Hydrosystems Engineering (EACEE 3250 / 4250)

Spring 2025

Homework #3 (Due Monday April 7th, 11:59 pm)

Homework Guidelines:

Your solutions to homework assignments will be submitted and graded through Gradescope (see the Gradescope tab on your Courseworks dashboard).

You will have two options for submitting your work in Gradescope, either: 1) upload individual scanned images of your handwritten pages (e.g., using your phone), one or more per question; or 2) upload a single PDF that you create which contains the whole submission (e.g., merge files on your computer or phone with a software of your choice).   Please use the naming convention Lastname_HWxx.pdf when submitting your homework assignment. You may choose to type up your calculations, in which case show all your steps and highlight your solution. Note: During the upload, Gradescope will ask you to mark which page/s each problem is on (see example here). It is important that you follow that step for grading purposes.

It is acceptable to discuss problems with your colleagues, and questions are encouraged during office hours, but all work must be done independently. Make sure to clearly show all work on each problem and that your solutions are  presented in an orderly fashion. It is your responsibility to make your solutions easy to grade.

Topics/Chapters covered:

• Chapter 8: Evaporation and transpiration processes

• Chapter 7: Soil/porous media properties, unsaturated zone, infiltration

Problem #1 Evaporation (20 pts)

Estimate evaporation from a lake surface (in [mm/day]) if the water temperature is 20 °C and the waves are 5 cm high. A micro-meteorological station with a 2 m tower measures the air temperature at 15°C, the air relative humidity at 80% and a windspeed of 1 m/s. Assume a nominal surface air density p = 1.2 kg/m3  and surface air pressure P = 105  Pa.

Problem #2 Evapotranspiration (25 pts)

Some plants may be more efficient in photosynthesis when the atmosphere is enriched with CO2. Increased CO2 levels may also raise air temperatures.

An experiment to test the potential impacts of greenhouse gases on vegetation is performed in a chamber. The air temperature is raised by 2.0 [C] under the experimental conditions listed below. These environmental conditions are maintained close to these nominal values.

Leaf Porometer (see picture) measurements of vapor release from the leaf surfaces indicates a 10% increase in plant transpiration. What is the change in the plant stomatal resistance of the plants in the chamber before and after the CO2 enrichment?

Note: The before enrichment case is referred to as the "Control" case in the experiment.

Experimental Conditions

Net Available Energy R n  - G = 200 [W m-2 ]

Air relative humidity = 80%

Air aerodynamic resistance r = 30 [s m-1 ] Air pressure P = 105  [Pa]

Moist air density= 1.3 [kg m-3 ]

Air temperature and latent heat flux (Control): T = 23 [ C ] and LE = 200 [W m-2  ]

Problem #3 Soil Properties (25 points)

A soil sample is analyzed via a sieve analysis and determined to have the following size distribution: 40% sand and 30% silt.

a) Identify the soil texture for this soil sample, and provide its porosity, saturated hydraulic conductivity, and saturated matric head based on the appropriate in the Margulis textbook.

b) Plot the matric head vs. volumetric soil moisture and hydraulic conductivity vs. volumetric soil moisture trends for this soil. You may use your plotting software of choice.

c) Compute matric head and conductivity at a volumetric soil moisture content (θ  = 0.40). What is the sign of matric head? Explain why.

d) On the same figure as (b) plot the matric head vs. volumetric soil moisture and hydraulic conductivity vs. volumetric soil moisture trends for a soil with 20% sand and 30% silt. Comment on the differences in the plot trends.

Problem #4 Infiltration (30 points)

The Philip and Green-Ampt equations provide models for “infiltration capacity” (or “potential infiltration”).

a) What assumptions are used in the development of the Philip and Green-Ampt infiltration capacity models? Clearly explain the difference between actual infiltration rate and infiltration capacity (potential infiltration).

b) Under what specific conditions are the two models the same?

c) A snowmelt event lasting 4 hours occurs with a uniform melt flux intensity of 0.65 mm/hr.

The volumetric soil moisture at this site is measured to be 0.02. Assume the following soil hydraulic properties: saturated hydraulic conductivity of 0.00125 cm hr-1, saturated matric head of -21.8 cm, porosity of 0.39, and Brooks-Corey parameter b of 4.9.

Is it possible that infiltration excess runoff will occur in the watershed given the same snowmelt event described above? Justify your response.

Using both the Philip and Green-Ampt models, compute the time to ponding under these conditions.

Will ponding occur for these conditions? Explain your reasoning.