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The liquid storage tank shown in Fig. E2.13 has two inlet

Process Dynamics and Control | 3rd Edition | ISBN: 9780470128671 | Authors: Dale E. Seborg ISBN: 9780470128671 148

Solution for problem 2.13 Chapter 2

Process Dynamics and Control | 3rd Edition

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Process Dynamics and Control | 3rd Edition | ISBN: 9780470128671 | Authors: Dale E. Seborg

Process Dynamics and Control | 3rd Edition

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Problem 2.13

The liquid storage tank shown in Fig. E2.13 has two inlet streams with mass flow rates w1 and w2 and an exit stream with flow rate w3. The cylindrical tank is 2.5 m tall and 2 m in diameter. The liquid has a density of 800 kg/m3. Normal operating procedure is to fill the tank until the liquid level reaches a nominal value of 1.75 m using constant flow rates: w1 = 120 kg/min, w2 = 100 kg/min, and w3 = 200 kg/min. At that point, inlet flow rate w1 is adjusted so that the level remains constant. However, on this particular day, corrosion of the tank has opened up a hole in the wall at a height of 1 m, producing a leak whose volumetric flow rate q4 (m3/min) can be approximated by where h is height in meters. (a) If the tank was initially empty, how long did it take for the liquid level to reach the corrosion point? (b) If mass flow rates w1, w2, and w3 are kept constant indefinitely, will the tank eventually overflow? Justify your answer.

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Trends in Evolution: ● Larger brains ● Larger and more muscles ● Upright limb posture (appendages directly underneath body weight) ● Nocturnal habits (led to development of 3 middle ear bones and whiskers for sensing at night) ● Homeothermy­ maintenance of a stable internal body temperature despite environmental influences; can be regulated through behavior or metabolism ○ Example: Pelycosaurs (not a dinosaur)­ evolved large flat organ on top of their bodies with lots of blood flow through; could cool themselves or turn to sun to absorb heat ○ Opposite=Poikilothermy­ internal body temperature varies with environmental conditions These developments cost a lot metabolically­ need ​ solutions​ for trade­offs: ● Heterodonty­ specialized teeth; could preprocess food so that digestive system absorbed more for each gram consumed ● Secondary palate­ membrane that separates digestive tract from respiratory system; could breath while eating so that there is a constant supply of oxygen ● Endothermy­ use of metabolism for heat; can regulate internal body temperature by metabolism. Also blood vessels kept in fossilized bones. Body Structure and Function: Fundamental challenges= obtain nutrients and oxygen, excrete wastes, move Natural selection lead to the more successful solutions being favored. If a trait has an adaptive function, its “form reflects its function.” This is seen at all levels: ­ Molecular: Enzymes have a specific structure for a specific substrate Phospholipids have characteristics (nonpolar and polar sides) to form bilayer ­ Cellular: Cells have a certain shape for their job; nerve vs epithelial vs muscle ­ Tissue: Groups of epithelial cells can be flat for a covering, vertically aligned to increase surface area, or shaped round a vessel Embryonic tissue layers (endoderm, mesoderm, ectoderm) for specific function *Give rise to different types of tissues, each with different function: ­Connective (support, connect or separate) ­Nervous (regulation and communication for control) ­Muscle (movement) ­Epithelial (line/cover) ­ Organs ­ Organ systems ­ Organism: body shape for fastest movement through water, or stride length for fastest movement on land ­ Specific solutions vary: For flight, pterodactyl has a single elongated digit to support flight membrane, while birds fused distal bony elements to support feathers, and bats elongated 4 digits. Themes of Form and Function: A) Body size Larger animals need more food, take longer to mature, and reproduce slowly, but they lose heat and water slowly. Smaller animals are the opposite with the tradeoffs. ~Metabolic rate­ amount of oxygen used per unit time­ a measure of cellular activity As animal size DECreases, metabolic weight per unit body mass increases (a shrew eats more per unit body weight than an elephant, even though it needs less total food). ~Longevity­ how long the typical lifespan of an animal is As body mass increases, longevity increases. Combining these relationships, the larger the animal, the slower the metabolic rate and the longer lifespan. The smaller the animal, the faster the metabolic rate and the shorter the lifespan. B) Surface area to volume ratios Surface area is needed for exchange (to obtain nutrients and oxygen and excrete wastes). Therefore as animal size increases, there must be a solution. Ex: salmon hatchlings begin with nearly all oxygen exchange occurring through their skin, but as they grow older, gills take over. In complex animals, each group of cells are specialized to increase surface area in their specific environment. Ex: cells that line the intestines form many folds, lung tissue is arranged for the most surface area with capillaries, and blood vessels branch throughout kidney. Adaptations: ­flattening ­folding ­branching C) Homeostasis and thermoregulation ~Homeostasis= keeping internal chemical and physical situations within a tolerable range despite external environment *Important for enzyme function (each enzyme has an optimal temperature), chemical reactions in body, proteins (to not denature), and cells (to not destroy by freezing or heat) ~Conformers­ body temperature varies with environmental temperature (poikilotherm) vs ~Regulators­ body temperature maintains fairly stable despite changing environment (homeotherm) Both use acclimatization­ adjustments to gradual environmental changes to stay near optimal performance. Ex: Daphnia changes what enzymes it mainly has for what works best at that new temperature. How to maintain homeostasis: Negative Feedback System­ 1. Set point­ the optimal conditions 2. Stimulus­ a change away from the set point 3. Sensor/control center­ detects change, initiates response; 4. Response­ reaction by turning off or activating a certain pathway to minimize effect ~Thermoregulation= maintaining internal temperature within normal range By method of… ~endothermy­ metabolism produces main source of heat. Positive: can sustain activity in different conditions or ~ectothermy­ use environment to absorb heat. Positive: requires less energy Mechanisms of Heat Exchange: ● Conduction: direct contact between solids ○ Ex­ snake on warm rock ● Convection: direct contact between solid and gas ○ Ex­ hare’s big, vascularized ears ● Radiation: no direct contact (principally refers to heat from sun) ○ Ex­ bird opening wings toward sunlight ● Evaporation: water has the special property of a high heat of vaporization, therefore it takes a lot of heat with it when evaporated ○ Ex­ dog panting Generating and Retaining Heat: ● Insulation­ layer of fur to form air barrier or layer of blubber for fat barrier ○ Nearly all in endothermic animals (to avoid loss of heat from internal metabolism) ○ Mainly in aquatic animals because water has high heat capacity (absorbs heat rapidly) ● Behavioral heat absorption and regulation­ basking in sun, hiding in shade, being active only certain times of day, etc ● Circulatory adaptations­ ​ Vasodilation and vasoconstriction​ = delivering different amounts of heated blood to skin surface to heat extremities/far tissues or cool blood (not the best because when heated blood is sent more to extremities, more heat is lost ■ Countercurrent exchange​ = artery ‘hugs’ vein so that heat flows from artery into vein before heated blood gets to extremities­ heat goes back up with veins and stays in body­ keeps core temperature up and extremities cold ● Metabolic heat production (endothermy) ○ Shivering thermogenesis­ constriction of muscles produces heat ○ Non­shivering thermogenesis­ burns brown fat for heat Thermoregulation and Energy Conservation (for endothermic animals) ● Torpor­ DAILY pattern of decreased physiological activity ○ Mainly for small endotherms with high metabolic rates; active at night, don’t move much during day ● Hibernation­ SEASONAL state of decreased physiological activity ○ Mainly mammals ● Aestivation­ “summer hibernation”­ often facultative ○ Mainly in hot areas where resources are limited in summer instead of winter All are heterothermy mechanisms­ they change their set point (like body temperature) in response to environmental stress *White nose syndrome­ fungus grows on nose of bats, saps energy as hyphae extend through and feed off tissues­ wakes bats early in year (January/February) before enough insects to survive.

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Textbook: Process Dynamics and Control
Edition: 3
Author: Dale E. Seborg
ISBN: 9780470128671

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The liquid storage tank shown in Fig. E2.13 has two inlet