There is no proof that hydraulics is always more "efficient" in every circumstance, however it might be in some applications.
What would happen if a pneumatic system took the place of the hydraulic system? There is no proof that hydraulics is always more "efficient" in every circumstance, however it might be in some applications.It is "more efficient" to use hydraulics when:mobile tools for earth moving and construction .Presses for shaping metal,machinery for extrusion, especially plastics.Various lift types, such as elevators and platforms than pneumatic machineryAlternatively, pneumatics:work more quickly than hydraulics.yastmastmastmastmas, and can be utilized for applications requiring significantly higher precision.are significantly safer around processes involving food, drinks, and medicines.are safer in terms of substantially lower flammability and the risks of piping failures that go along with it.To learn more about hydraulic refer
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1. Consider the supply contract problem scenario that we discussed in class (and in Chapter 4). That is, the seller (supplier) is MTO; the seller pays a fixed cost of $100,000 to produce, and its per unit production cost is $35; the buyer pays the seller $80 per item purchased, and sells the items, for which there is a demand, for $125; the residual price is $20. As discussed, the globally optimal solution which maximizes the combined expected profit, is for the buyer to purchase Q* = 16,000 items. This results in a combined expected profit of $1,014,500. Suppose that the buyer and seller do not share any information beyond that given in the following contract: Suppose that the buyer and seller have a revenue sharing contract with Chew being the new cost per unit for the buyer in exchange for x% revenue sharing. Suppose Chew = CM = 35. Does there exist a value of x that will both: yield both the maximum combined expected profit and equally split it between the buyer and the seller? If so, determine this value of x. If not, explain why no such value exists.
No, there is not a value of x that will yield both the maximum combined expected profit and equally split it between the buyer and the seller. This is because the maximum combined expected profit ($1,014,500) is not evenly divisible by two. Therefore, the buyer and seller cannot split the expected profit equally. The theory at play here is the game theory.
What are the basics of game theory in economics?The study of an intuitive decision in which the outcome for each respondent or "player" is influenced by the actions of everyone else is known as game theory. If you are a participant in such a game, you must analyze the actions of others before deciding on your course of action or "strategy."
The following framework is useful for considering a scenario in which game theory is applicable. Define the issue
2. Determine the important components. Differentiated goods, first-mover advantage, entrance and exit charges, variable costs, and so on are examples of key elements.
3. Create a model, such as a bimatrix or extended-form game.
4. Use the model to hone your intuition.
5. Create a plan that addresses all probable eventualities.
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while examining a valve spring from an engine that is being overhauled, technician a says that valve springs should be checked for free length and cracks. technician b says the spring should be checked for compressed spring pressure, nicks, and straightness. who is correct?
A thin calibrated plastic strip serves as a plastic gauge. It can be used to measure gaps and monitor bearing clearance.
It is utilized at locations on crank or connecting rod bearings where a micrometer measurement cannot be made quickly. Compression braking, commonly referred to as engine braking, is a technique that can be applied to bigger commercial vehicles. The procedure is a little different, and a Jacobs brake (also known as a jake brake), which is designed specifically for diesel engines, aids in the procedure. Despite being sufficiently flat, bearings cannot be reliably measured with calipers; a micrometer is required. Although there are specialized micrometers available for measuring rounded interior surfaces, you are not required to own one.
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Consider a unity-feedback control system with the open-loop transfer function G(s) = K/ (s(s^2+s+4)
A) Determine the value of the gain K such that the phase margin is 50∘?
B) What is the gain margin for this case?
A) The phase margin is given by PM = -tan-1 (ωc/ζ) - 180
where ωc is the critical frequency and ζ is the damping ratio.
For a phase margin of 50°, we have
-tan-1 (ωc/ζ) = -130°
or
ωc/ζ = tan 130°
Now, the damping ratio is given by
ζ = -log(GM)/(√π2 + log2(GM))
where GM is the gain margin.
Substituting for ζ in the above equation, we get
ωc = tan 130° × -log(GM)/(√π2 + log2(GM))
Solving for GM, we get
GM = exp(-tan 130° × √π2 + log2(GM))
Now, we can calculate the gain K from the open-loop transfer function G(s) = K/ (s(s2 + s + 4))
K = GM × (s2 + s + 4)
Substituting for GM, we get
K = exp(-tan 130° × √π2 + log2(GM)) × (s2 + s + 4)
Hence, the value of the gain K such that the phase margin is 50° is given by
K = exp(-tan 130° × √π2 + log2(GM)) × (s2 + s + 4).
B) The gain margin for this case is given by
GM = exp(-tan 130° × √π2 + log2(GM))
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technician a states the mil lamp is required to come on any time a dtc is stored in an ecu. technician b says the mil light is required to come on any time there is a failure that could cause the emissions of the vehicle to exceed 1.5 times the emission standards for that vehicle. who is correct?
Both technicians are correct as the statement made by both are true. Therefore, Option C is the correct option.
Who are technicians?Technicians are knowledgeable professionals who work in almost every industry. They are asked to service, install, replace, and repair a variety of systems and equipment. They are adept in the relevant knowledge, abilities, and methods required by their line of work, which includes the automotive, maintenance, HVAC, and pharmaceutical industries.
Technicians examine, analyze, and troubleshoot client systems and equipment. They perform tests and analyze the results to formulate sound advice on how to repair malfunctioning or damaged equipment. They will negotiate prices with suppliers and customers to obtain replacement parts when necessary during repairs.
Before beginning a job, they will offer time and material cost estimates as well as repair and replace damaged equipment. Some technicians draft reports, safety guidelines, and preventive maintenance schedules.
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What is the driving force for (a) heat transfer, (b) elec- tric current flow, and (c) fluid flow?
Answer:
A: mobile elecrons
B: electromotive force
c:bonds in the ions
Which of the following are fundamental intuitions behind collaborative filtering? A) Similar users will rate the items similarly B) Similar users will not rate the items similarly C) Similar items will be rated similarly Answer choices Select only one option Only A and BOnly B and C Only A and C Only A
Option A is correct. Similar users will rate the items similarly are fundamental intuitions behind collaborative filtering.
A line segment's exact midpoint is the point that lies halfway between its two endpoints. It is therefore the average of the two endpoints, which is the average of the two x- and y-coordinates. Discover the endpoints' coordinates. As a result, the electric field along OB at midpoint O is 5.4 106 N C1. (b) At mid-point O, a test charge in the amount of 1.5 109 C is positioned. Line OA is the direction of the force. This is due to the fact that the charge applied at point B repels the negative test charge whereas point A attracts it.
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technician a says that power-split cvts use a torque converter. technician b says that power-split cvts use an electric transmission fluid pump. which technician is correct?
Neither technician is correct.
What is torque-converter?The torque converter is used in CVTs to transmit engine output. The torque converter, which functions like a clutch and is equipped with an ATF, is a crucial component of the vehicle for boosting torque and transmitting significant kinetic force during taking off.
Modern torque-converter autos are pushing as high as nine gears, modern twin-clutch systems have seven gears, and CVTs can create nearly unlimited ratios, making them the most fuel-efficient. Automatic transmissions can shift faster than the fastest manual drivers, but they can't accelerate as quickly.
One of the most crucial and underappreciated components of the car is the torque converter. It is essential to the operation of automatic transmission vehicles and plays a significant role in determining your fuel efficiency.
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Explain on a structural basis the differences in the glass transition temperature of polyethylene ( =-140°C), polyvinylchloride (T-87 C), and polysityrene (Tg= 100 c)
The "glass transition" temperature is the point at which it happens. For instance, low-density polyethylene has a glass transition temperature, or Tg, of about 100°C.
He claims that the fact that the Tg of PVC/CF composite is higher (86.7 °C) than the Tg of pure PVC (76.8 °C) indicates that there is a physical interaction between the polymer and the CF surface, which reduces chain mobility and free volume and increases Tg. Pressure and free volume. Increased surrounding pressure causes a decrease in free volume, which ultimately results in increased Tg. The glass transitioning temperature of polymers is also significantly influenced by other elements such as branching, alkyl chain length, bond interaction, flexibility of the polymer chain, film thickness, etc.
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A box with two gases separated by an impermeable membrane is in an environment with temperature T. The membrane can move back and forth, but the gases cannot penetrate the membrane. We will assume that equipartition applies to both gases, but gas A has an excluded volume. . UA-? NAkT + constant . UB-aNBkT +constant Keep in mind that the total box volume is constant, so VA + VB = constant. equilibrium value of VA m
The thermal effects caused by putting a cylindrical fiber in an inviscid, perfect gas that an auditory wave travels through are described.
The thermal effects caused by putting a cylindrical fiber in an inviscid, perfect gas that an auditory wave travels through are described. The thermal conductivities and heat capacity of the fibers and the gas are limited. There are established expressions for the temperature distribution in the material and the gas.
Pressure oscillations in the gas, which are brought on by an acoustic wave's passage, are what cause the temperature distribution. It has been discovered that a dimensionless parameter's relative value can help determine whether the solution should be based on exact or approximative equations. This parameter depends on the thermal conductivities, heat capacities, acoustic frequency, and fiber diameter of the gas and fiber.
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some fiber optic communication systems use laser amplification to boost the intensity of light pulses passing through an optical fiber. a short segment of laser amplifier fiber is spliced into the main fiber so that the light pulses must pass through the laser amplifier fiber on their way to their destination. the light emerging from the laser amplifier fiber is much brighter than it was when it entered. one interesting aspect of the light emerging from the laser amplifier fiber is that it
In some fiber optic communication, the light emerging from the laser amplifier fiber is much brighter than it was when it entered. one interesting aspect of the light emerging from the laser amplifier fiber is that ithas the same color as the light entering the amplifier fiber.
What is Fiber amplifiers?
Fiber amplifiers are optical amplifiers that use optical fibers for laser gain. A glass fiber do*ed with rare earth ions such as erbium (EDFA = erbium-do*ed fiber amplifier), neodymium, ytterbium (YDFA), praseodymium, or thulium is typically used as the gain medium.
This active dopant is pumped (charged) with light from a laser, such as a fiber-coupled diode laser; in almost all cases, the pump light travels through the fiber core with the signal to be amplified. Raman amplifiers are a type of fiber amplifier that is not commonly used.
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bananas are to be cooled from 24 to 13 c at a rate of 215 kg/h by a refrigeration system. the power input to the refrigerator is 1.4 kw. determine the rate of cooling, in kj/min and the cop of the refrigerator. the specific heat of a banana above freezing is 3.35 kj/kg c
The refrigerator receives a 9.8 kW power input. The proportion of electrical power consumption to heat dissipation is known as the Coefficient of Performance (COP).
It is the criterion used to assess the performance of the air conditioning system. It demonstrates the efficiency of heating and cooling systems. The following list of COP features includes:
The compressor power input to refrigeration output ratio is what determines this.
A rising coefficient of performance (COP) indicates that the cooling output will increase proportionately to the input of electricity. The ratio of electrical power consumption to heat dissipation is known as the Coefficient of Performance (COP). Any system's efficiency will improve with higher COP, and vice versa.
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synthetic oils used in turbine engines have advantages over petroleum based oils. two of these advantages are
The two of these advantages of synthetic oils are improved thermal and oxidative stability. More desirable viscosity-temperature characteristics.
What is synthetic oil ?A lubricant called synthetic oil is made of chemical substances that have undergone artificial modification or synthesis. In addition to being made from alternative raw materials, synthetic lubricants can also be produced utilising chemically altered petroleum components rather than full crude oil. However, the majority of the underlying material is still crude oil, which is distilled before being physically and chemically altered. It will differ between producers and is typically a business trade secret how additives are actually made.In situations where operating temperatures are extremely high, synthetic oil is utilised in place of petroleum-refined oils. For instance, synthetic oils are necessary for aircraft jet engines but not for aircraft piston engines. In addition, synthetic oils are utilised in metal stamping to offer advantages over traditional petroleum- and animal-fat-based goods in terms of the environment and other factors.To learn more about synthetic oil refer :
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A Frenkel defect is composed with which of the following? (a) A cation interstitial and a cation vacancy (b A cation interstitial and an anion interstitial (c) A catio (d) An anion interstitial and an anion vacancy
A Frenkel defect is composed with A cation interstitial and a cation vacancy.
What is a Frenkel defect composed of?A Frenkel defect, named after its discoverer Yakov Frenkel, is a particular kind of point defect in crystalline solids used in crystallography. The defect develops when an atom or smaller ion (often a cation) vacates its position in the lattice, leaving a vacancy, and then settles in the vicinity to produce an interstitial.
Ionic crystals with the Frenkel defect have an anion that is bigger than a cation. The solid crystal loses both the anion and the cation. The smaller ion cation typically breaks free from the original lattice structure.
straightforward interstitial defect An atom shifts from its usual lattice location to one of the interstitial sites, causing a specific type of point defect. In crystals with this flaw, the density of the crystal does not change. generally demonstrated by non-ionic solids.
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explain how lead and lag indicators are used in a quality program to develop measurement systems, and link your response with the use of a sweatt model, as discussed during week 4.
A leading indicator anticipates future results and occurrences.
A trailing indicator evaluates whether the desired outcome was realised in the past.
Why lead and lag indicators used ?In performance evaluation and management, the terms "leading indicator" and "lagging indicator" have come to be considered standard language. However, the line separating the two can occasionally be a little blurry; some indications, for example, are a little of both.
If managers want to develop a precise picture of performance, they must ensure that both types of metrics are in place and grasp the differences between the two.
A leading indicator anticipates future results and occurrences.
A trailing indicator evaluates whether the desired outcome was realised in the past.
The goal of leading indicators is future prediction. In economics, the phrase "leading indicator" refers to a quantifiable economic factor that shifts before the economy begins to exhibit a certain pattern or trend.
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when choosing building-construction materials, what kinds of materials would you choose, all other things being equal? materials with a relatively small shear modulus materials with a relatively small bulk modulus materials with a relatively large bulk modulus any kinds, as long as the building is not too tall either materials with a large or a small bulk modulus
when choosing building-construction materials i will chose a materials with a relatively large bulk modulus.
A substance's bulk modulus serves as a gauge of its compressibility resistance. It is described as the proportion between an increase in pressure that is infinitesimally small and the resulting relative decrease in volume.Any substance that may be utilized in construction is considered a building material. It frequently consists of wood, steel, concrete, cement, aggregates, bricks, clay, metal, and much more. In the past, humans have used nothing but pure bricks, wood, or straw. Wood, cement, aggregates, metals, bricks, concrete, and clay are among the most fundamental types of building materials used in construction. When choosing materials, it's important to take into account a variety of elements, including manufacture, durability, environmental effect, and specialized features for particular applications.
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2. jasmone is a valuable material in the perfume industry and used in many soaps and cosmetics. suppose we are recovering this material from a water suspension of jasmine flowers by an extraction with benzene. the local mass transfer coefficient for jasmone in benzene is 3.0 x 10-4 cm/s. the local mass transfer coefficient of jasmone in the water is 2.4 x 10-3 cm/s. jasmone is 170 times more soluble in benzene than water (this is the partition coefficient). determine the overall resistance based on the water phase. write an expression for the correct driving force to be used with this resistance?(ans
Overall resistance = (1/KD)(1/k water) = (1/(170))(1/2.4 x 10-3 cm/s) = 0.00588 cm/s
Driving force = (Conc. Benzene - Conc. Water)/Overall Resistance = (CB - CW)/0.00588 cm/s
What is resistance ?
Electrical resistance, or resistance to electricity, is a force that opposes the flow of current. It acts as a gauge for the difficulty of current flow in this way. Ohms () are used to express resistance values. Electrical will flow from to low when two terminals have an electron difference. That flow is countered by resistance. The current decreases as resistance increases. On the other hand, the current increases as the resistance decreases.
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isotropic point sources each emitting s neutrons/sec are placed in an infinite moderator at the four comers of a square of side a. compute the flux and current at the midpoint of any side of the square and at its center.
The flux and current at the midpoint of any side of the square and at its center are given by 16 x (s/a2) and 16 x (s/a) respectively.
The total flux at the midpoint of any side of the square is given by:
Flux = 4 x (s/a2)
The total current at the midpoint of any side of the square is given by:
Current = 4 x (s/a)
Flux and current at the center of the square
total flux at the center of the square is given by:
Flux = 16 x (s/a2)
The total current at the center of the square is given by:
Current = 16 x (s/a)
Therefore flux and current at the midpoint of any side of the square and at its center are given by 16 x (s/a2) and 16 x (s/a) respectively
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TRUE/FALSE. circuit components that are connected in such a way that they provide different current paths are said to be connected in parallel.
It's TRUE that circuit components that are connected in such a way that they provide different current paths are said to be connected in parallel.
What is Circuit?
A circuit in electronics is a complete circular path through which electricity flows. A basic circuit is made up of a current source, conductors, and a load. The term circuit can be used broadly to refer to any fixed path through which electricity, data, or a signal can travel.
How electronic circuits function?
In an electronic circuit, electrons exit the power source, travel along conductors, perform work in a load, and then return to the power source. The electrons flow in a circular path, which is why it is called a circuit. Ohm's Law describes the relationship between electrical flow and load. Electrons in a circuit travel from the negative side of the power supply to the positive side.
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which one of the four types of chip would be expected in a turning operation conducted at low cutting speed on a brittle work material: (a) continuous, (b) continuous with built-up edge, (c) discontinuous, or (d) serrated?
In a turning operation carried out at a slow cutting conditions on a brittle work material, discontinuous forms of chips would be anticipated.
what is speed?
An object's speed, also known as "v," is the amount by which its position changes over time or by how much it changes per unit of time, making it a scalar number. The instantaneous speed is the upper limit of the average speed as that of the duration of the time period approaches zero. The average speed of an item in a period of time is equal to the distance travelled either by object divided either by duration of the term. Velocity and speed are not the same thing.
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technician a says that some dc motors use brushes. technician b says that an ac synchronous motor uses a permanent magnet rotor. which technician is correct?
When technician A claims that some dc motors employ brushes, technicians B and A both make the appropriate corrections. An ac synchronous motor, according to technician B, uses a permanent magnet rotor.
What applications do AC synchronous motors serve?For applications where the load must be driven at a precise rate of speed and where it is preferred not to alter the motor speed using an AC speed control, synchronous fixed-speed gearmotors or motors are perfect (VFD).
Which two main rotor types are employed in synchronous generators?The synchronous machine's rotating component is referred to as the rotor. It carries the twisting field. Salient Pole Rotor and Cylindrical Pole Rotor are the two sorts of rotors that are available in terms of construction.
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which fields in an ip packet header are examined by netflow to determine whether or not a given packet is part of a flow? (select two.) answer header
Destination port, Layer 3 Protocol Type.
What is neflow?Around 1996, Cisco routers began to include a function called NetFlow that allowed users to record IP network data as it entered or left an interface. A network administrator can identify factors like the source and destination of traffic, the class of service, and the reasons for congestion by evaluating the data produced by NetFlow. Three primary parts make up a typical flow monitoring configuration (using NetFlow):Aggregating packets into flows, a flow exporter sends flow records to one or more flow collectors.The flow exporter sends data to a flow exporter, which the flow collector receives, stores, and pre-processes.Application for analysis: Examines received flow data in the context of traffic profiling or intrusion detection.To learn more about netflow, refer to
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what's the maximum size branch circuit protection for a single motor load if the motor is 480v, 3 phase, 11a using non-time delay
A 5-hp, 230V, single-phase motor's branch-circuit short-circuit protection (dual-element fuse) cannot be greater than 50A. A 25-hp, 460V, 3-phase synchronous motor's branch-circuit short-circuit protection (inverse-time breaker) must be greater than 70A.
What size branch circuit overcurrent protection is required for a motor?For a single motor utilized in a continuous duty application, under 430.22, the motor branch-circuit conductors must have an ampacity of at least 125 percent of the motor full-load current rating.
What is the motor branch's maximum rating?This gadget can withstand a maximum rating of 60A. It must be size down to 60A so as not to exceed the calculated 61A. The discussion of single motor computations and the Code is now complete.
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draw the shear and moemnt diamgrams for the beam subjected to the concentrated loads. what are the values of the shear force and bending moment at x
Since the beam is symmetrical, the support reaction will be same i.e. VA = VC = 100 kN. shear force is zero & bending moment is zero
Share force is SFaleft=0Staright
100KNSFbleft=100KNSFbright=100-200
=-100KNSFcleft=-100KNSFcright=0
Bending moment is BMa=0Bmb
=100*5
=500KNBMc
=100*10-200*5=0
All the forces operating on either side of the section are added together algebraically to form the shear force. The total of all the moment of the forces operating on either side of the section is called the bending moment, and it is calculated algebraically. For example, the pressure of air flow across an airplane wing is an example of shear force, which is a force operating in a direction parallel to a surface or cross section of a body. The term's use of the word shear alludes to the notion that a force of this kind may cut through a surface or other item that is under stress.
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a technician is sent out to service a spark type ignition system on a gas furnace. the main burners light, but the spark igniter continues to spark. after 60 seconds, the blower fan comes on and the burner goes out. the technician suspects a faulty:
The burner extinguishes and the blower fan turns on after 60 seconds. The technician thinks there could be a broken pilot bi-metal.
Next, the main burner flame or the pilot bi-metal flame are ignited by this igniter. to cool and saturate the flue gases while the furnace is running, the furnace draws air from the surrounding space. However, manufacturers have mostly switched to direct spark ignition or hot surfaces, and this method operates as follows: Thermostat heat request Control board conducts a safety inspection (limit switches, roll out switches). The inducer motor turns on. Powering the ignitor requires turning on the test power cable switch. The ends of the ignitor clip should be checked for sparks. Test the secondary coil below whether a spark appears. Indicator is faulty and has to be changed if spark does not leap the gap or jumps only sometimes.
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assume it is important that the warping not exceed 0.5 mm. an engineer suggests that if the temperature is kept below the level computed in part (e), we can be sure that the warping will not exceed 0.5 mm. is this a correct conclusion? explain.
This is not the right conclusion, no. Temperature is one of many factors that might induce warping, but this is not the only one. Warping can also be influenced by other elements like humidity.
What is temperature ?
The physical concept of temperature indicates in numerical form how hot or cold something is. A thermometer is used to determine temperature. Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points and calorimetry substances. As a result, maintaining the temperatures below the value calculated in part (e) is insufficient to ensure that the warping is not greater than 0.5 mm.
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tech a states that several types of superchargers are manufactured for use on vehicles. tech b states that the oldest version is the roots-style supercharger. who is correct?
Available superchargers include blowers or "turbochargers" powered by engines. The turbocharger is the most popular way of supercharging these engines, with the exception of a few small engines.
Exhaust gas expansion is used by turbochargers to pump combustion air into an engine. Another innovation in internal combustion engines of the piston type that boosts performance is the supercharger. It is an air compressor that raises the pressure or density of air that enters the combustion chamber of an engine to facilitate heavy duty operation. The roots style supercharger is the oldest type of supercharger and was first used as an industrial air-moving device in the early 1900s.
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A rocket launches with a constant acceleration of a all the way to outer space, straight up. You are not sure what a is, but it is relative small (between 2 ft/s2 and 10 ft/s?). Ignore compressibility effects. The atmosphere follows a standard temperature and pressure profile (so you can compute the density ratio directly from 0). a. As a function of a, at what altitude will the rocket experience maximum dynamic pressure q? b. What is that pressure as a function of a? c. How does the answer vary with acceleration?
The abbreviation "Maximum dynamic pressure" is Max Q. It occurs when the rocket or spacecraft is under "maximum mechanical stress" during the launch.
Which simply means that the rocket is experiencing significant physical pressure as a result of traveling through the atmosphere's air at a very high speed. After the rocket has been launched for around 60 seconds and has reached an altitude of 11 km, Max Q occurs. Max Q for the Space Shuttle happens at a similar altitude, about. The maximum dynamic pressure, or Max Q, is reached when the dynamic pressure reaches its greatest level due to the increasing velocity.
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8-33. Bar abc has a rectangular cross section of 300 mm by 100 mm. Attached rod db has a diameter of 20 mm. Determine the slope at a due to the loading. Consider only the effect of bending in abc, and axial force in db. E-200 gpa. D. O300 mm 20 kn 100 mm.
Answer: the answer is in the photo
Explanation:
I need help with this problem
Answer:
good question but i cant solve
let $o$ denote the centroid of triangle $abc$. let $m$ and $n$ be points on sides $ab$ and $ac$, respectively, so that $m$, $o$, and $n$ are collinear, and $am/mb
The solution is 4/9≤r<1/2.The total area that is bounded by a triangle's three sides is referred to as the triangle's area.
Find the solution ?The total area that is bounded by a triangle's three sides is referred to as the triangle's area.In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h.
AB→=b→,AC→=c→AM→=λ(b→)AN→=μ(c→)
Let G divides MN in the ratio K:1
So, K+1Kμ(c→)+λ(b→)=3b→+c→
⇒K+1Kμ=31K+1λ=31K=μλλ1+μ1=31A.M≥G.M2λ1+μ1≥λ1.μ1
⇒λμ
≥32
Now, Area△ABCArea△AMN=21∣∣∣∣∣(b→)×(c→)∣∣∣∣∣21λμ∣∣∣∣∣(b→)×(c→)∣∣∣∣∣
=λμ
using λ1+μ1=31
Ratio =3λ−13λ2
which has a maximum value 21
So option C is correct
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