CEE 577 28 March 2006

# MID-TERM EXAM

Closed book, 1 sheet of notes allowed.

I.                    (50%) Whole Hog creek flows through and area of the North Carolina Piedmont that is heavily populated with pig farms.  The creek discharges into a lake used for recreational purposes.  Concern over phosphorus loading of the lake has led to a short-term study of nitrogen imputs during storm events.  Data from this brief, 8-day survey period is shown below.

a.       Determine the total phosphorus concentration for each day using the standard log-log model

b.      Estimate the mean mass loading of phosphorus (in kg/d) into the reservoir based on these values.

 Day Flow (m3/s) Total Phosphorus Concentration (µg/L) 1 0.2 2 0.5 12 3 4.2 4 13.1 55 5 2.2 6 8.3 7 2.3 8 0.9

## Solution:

II.                 (50%)  Lake Noir is an urban surface water that has received inputs of lead for many years.  Efforts to clean up the lake resulted in the termination of nearly all point loads of lead as of 1990.  Since that time lake levels have dropped due to decay (0.00005 d-1) and hydraulic flushing.  Unfortunately, Senator Porkbarrel succeeded in getting his brother's button cell battery business exempted from the lead ban.  The amount of lead discharged is directly related to the number of batteries produced.  Due to changes in the battery industry, production of this particular type has dropped off since the business began (see table below).  During this time lead waste has been constant at 800 µg Pb per battery produced.  The output data below were collected for last year (2005) and projected into the future.  It’s also important to know that the Porkbarrel button cell battery company had just moved to the shores of Lake Noir and began discharging on January 1, 2005.  Also, as of this date, the lake concentration of lead was 0.13 µg/L.  The lake has a volume of 1.25 million cubic meters, a surface area of 0.3 million square meters, and an outflow of 800 cubic meters per day.  Ignore any temperature effects or sorption to sediment.

### Porkbarrel Battery Co. Data

 Year Output (batteries/yr) 2005 5,800,000 2010 5,100,000 2015 4,400,000 2020 3,700,000 2025 3,000,000

1. Calculate the expected lead concentration at the beginning of the year 2020.
2. Determine the year when the maximum Pb concentration will drop below 0.05 µg/L.

## Solution:

This is a problem with: (1) a pre-existing concentration that decays; (2) a step loading in 1/1/05, and a linear loading with a negative slope.

1. 10.4 ug/L
2. Year 2060.  This is after the loading drops to zero (in mid-year 2046).  This requires two consecutive models; one with loading and one without.

III.       (50%) On a separate sheet of paper, answer any five (5) of the following questions.

A.                 Describe the difference between mechanistic and empirical modeling

·        Mechanistic is based on a some mechanism grounded in first principles or theory; a deductive approach

·        Empirical is based on a statistical analysis of real environmental data.  The model need not resemble actual fundamental relationships; an inductive approach

B.                 Is a first order reaction always faster than a zero order reaction?  Explain.

·        No. It depends on the reaction rate constant.  First order loss processes do show a higher rate of reaction at the beginning than at the end.  Zero order rates are constant throughout.

C.                 Sketch out a qualitative concentration vs distance (downstream) profile for a river with a point discharge at x=0 and a distributed source that runs from x=3 to x=6 miles.  Show qualitatively how increases in the 1st order decay rate for a pollutant changes this profile.

Note that these are arbitrary concentration levels

D.                 Explain the relationship between Secchi-disk depth and lake trophic state.  Why is there such a relationship?

·        As trophic state increases, there is more algal growth, more light scattering due to algal cells and Secchi depth is smaller, because of the inability to see the Secchi disk at greater depths

E.                  Describe 3 different methods for determining stream velocity.

·        Dye: inject it and follow concentration versus time at a point downstream

·        Current Meter: hand-held or suspended meter to measure velocity at various depths and cross-sections

·        Surface floating device: (oranges), only get surface velocity that way, look at different locations across stream width

·        Drogue: follow movement of device, sail can be set to different depths

·        Theoretical relationship based on roughness, slope, etc: e.g., Manning’s equation

F.                  Describe 2 different ways of measuring drainage basin area

·        Cut and weigh: trace drainage basin on topo map, cut it out and weigh paper

·        Counting squares: same as above, but use graph paper and determine area by counting squares

·        Planimeter method: trace out basin in topo map

·        GIS delineation: requires GIS software and proper elevation data

G.                 Describe the factors that determine re-aeration in rivers, and contrast this with the factors that determine re-aeration in lakes.  In your description, relate micro-scale processes (molecules) to macro-scale (bulk water or air)

·        Mixing is drives it.  2-film model interprets this as reducing the stagnant film thickness

·        Water side mixing is most important, and it is determined by turbulence and water depth

·        Water side turbulence is high with high velocity flow and roughness of stream channel.  High flow and turbulence is cause by elevation drop (slope, free fall over a weir), and by wind turbulence on the surface

·        Air side mixing is less important but affected by wind speed also