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Environmental Engineering I−61350

An-Najah National University College of Engineering. Environmental Engineering I−61350. Chapter 3. Dr. Sameer Shadeed. Section 1 : Units and Measurements. General Introduction.

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Environmental Engineering I−61350

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  1. An-Najah National University College of Engineering Environmental Engineering I−61350 Chapter 3 Dr. Sameer Shadeed Section 1: Units and Measurements Dr. Sameer Shadeed

  2. General Introduction • Nearly all applications which involve descriptions of things in the real world require some sort of measurement units and/or coordinates • Examples range from simple notions of length (for page layout) to mass or volume for bulk commodity transactions, to various types of date-time specifications (temporal coordinates) to measurement of various concentrations for medical or environmental monitoring • Measurement units are perhaps the oldest standards in human history • Detailed study of measurement semantics (i.e., dimensional analysis) dates back more than a century Dr. Sameer Shadeed

  3. General Introduction • Measurement units are a key aspect of data representation and exchange for many important communities, including electronic commerce (of bulk commodities), medicine, engineering, environmental monitoring, and other scientific applications • Inadequately documented units specifications render the corresponding measurements meaningless and are a chronic source of errors in data exchange Dr. Sameer Shadeed

  4. Engineering Dimensions and Units • A fundamental dimension is a unique quantity that describes a basic characterstics, such as, mass (m), length (L), and time (T) • Derived dimensions are calculated by an arithmetic manipulation of one or more fundamental dimensions • For example, velocity has the dimensions of length/time (L/T) and volume is (L3) • Dimensions are descriptive but not numerical; they cannot describe how much, they simply describe what • Units, and the value of those units, are necessary to describe something quantitatively • For example, the length (L) dimension may be described in units as meter, or foot • Adding the value, we have a complete description, such as 3 meters, or 10 feet Dr. Sameer Shadeed

  5. Units of Measurements • Two system of units are in common use: the International System of Units (SI) and the U.S. Customary System (USCS) • Worldwide, environmental quantities are measured and reported in both systems (SI and USCS) and so it is important to be familiar with both • At the heart of the SI system is a short list of base units defined in an absolute way without referring to any other units • In all there are seven SI base units: Dr. Sameer Shadeed

  6. Units of Measurements • Other SI units, called SI derived units, are defined algebraically in terms of these fundamental units • For example, the SI unit of force, the newton, is defined to be the force that accelerates a mass of one kilogram at the rate of one meter per second • This means the newton is equal to one kilogram meter per second squared, so the algebraic relationship is N = kg·m/s2 • Currently there are 22 SI derived units • They are listed in the following table Dr. Sameer Shadeed

  7. Units of Measurements Dr. Sameer Shadeed

  8. Units of Measurements Dr. Sameer Shadeed

  9. Conversion Factors from USCS to SI Metric Units Dr. Sameer Shadeed

  10. Conversion Factors from USCS to SI Metric Units Dr. Sameer Shadeed

  11. Conversion Factors from USCS to SI Metric Units Dr. Sameer Shadeed

  12. Conversion Factors from USCS to SI Metric Units Dr. Sameer Shadeed

  13. Conversion Factors Software's • Brows the internet for free downloadable conversion factors software’s • Master Converter is one Dr. Sameer Shadeed

  14. Conversion Factors Software's • Convert is Another one Dr. Sameer Shadeed

  15. Get to Know SI Prefixes • In the study of environmental engineering, it is quite common to encounter both extremely large quantities and extremely small ones • The concentration of some toxic substance may be measured in parts per billion (ppb), for example, while a country‘s rate of energy use may be measured in thousands of billions of watts (tetrawatts) • To describe quantities that may take such extreme values, it is useful to have a system of prefixes that accompany the units Dr. Sameer Shadeed

  16. Get to Know SI Prefixes Dr. Sameer Shadeed

  17. An-Najah National University College of Engineering Environmental Engineering I-61350 Chapter 3 Dr. Sameer Shadeed Section 2: Some Expressions in Environmental Engineering Dr. Sameer Shadeed

  18. Density • The density of a substance is defined as its mass divided by a unit volume, or whereρ = density M = mass V = volume • In the SI system the base unit for density is kg/m3, whereas in USCU, density is commonly expressed as IbM/ft3[IbM = pouns (mass)] • Water in the SI system has a density of 1×103 kg/m3, which is equal to 1.0 g/cm3 • In the USCU, water has a density of 62.4 IbM/ft3 Dr. Sameer Shadeed

  19. Concentration • The derived dimension concentration is usually expressed gravimetriclly as the mass of a material A in a unit volume consiting of material A and some other materials B • The concentration of A in a mixture of B is whereCA = concentration of A MA = mass of material A VA = volume of material A VB = volume of material B • In the SI system, the unit for concentration is kg/m3, although the most widely used concentration term in environmental engineering is milligrams per liter (mg/L) Dr. Sameer Shadeed

  20. Concentration Example 1: Plastic beads with a volume of 0.04 m3 and a mass of 0.48 kg are placed in a container and 100 liters of water are poured into the container. What is the concentration of plastic beads in mg/L? Solution: whereA represents the beads and B represents the water Dr. Sameer Shadeed

  21. Concentration • Another measure of concentration is parts per million (ppm) • This is numerically equivalent to mg/L if the fluid in question is water since one milliliter (mL) of water weights one gram, that is, the density is 1.0 g/cm3 • Note that mg/L = ppm if ρ =1.0 g/cm3 by the following conversion: • Or one gram in million grams, or one ppm Dr. Sameer Shadeed

  22. Concentration • Some material concentrations are most conveniently expressed as percentages, usually in terms of mass as follows: whereΦA = percent of material A MA = mass of material A MB = mass of material B • ΦAcan, of course, also be expressed as a ratio of volumes Dr. Sameer Shadeed

  23. Concentration Example 2: A wastewater sluge has a solids concentration of 10,000 ppm. Express this in percent solids (mass basis), assuming that the density of the solids is 1.0 g/cm3 Solution: • This example illustrate a useful relationship: 10,000 mg/L = 10,000 ppm (if density = 1) = 1% (by weight) Dr. Sameer Shadeed

  24. Flow Rate • In engineering processes the flow rate can be either gravimetric (mass) flow rate (kg/s, or lbM/s) or volumetric (volume) flow rate (m3/s, or ft3/s) • The mass and volumetric flow rates are not independent quantities, since the mass (M) of material passing a point in a flow line during a unit time is related to the volume (V) of that material as [mass] = [volume]× [density] • Thus a volumetric flow rate (QV) can be converted to a mass flow rate (QM) by multiplying by the density of the material QM = QVρ • where QM = mass flow rate, QV = volume flow rate, and ρ = density • The symbol Q is almost universally used to denote flow rate Dr. Sameer Shadeed

  25. Flow Rate • The relationship between mass flow, of some component A, concentration of A, and the total volume flow (A plus B) is Example 3: A wastewater treatment plant discharges a flow of 1.5 m3/s (water plus solids) at a solids concentration of 20 mg/L (20 mg solids per liter of flow, solids plus water). How much solids is the plant discharging each day? Solution: [mass flow] = [concentration] × [volume flow] Dr. Sameer Shadeed

  26. Flow Rate Example 4: A wastewater treatment plant discharges a flow of 34.2 mgd (million gallon per day) at a solids concentration of 0.002% solids (by weight). How many pounds per day of solids does it discharge? Solution: [mass flow] = [concentration] × [volume flow] Note first that 0.002% = 20 mg/L (assuming ρ = 1.0 g/cm3) Dr. Sameer Shadeed

  27. Flow Rate • The volumatric flow rate can be expressed as where V = volume t = time A = cross sectional area v = flow velocity Dr. Sameer Shadeed

  28. Residence Time • One of the most important concepts in treatment processes is residence time (sometimes called detention time or retention time), defined as the time an average particle of the fluid spends in the container through which the fluid flows, or the time it takes to fill the container • Mathematically, if the volume of a container such as a large holding tank, is V (m3), and the flow rate into the tank Q(m3/s), then the residence time (seconds) is • Ƭ = V/Q • The average residence time can be increased by reducing the flow rate Q or increasing the volumeV, and decreasing by doing the opposite Dr. Sameer Shadeed

  29. Residence Time Example 5: A lagoon has a volume of 1500 m3 and the flow into the lagoon is 3 m3/hour. What is the residence time in this lagoon? Solution: Ƭ = V/Q = 1500/3 = 500 hours Dr. Sameer Shadeed

  30. An-Najah National University College of Engineering Environmental Engineering I-61350 Chapter 3 Dr. Sameer Shadeed Section 3: Materials Balance Dr. Sameer Shadeed

  31. Materials Balance • The law of conservation of mass says that when chemical reactions take place, matter is niether created nor destroyed • What this concept allows us to do is track materials (e.g. Pollutants) from one place to another with mass balance equations • The first step in a mass balance analysis is to define the particular region (e.g. Chimecal mixing tank, a lake, stream, air basin above a city) in space that is to be analysed • By picturing an imaginary boundary around the region (see Figure 1 in the next slide) we can then begin to identify the flow of materials across the boundary as well as accumulation of materials withen the region Dr. Sameer Shadeed

  32. Materials Balance Figure 1: A material balance diagram Dr. Sameer Shadeed

  33. Materials Balance • A substance that enters the region has three possible fates: • Some of it may leave the region unchanged • Some of it may accumulate within the boundary • Some of it may be converted to some other substance • Thus, using Figure 1 as a guide, the following materials balance equation can be written for each substance of intrests: Dr. Sameer Shadeed

  34. Materials Balance Steady-State Conservative Systems • The simplest systems to analyze are those in which steady state is assumed (accumulation rate is set equal to zero) and the substance in question is conservative (the decay rate term is zero). In these cases the mass balance equation can be simplify as: Figure 2: A steady-state conservative system Dr. Sameer Shadeed

  35. Materials Balance Steady-State Conservative Systems • Consider the steady-state conservative system shown in Figure 2 • One inpute to the system is a stream of water with a flow rate Qs(volume/time) and pollutant concentration Cs (mass/volume) • The other input is assumed to be a waste stream with flow rate Qw and pollutant concentration Cw • The output is a mixture with flow rate Qm and pollutant concentration Cm • Assuming steady-state conditions, the following equation obtained CsQs + CwQw = CmQm Dr. Sameer Shadeed

  36. Materials Balance Steady-State Conservative Systems Example 1:A stream flowing at 10 m3/s has a tirbidity feeding into it with a flow 5 m3/s. The stream`s concentration of chlorides upstream of the junction is 20 mg/L and the tirbutary chloride concentration is 40 mg/L. Treating chlorides as conservative substance, and assuming complete mixing of the two streams, find the downstream chloride concentration. Dr. Sameer Shadeed

  37. Materials Balance Steady-State Conservative Systems Example 1(Solution): CsQs + CwQw = CmQm Rearranging the above equation to solve for the chloride concentration downstram gives us Cm =(CsQs + CwQw)/Qm =(CsQs + CwQw)/(Qs +Qw) = (20×10 + 40×5)/(10 + 5) = 26.67 mg/L Dr. Sameer Shadeed

  38. Materials Balance Conservative Systems • For conservative systems, it is assumed that the decay rate term is zero • In this case the mass balance equation can be simplify as: Dr. Sameer Shadeed

  39. Materials Balance Conservative Systems Example 2:A sanitary landfill has available space of 16.2 ha at an average depth of 10 m. Seven hundred sixty-five (765) cubic meters of solid waste are dumped at the site five days per week. This waste is compacted to twice its delivered density. Estimate the expected life of the landfill in years. Dr. Sameer Shadeed

  40. Materials Balance Conservative Systems Example 2 (Solution): • Accumulation = Input – Output • Input = the volume of dumped waste • Output = zero • Landfill volume = Area × Depth = (16.2×104)×10 = 162×104 m3 • Solid waste volume = 765 × 5days = 3825 m3/week • Because the waste is compacted to twice its delivered density, the waste volume decreases to half its delivered volume. So, waste volume is 1912.5 m3/week • Life time of the landfill = landfill volume/solid waste dumping rate (V/Q) = 162×104 m3/1912.5 m3/week = 847 week • 1 year = 52.14 week • So, the life time in years = 847/52.14 = 16.24 years Dr. Sameer Shadeed

  41. Water Balance Conservative Systems • Within a catchment, the hydrologic cycle reduces to a balance between the input from precipitation P and outflows evapotranspiration E and runoff R. Thus, • P + I = ET + R + ΔS • Input = Output + Accumulation • (P + I) = (ET + R) + ΔS • where I is the applied irrigation and (ΔS = Sf– Si) is the change in soil water storage, which usually becomes zero over the long term • Si is the initial soil water storage and Sf is the final soil water storage Dr. Sameer Shadeed

  42. Water Balance Conservative Systems Example 3:Consider a catchment of area A = 110 km2in which the annual total precipitation P is 1800 mmand the annual discharge Q is measured as 77 x 106 m3/yr . What is the annual evapotranspiration ET in mm? (Assume ΔS = 0) Dr. Sameer Shadeed

  43. Water Balance Conservative Systems Example 3(Solution): Runoff R is the area-averaged discharge, or R = Q/A Since A = 110 km2 = 110 x 106 m2, R = (77 x 106 m3/yr)/ (110 x 106 m2) = 0.7 m = 700 mm/yr Therefore ET = P – R = 1800 – 700 = 1100 mm Dr. Sameer Shadeed

  44. Water Balance Conservative Systems Example 4:In a one week period; P = 5 mm, I = 0 mm, R = 2 mm, Soil water content at beginning of week (Si) = 10 mm, and Soil water content at end of week (Sf) = 6 mm. How much water was evaporated or transpired (ET) during week? Solution: P = ET + R –I + ΔS → ET = P + I – R – ΔS ET = 5 + 0 – 2 – (6 – 10) = 7 mm Dr. Sameer Shadeed

  45. Materials Balance Reactions • In most systems of environmental interest, transformations occur within the system: by products are formed or compounds are dystroyed • Because many environmental reactions do not occur instantaneously, the time dependence of reaction must be taken into account • Time-dependent reactions are called kinetic reactions. The rate of transformation, or reaction rate (r) is used to describe the rate of formation or disappearance of a substance or chemical species Dr. Sameer Shadeed

  46. Materials Balance Reactions • The reaction rate is often some compex function of temperature, pressure, the reaction components , and products of reaction • Where, k = reaction rate constant (in s-1or d-1) • C = concentration of substance • n = exponent or reaction order • The minus sign before reaction rate, k, indicates the disappearence of a substance or chemical species Dr. Sameer Shadeed

  47. Materials Balance First-Order-Reaction • Consider a reaction or process in which the concentration C of reactant X decreases with time and the reaction rate, r, is assumed to be directly proportional to the amount of material remaining, that is the value of n = 1. This is known as a first-order reaction. • In the first-order reactions, the rate of loss of substance is proportional to the amount of substance present at any given time, t Dr. Sameer Shadeed

  48. Materials Balance First-Order-Reaction • The previous differential equation may be integrated to yield either • Where, C = concentration at any time t • CO = initial concentration of substance Dr. Sameer Shadeed

  49. Materials Balance First-Order-Reaction • For simple completely mixed systems with first-order reactions, the total mass substance (M) is equal to the product of concentration and volume (CV) and, when V is a constant, the mass rate of decay of the substance is • Because first-order reactions can be described as (-kC = dC/dt), this yields Dr. Sameer Shadeed

  50. Materials Balance First-Order-Reaction Example 5: A reactant is initially present in a concentration Co. After 2 days it is observed to decrease to a concentration 0.9 Co. Assuming a first-order reaction, what will be the concentration in 10 days? Solution: C = Coexp(-kt) and ln C/Co = - kt For t = 2 days ln(0.9) = - 2 k = -0.105 So k = 0.053 . For t = 10 days C/Co = exp (-10 x 0.053) = 0.59 Dr. Sameer Shadeed

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