe the forces in soil which reduce the potential energy of water relative to the reference state. b. Explain the purpose and basic operation of the pressure plate. c. . Briefly describe the principle of operation of Neutron Attenuation (neutron probe) and Time Domain Reflectometry. What do these measure and how? d. Concisely discuss the key physical and chemical characteristics of the soil solid phase involved with the adsorption and retention of water. e. Briefly explain why some soils change dimension (swell) upon wetting while others do not. f. A friend suggests that you use a tensiometer for the indirect measurement of soil water content. Briefly discuss the operation of the tensiometer, what it measures, and list pros and cons of using it for measuring soil water content. g. A certain soil is known to change dimensions with changing water content if the dominant cation in the soil is calcium but not if the dominant cation is potassium. Why?

4) Using a sketch, compare and contrast θ(h) for a fine and a coarse textured soil. Explain the similarities and differences (if any) between the curves. 5) A volume of soil (Vtotal) is the sum of the volume of pores (Vpores) and the volume of solids (Vsolids). Derive in a few steps the porosity φ expression 𝜙 = 1 − 𝜌𝑏

𝜌𝑠

where ρb is the soil bulk density and ρs is the particle density.

Quantitative

6) A bucket (20 cm diameter by 10 cm depth) contains a loam soil with a particle density of 2.7 g/cm3 and a porosity of 40%. The soil is at a volumetric water content of 0.10. If the bucket receives 2.0 cm of rainfall,

a. Determine the soil water content after the rainfall (you may assume that the rainfall mixes uniformly throughout the soil volume). b. Determine the weight of the bucket of soil after the rainfall (you may disregard the weight of the empty bucket).

7) A cylinder (4 cm diameter by 10 cm long) contains 210.0 g of oven-dry mineral soil. Estimate the grams of water required to fully saturate the soil in the cylinder. 8) Suppose a layer of soil (20 cm thick, overlying impermeable bedrock) has a known θ(h) relationship

𝜃(ℎ) = 0.46 � −5 ℎ � 0.25

If the soil is initially at h= -1000 cm, how much rainfall would be required to increase h to -100 cm throughout the soil layer? (You may assume that the added water is mixed uniformly throughout the 20 cm layer and that there is no evaporation or drainage losses.) 9) Two soil samples, A and B, are placed next to each other with good contact. Soil A is at θ=0.28, while soil B is at θ= 0.15. The soil water characteristic curve for each soil is

a. Will soil water move from one soil to the other? If so, which sample will lose water? Briefly explain. b. Which soil would you argue has the narrower distribution of pore sizes and why?

10) Suppose you have a homogeneous soil sample with a volume of 100 cm3 and a known moisture retention function (for h<-8 cm),

𝜃(ℎ) = 0.48 � −8 ℎ � 0.15

100

150

200

250

300

0 0.1 0.2 0.3 0.4 0.5

So il

w at

er te

ns io

n (c

m )

Water Content (vol/vol)

Soil A Soil B

If the average matric potential of the sample is -2170 cm, a. What is the water content of the sample? b. How much water would you need to add to the soil sample (assuming the water is mixed uniformly with the soil) in order to increase the matric potential to -100 cm? c. What is the physical interpretation of the -8 cm in the moisture retention function?

11) a. What do you need to know in order to determine the direction of water flow between

two points?

b. The matric potential (or water pressure) is measured at three soil depths. Use the data in the following table to determine the direction of water flow between depths 1 and 2 and depths 2 and

Soil depth (cm) soil texture h or p (cm) Pair (atm) 100 sandy loam -400 1 300 clay loam -80 1 400 loamy sand +5 1

12) A field soil is instrumented with tensiometers at three depths as shown below. You wish to know the direction of water flow (up or down) in the soil between the measurement depths.

a. Describe (without a calculation) how you would use the information in the diagram to

assess the direction of water flow. b. Now use the data provided in the figure in a calculation to determine the direction of

water flow in the soil between 15 to 40 cm depth and in the soil between 40 to 100 cm depth.

Pair(gauge)=-310 cm Pair(gauge)=-260 cm

Pair(gauge)=-510 cm

porous ceramic cup

capped air pocket

water filled tube

soil surface

Scale (cm)

100

13) A long capillary tube (radius=0.0015 cm) with a semi-permeable membrane on the lower end is oriented vertically and placed in a dilute sodium chloride solution at T=20OC. If the height of rise of water in the tube is 20 cm,

a. What is the solute potential (in head units) of the solution? State assumptions. b. Estimate the concentration of the sodium chloride solution.

14) Consider the following cylindrical pores. Determine the height of rise in each configuration. You may assume a contact angle of zero and 20 oC. 15) Suppose you have a homogeneous soil sample with a volume of 400 cm3 and a known

moisture retention function,

𝜃(ℎ) = 0.43 � −5 ℎ � 0.40

If the average matric potential of the sample is -1000 cm, how much water would you need to add to the soil sample (assuming the water is distributed uniformly in the soil) in order to increase the matric potential to -100 cm?

16) Suppose you have a homogeneous soil sample with a known moisture retention function; 𝜃(ℎ) = 0.48 𝑓𝑓𝑓 |ℎ| ≤ 10 𝑐𝑐

𝜃(ℎ) = 0.48 �10 |ℎ| � 0.20

𝑓𝑓𝑓 |ℎ| > 10 𝑐𝑐

If you have a 100 cm3 sample that is water saturated, how many grams of water can you remove by applying a suction of 0.40 atm?

10 cm

r=0.01 cm

r=0.10 cm

10 cm

r=0.01 cm

r=0.10 cm

17) Two soil samples, A and B, are placed next to each other with good contact. Both soils are at θ=0.25. The soil water characteristic function for each soil is given below. Will soil water move from one soil to the other? If so, which sample will lose water? Briefly explain.

Soil A: 𝜃(ℎ) = 0.55 ∗ �−18 𝑐𝑐 ℎ 𝑐𝑐

� 1 3

Soil B: 𝜃(ℎ) = 0.48 ∗ �−12 𝑐𝑐 ℎ 𝑐𝑐

� 1 2

18) The horse-shoe shaped soil system below contains a homogeneous loam and is at

equilibrium. Prior to setting the horse-shoe into water as shown below, the soil on the left was saturated with water while the right side was oven dry.

a. Provide a qualitative sketch of the water content vs. elevation above the water table for the two sides of the horse-shoe. Provide a brief explanation. b. If the divider at the top of the horse-shoe is removed, will water move to the right? Explain. c. If a hole is drilled in the sidewall of the arc holding the soil, will water drip out? Explain.

Initially water saturated Initially air dry

10 m

water

divider

19) Consider the following soils separated by a no flow barrier. The soils are resting in water

at equilibrium.

a. Provide a qualitative sketch of the soil water content distribution (that is, θ vs. distance) above the water-table in the two soils. Explain the similarities or differences in the sketches for the two soils. b. Suppose that a portion of the no flow barrier at 3 m above the water is carefully removed allowing contact between the two soils. Will water move from the clay to the sand? From the sand to the clay? Explain.

20) A freely draining field soil (soil profile shown below on left) has a uniform matric potential of -150cm several days after a rain-storm that had saturated the soil profile. Provide a qualitative diagram (no calculations needed) of the relative water content versus depth using the axes on the right. Briefly explain your rationale.

20 m

0 m

sand clay

θv

D e p t h

Soil surface

Sandy loam (60% sand, 10% clay)

Clay loam (30% sand, 35% clay)

Loam (45% sand, 15% clay)

Sand (90% sand, 5% clay)

Equilibrium diagram problems- These examples cover the type problems that will appear on the exam but the actual exam problem may be altered. 21) A sandy loam soil sample is placed on a saturated porous plate in contact with water as

diagramed below. Determine the equilibrium matric potential or hydrostatic pressure (in your choice of unit systems) in the soil at point A. Would you expect this soil to be saturated? Why or why not.

22) The following system is at equilibrium. a. Find the matric potential (at the midpoint) in the sand and in the silt. b. At equilibrium, how do you expect the water content to compare in the two soils (circle one):

θsand = θsilt θsand < θsilt θsand > θsilt

Explain your reasoning.

sand silt

Pair=1.50 atm Pair=0.90 atm

water

water saturated porous plate

air chamber

10 cm

70 cm

80 cm

Pair (gauge)= -200 mbar

Air chamber

Pair= 850 mbar

0.10

1.00

A∙

porous plate

water

23) The following system is at equilibrium. Find the water pressure term (h or P) of the total soil water potential at point A and point B. You may express your response in either energy/volume or energy/weight of water. 24) The following soil-water systems are at equilibrium (two separate problems). Find the requested information (indicated by the question mark) in each figure. You may express your response in either energy/weight or energy/volume of water.

a. b.

Semi-permeable membrane

Pair=813 mbar

s=-100 cm

Not semipermeable to solutes

Pair=1000 mbar

1.0 m

2.0 m

3.0 m

0.5 m

sandy loam

clay loam

Saline solution (ρ=1.0 g/cm3) Solute free

capped air pocket Pair = ?

50cm

water table

saturated soil

rigid, unsaturated soil

10 cm

Pair=1 atm

porous cup

capped air pocket

rigid, unsaturated soil

h=?

water filled tube

Pair=-0.20 m

60 cm

water filled tube

Pair=1 atm

25) A soil sample is placed on a saturated porous plate and then subjected to a series of manipulations. Determine the equilibrium matric potential at the midpoint of the soil sample (in your choice of unit systems) at each step in the sequence.

Step 1: Step 2: Step 3: Step 4:

Pair (absolute) = 0.60 atm Semipermeable membrane

saline solution, s = -Π

60 cm

10 cm

40 cm

20 cm

10 cm

Semipermeable membrane

saline solution, s = -Π

Notes- • No evaporation • Surrounding air pressure=1 atm • Π= 4.9 x 104 Pascal

soil

water saturated porous plate water

26) The following soil-water system is at equilibrium. Find all the components of the soil water potential head at locations A, B, and C.

Pair=1.15 atm

Pair= 1 atm No evaporation

50 cm

∙ B

C ∙

A ∙

s=-200 cm

semipermeable membrane Porous ceramic

water

saline solution