Pdf modification of the streeterphelps system with the. Models can range in detail from dilution models or simple streeter phelps type models of dissolved oxygen to complicated models of stream ecosystems which include many interacting processes and vari ables, for example, oxygen dynamics, nutrient cycles, and algal and zooplankton dynamics the major distinctions between different models are the. The tansui river is the main source of water supply for northern taiwan, and the water quality of its stream is significantly affected by tides. The streeter phelps oxygen dynamics model was originally developed in 1925, almost a century ago.
Solution of eq 3 is known as the classic streeterphelps oxygen sag. The streeterphelps equation is the solution to the differential equation. Oxygen sag curve solved examples waste water engineering. Two mechanisms are known to contribute oxygen to surface waters. It uses the streeter and phelps equation to calculate the impact of a single point source bod load on do. O2, kd is the degradation rate of organic matter, l0 is the total carbonaceous oxygen demand, and kr is the river oxygen aeration coe. Aquadoc campana, hydrogeologist, hydrophilanthropist, professor of hydrogeology and water resources management in the geography program of the college of earth, ocean, and atmospheric sciences ceoas at oregon state university and emeritus professor of hydrogeology at the university of new mexico. Handbook stream sampling for waste load allocation. Study of auto purification capacity of river atuwara in nigeria. Problem illustrating the use of the streeterphelps equation.
Hence the model is referred to as the streeter phelps model. The following thoughts are to be a contribution to a more realistic theoretical model of the selfpurification process in rivers. The do sag curve and the streeter phelps equation one of the earliest mathematical water quality models was developed by for the ohio river by h. Pdf inverse algorithm for streeter phelps equation in water. Streeter pheps equations matlab answers matlab central. Lecture 4 ce 433 excerpts from lecture notes of professor m. Until recently, the classical streeterphelps equation was. Environmental free download as powerpoint presentation. Streeter phelps simplified wasteload allocation boddo. March 11, 2015 this version of the pdf is optimized for presentation use the side bar for convenient navigation feedback and. Onestep equations multiply and divide fractions solve each equation. Problem illustrating the use of the streeter phelps equation a city discharges 25 million gallons per day mgd of domestic sewage into a stream with a typical flow rate of 250 cubic feet per second cfs.
The last differential equation can be integrated to. Reaeration in openchannel flow usgs publications repository. The streeterphelps equation is used in the study of water pollution as a water quality. March 11, 2015 this version of the pdf is optimized for presentation use the side bar for convenient navigation feedback and bug reports are welcome. Inverse algorithm for streeterphelps equation in water pollution.
The velocity of the stream is approximately 3 miles per hour. Developing the streeter phelps rate of reoxygenation k 2 d d deficit in d. This yields the do sag where d stream deficit at time t, mgl. Oxygen demand concepts and dissolved oxygen sag in streams. The streeterphelps equation is used in the study of water pollution as a water quality modelling tool. Such physical incorrectness is still potentially hazardous for more complex systems of differential equations. Analysis of autopurification response of the apies river, gauteng, south africa, to treated wastewater effluent. We will include oxidation of bodl and reaeration from the atmosphere. Derivation of the dissolved oxygen sag equation consider an element of water in a stream. I need to do a program in matlab with two firstorder differential equations with the streeter phelps model. Problem statement use the extended streeter phelps equation including cbod deoxygenation, nbod deoxygenation, and sod and model the ware river from the ware wwtp discharge river mile 10. Phelps equation which describes how the dissolved oxygen varies in a stream, in a running. Exponent on velocity in the streeter and phelps 1925 prediction equation for. Dobbins 1964 expanded the fundamental streeterphelps equation to.
The temperature of the sewage is 21 c, while that of the stream is 15 c. The streeter phelps equation is used in the study of water pollution as a water quality modelling tool. Four miles into this agricultural region is a municipal wastewater discharge from the. Chapter 10 models for water and air quality management. Combining the rates of thesetwo reactions, and writing the. Play you can explore the model by hitting the simulate button, and you can use the three sliders below to i switch the spill on or off 1 or 0. Pdf analysis of autopurification response of the apies. Description this applet is a do sag curve calculator.
Mathematical modeling of the self purification of rivers. Pdf study of auto purification capacity of river atuwara in. Phelps equation to plot do sag curve downstream of a wastewater treatment plant discharge point assume bod at the discharge point, bod0, is 15 mgl 2. When two streams or rivers merge or water is discharged to a stream it is possible to determine the bod and do. Flow diagram of river yamuna indicating the point of joining the drains to the river. View notes derivation streeter phelps equation from ce 170 at university of toronto. Stratification prevents oxygen transport to the bottom layer.
Mar 30, 2012 a modified streeterphelps equation and the hydrological engineering centers river analysis system hecras were combined to assess water quality of the tansui river and its tributaries. More realistically, assume that bod0 has a normal distribution rather than a constant. Universal soil loss equation and revised universal soil loss equation 9 include any impact either erosion or deposition of the concentrated flow channels that form in the natural swales at the bottom of the roughly planar hillslopes, and certainly did not address classical gullying processes that often occur at steep bound. The streeter phelps equation determines the relation between the dissolved oxygen concentration and the biological oxygen demand over time and is a solution to the linear first order differential equation. K f nature of waste, ability of bacteria, temperature k can be determined in laboratory along with l 0 by measuring bod t at two different times. This equation is known as the do sag equation for its distinctive shape or the streeter phelps equation, after the gentlemen who first published it in 1925. The streeter phelps equation for the oxygen deficit represents both of these interacting processes the solution to the streeter phelps equation is. This video covers solved examples to find out the deficit in dissolved oxygen at a location and to calculate the critical deficit and time to critical deficit. Derivation streeterphelps equation professor john r. I need to do a program in matlab with two firstorder differential equations with the streeter phelps. Streeterphelps equation the streeterphelps equation is the solution to the di erential equation dd dt kdl0 exp kdt krd. Streeter phelps equation oxygen conditions in lakes significant reduction in the oxygen content in the bottom layer of deep lakes d1015 m occurs during the summer season.
Streeterphelps equation the streeterphelps equation is the solution to the di. The model describes how dissolved oxygen do decreases in a river or stream along a certain distance by degradation of biochemical oxygen demand bod. Modeling excessive nutrient loading in the environment. Usle is an empirical equation based on measueasue etsateta teoyrements rather than theory b.
Pdf evaluation and development of reaeration equation using. View notes lecture 47 from cee 260 at university of michigan. Do sag equation taking a mass balance of do as a reactive substance expressed as the deficit we get the streeter phelps oxygen sag curve rate of increase of the deficit rate of deoxygenation rate of oxygenation k l k d dt dd d r dddt the change in oxygen deficit d per unit time, mgl. Mathematical modelling of selfpcrificationof rivers h. Please state any additional assumptions you made, and show all work. This differential equation states that the total change in oxygen deficit d is equal to the difference between the two rates of deoxygenation and. Well begin by developing the oxygen deficit as a function of time in a completely mixed batch reactor no inflow and no outflow with initial concentrations of biochemical oxygen demand bodl and dissolved oxygen. A fundamental feature of the classic streeter phelps system of equations is the lack of a feedback between dissolved oxygen concentration and the rate of organic matter oxidation. Applying the wellsriley equation to the risk of airborne. Bv equation can be used as it is under any circumstances. This may result in physically incorrect solutions, in which dissolved oxygen concentration is negative.
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