Air at a velocity of 5 m/s, at a temperature of 32°C and a pressure of 1.9 bar, flows through a pipe with a diameter of 12 cm. The air is then heated when flowing through the pipe and finally leaves at a pressure of 1.7 bar and a temperature of 55°C.
We need to determine the velocity of air at the exit. At state point 1:
V₁ = 5 m/s,
P₁ = 1.9 bar,
T₁= 32°C = 305K At state point 2:
P₂ = 1.7 bar,
T₂ = 55°C
= 328K We first calculate the inlet area of the pipe:
r = d/2
= 12/2
= 6 cm
= 0.06 m Area of the pipe,
A₁ = πr²
= π(0.06)²
= 0.01131 m²
We now need to calculate the mass flow rate of air, which is the same at both inlet and outlet points since it is a steady-flow process. For that, we use the following equation:
m₁ = m₂P₁A₁V₁
= P₂A₂V₂
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describe in great detail what is turntable & phono signals
are and how they apply to an Audio channel mixer circuit.
A turntable is a music player that plays records. Phono signals are low-level signals generated by a turntable cartridge that require a preamp to bring them to line level. In this regard, the audio channel mixer circuit plays an important role. Let's delve into more detail about turntables and phono signals and how they apply to an audio channel mixer circuit.
TurntableTurntables are sometimes known as record players. It is a music player that plays vinyl records. Turntables are well-known for their sound quality, which is warm, rich, and natural. A turntable typically has a tonearm, which is used to position a cartridge over a vinyl record. The cartridge contains a stylus that reads the grooves in the record and transforms the mechanical energy of the stylus into an electrical signal that can be amplified and played back through speakers.Phono SignalsThe electrical signal generated by a turntable's cartridge is known as a phono signal. Phono signals are low-level signals that are not strong enough to drive a speaker directly. A preamp is required to bring phono signals to line level. In the early days of home stereo systems, phono preamps were often built into receivers and amplifiers.
However, most modern stereo equipment does not include a phono preamp. In this case, an external phono preamp is needed.Audio Channel Mixer CircuitAn audio channel mixer circuit is a device that enables various audio signals to be mixed and controlled. It takes the signals from various sources and combines them into one or more outputs, allowing for the adjustment of the relative volume levels of each input source. A turntable can be connected to an audio channel mixer circuit in the same way as any other audio source. However, since phono signals are low-level signals, they need to be pre-amplified before they can be mixed with other sources. Some audio channel mixer circuits include a phono preamp built-in, while others require an external phono preamp to be connected separately.
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Conduct FEM stress analysis on the wing structure of an aircraft using ABAQUS. Educate yourself on the
structural members of a wing such as spurs and etc. Only one engine is attached to the wing. Consider the
wing as a taper beam. The wing structure should survive during steady flight, take off, landing, and
common aircraft maneuvers. In addition to static loading, consider dynamic loading for design
purposes.
Finite Element Method (FEM) stress analysis is a crucial step in the design of an aircraft. FEM provides solutions to a broad range of complex engineering problems, including stress, vibration, and fluid flow analysis.
FEM helps to identify the areas of a structure that will experience the most stress, which can then be reinforced to ensure that the structure can withstand the forces that it will be subjected to during normal operations. This process is particularly important in aircraft design, where weight is a critical factor that must be considered in all design decisions.
The structural members of a wing include spars, ribs, skin, and stringers. These components are responsible for carrying the wing's weight and transmitting the aerodynamic forces generated by the wing during flight. Spars are the primary structural members of a wing and run from the wing root to the wingtip. They are typically made of aluminum or composite materials and are responsible for carrying most of the wing's weight. Ribs are used to support the skin of the wing and are spaced along the length of the spar. They are typically made of lightweight materials such as balsa wood or foam.
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A room in a single-story building has three 3 x 4 ft double-hung wood windows of average fit that are not weather-stripped. The wind is 23 mph and normal to the wall with negligible pressurization of the room. Find the infiltration rate, assuming that the entire crack is admitting air.
Given that the room in a single-story building has three 3 x 4 ft double-hung wood windows of average fit that are not weather-stripped.
The wind is 23 mph and normal to the wall with negligible pressurization of the room. We are to find the infiltration rate, assuming that the entire crack is admitting air. The infiltration rate can be defined as the volume of outside air entering into the building through cracks, joints, and the unsealed doors, and windows.
The formula for infiltration rate is given as, Infiltration rate = (C * A * √2gh) / (144 * 60)Where, C = infiltration coefficient (1.0 for cracks, and joints 0.6 for doors and windows),A = the area of the opening, g = acceleration due to gravity, h = height of the opening, and √2 = windward pressure coefficient.
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Question 1 A vehicle driven by rear wheels on a level road has a wheel base of 3 m and the center of gravity of 800 mm above the road level. The center of gravity is 1.95 m in front of the rear axle. The coefficient of friction between the wheels and the road is 0.5. Calculate: (a) The maximum acceleration of the vehicle without slipping of the wheels. (b) The maximum acceleration of the vehicle if the rear brakes are applied.
a)The maximum acceleration of the vehicle without slipping of the wheels is 4.905 m/s² and
b) The maximum acceleration of the vehicle if the rear brakes are applied is 2.455 m/s².
(a) The maximum acceleration of the vehicle without slipping of the wheels.
The maximum acceleration of the vehicle without slipping of the wheels is given as,a = μg = 0.5 × 9.81 m/s² = 4.905 m/s²
(b) The maximum acceleration of the vehicle if the rear brakes are applied.The maximum acceleration of the vehicle if the rear brakes are applied is given as,a = μg(1 – d/l)
where,d is the distance between the center of gravity and the rear wheels,l is the wheelbase of the vehicle
.Substituting the given values, we geta = 0.5 × 9.81 × (1 - 1.95/3)= 2.455 m/s²
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When a Zener diode is reverse biased it a. None of the Above b. Has a constant voltage across it c. has constant current passing through d. Maintains constant resistance
When a Zener diode is reverse-biased, it has a constant voltage across it.
The correct option is b.
This is because Zener diodes are designed to operate in reverse breakdown mode.
Thus, when a voltage exceeding the Zener voltage is applied to the diode, the current flows through the diode, and the voltage across it remains constant.
The reverse breakdown voltage, also known as the Zener voltage, is the key feature of the Zener diode.
The voltage across the diode remains stable when the reverse voltage applied to the Zener diode exceeds the breakdown voltage, and it remains constant over a wide range of current variations.
This characteristic of a Zener diode makes it useful in voltage regulation circuits.
Hence, the correct option is b. Has a constant voltage across it.
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1-Given A = 5ax - 2a, + 4a, find the expression for unit vector B if (a) B is parallel to A (b) B is perpendicular to A and B lies in xy-plane.
(a) B is parallel to A:For any vector A, the unit vector parallel to it is given by:
[tex]B = A/ |A|[/tex]For the given vector A,[tex]|A| = √(5² + 2² + 4²) = √45[/tex]
Thus, the unit vector parallel to A is given by:
[tex]B = A/ |A| = (5ax - 2ay + 4az)/√45[/tex]
(b) B is perpendicular to A and B lies in xy-plane:
For any two vectors A and B, the unit vector perpendicular to both A and B is given by:
B = A x B/|A x B|Here, [tex]A = 5ax - 2ay + 4az[/tex]For B,
we need to choose a vector in the xy-plane. Let B = bx + by, where bx and by are the x- and y-components of B respectively.
Then, we have A . B = 0 [since A and B are perpendicular]
[tex]5ax . bx - 2ay . by + 4az . 0 = 0=> 5abx - 2aby = 0=> by = (5/2)bx[/tex]
[tex]B = bx(ax + (5/2)ay)[/tex]
Therefore,[tex]B = bx(ax + (5/2)ay)/ |B|[/tex]For B to be a unit vector, we need[tex]|B| = 1⇒ B = (ax + (5/2)ay)/ √(1² + (5/2)²)[/tex]
Thus, the expression for unit vector B is given by: [tex]B = (5ax - 2ay + 4az)/√45(b) B = (ax + (5/2)ay)/√(1² + (5/2)²).[/tex]
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For aviation, if you are going to teach a course in hardware
design of an aircraft how would you conduct it, explain in
steps with a detail explanation foe each one.
Hardware design involves creating and developing the physical components and systems of electronic devices, such as circuit boards, processors, and peripherals. It encompasses the design, testing, and optimization of hardware to ensure functionality, performance, and reliability, while considering factors like cost, power consumption, and size constraints.
If you are going to teach a course in hardware design of an aircraft for aviation, you would conduct it as follows:
Step 1: Introduce the CourseYou would start by introducing the course, explaining what hardware design of an aircraft is all about, what the course will cover, and what the students can expect to learn.
Step 2: Teach the BasicsYou would then teach the students the basics of hardware design of an aircraft, including the history of aviation, the science of flight, and the different types of aircraft and their components.
Step 3: Teach the Design PrinciplesYou would then teach the students the design principles of hardware design of an aircraft, including the materials used, the forces that aircraft are subjected to, and the importance of safety.
Step 4: Teach the Design ProcessYou would then teach the students the design process of hardware design of an aircraft, including the different stages of design, the tools used in design, and the importance of testing and evaluation.
Step 5: Conduct Practical SessionsYou would then conduct practical sessions where students can put into practice what they have learned so far, including using software to design an aircraft, building aircraft components, and testing them in a simulated environment.
Step 6: Introduce Advanced TopicsFinally, you would introduce the students to advanced topics in hardware design of an aircraft, including the latest technologies used in aviation, and the future of aircraft design and development. You can also include 150 by specifying the maximum number of students that can be enrolled in the course or the maximum duration of the course (e.g., 150 hours).
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A 70 kg man falls on a platform with negligible weight from a height of 1.5 m it is supported by 3 parallel spring 2 long and 1 short springs, have constant of 7.3 kN/m and 21.9 kN/m. find the compression of each spring if the short spring is 0.1 m shorter than the long spring
The objective is to find the compression of each spring. By considering the conservation of energy and applying Hooke's Law, the compressions of the long and short springs can be determined. The compression of the long springs is 0.5 cm each, while the compression of the short spring is 0.3 cm.
To determine the compression of each spring, we can consider the conservation of energy during the fall of the man. The potential energy lost by the man when falling is converted into the potential energy stored in the springs when they are compressed.
The potential energy lost by the man can be calculated using the formula: Potential Energy = mass * gravity * height. Substituting the given values, the potential energy lost is 70 kg * 9.8 m/s^2 * 1.5 m = 1029 J.
Since there are three parallel springs, the total potential energy stored in the springs is equal to the potential energy lost by the man. Assuming the compressions of the long springs are equal and denoting the compression of the long springs as x, the potential energy stored in the long springs is (0.5 * 7.3 kN/m * x^2) + (0.5 * 7.3 kN/m * x^2) = 14.6 kN/m * x^2.
The potential energy stored in the short spring is given by 21.9 kN/m * (x - 0.1)^2.
Equating the potential energy lost by the man to the potential energy stored in the springs, we have 1029 J = 14.6 kN/m * x^2 + 14.6 kN/m * x^2 + 21.9 kN/m * (x - 0.1)^2.
Simplifying the equation, we can solve for x, which represents the compression of the long springs. Solving the equation yields x = 0.005 m, which is equivalent to 0.5 cm.
Since the short spring is 0.1 m shorter than the long springs, its compression can be calculated as x - 0.1 = 0.005 - 0.1 = -0.095 m. However, since compression cannot be negative, the compression of the short spring is 0.095 m, which is equivalent to 0.3 cm.
In conclusion, the compression of each long spring is 0.5 cm, while the compression of the short spring is 0.3 cm.
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1-Describe the working principal and the construction of Transformers. Use figures and equations when required. [2 Points]
Transformers work on the principle of mutual induction. They consist of a magnetic core and two coils of wire wound around the core. An alternating current in one coil induces a changing magnetic field which induces an alternating current in the second coil.
The construction of a transformer consists of two coils of wire wound around a magnetic core. The primary coil is connected to a source of alternating current, which creates a magnetic field that induces a voltage in the secondary coil through the principle of mutual induction.
The voltage induced in the secondary coil is proportional to the number of turns in the coil and the rate of change of the magnetic field.The working principle of a transformer is based on the principle of mutual induction, which states that a changing magnetic field in a coil of wire induces a voltage in a second coil of wire.
This voltage is proportional to the rate of change of the magnetic field and the number of turns in the coil. The transformer is used to step-up or step-down the voltage of an AC power supply.
This is done by varying the number of turns in the primary and secondary coils
Transformers are essential devices in the power transmission and distribution system as they help in the efficient transfer of electrical energy from one circuit to another by electromagnetic induction. They work on the principle of mutual induction, which states that when a current-carrying conductor generates a magnetic field, it induces an electromotive force (EMF) in an adjacent conductor.
The basic construction of a transformer consists of two coils of wire wound around a magnetic core. The primary coil is connected to a source of alternating current, which creates a magnetic field that induces a voltage in the secondary coil through the principle of mutual induction.
The voltage induced in the secondary coil is proportional to the number of turns in the coil and the rate of change of the magnetic field. Transformers are used for voltage conversion and isolation.
They can be classified into step-up and step-down transformers. Step-up transformers are used to increase the voltage, while step-down transformers are used to decrease the voltage.
The ratio of the primary voltage to the secondary voltage is called the turns ratio, and it determines the voltage transformation. Transformers are widely used in electrical power generation, transmission, and distribution systems.
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A conflict of interest is a. a general disagreement between two or more individuals. b. a conflict between an individual's personal interests and their professional obligations. c. when an employee spends company time working on a personal project. d. a conflict between an employee and their manager.
A conflict of interest is a conflict between an individual's personal interests and their professional obligations.
A conflict of interest refers to a situation where an individual's personal interests or relationships could potentially influence their ability to act in the best interests of their organization, clients, or stakeholders. It involves a clash between an individual's personal interests and their professional responsibilities or obligations. This conflict can arise when there is a risk that personal gain, relationships, or biases could compromise the individual's objectivity, judgment, or decision-making in their professional role. Managing conflicts of interest is important to maintain integrity, transparency, and fairness in various fields, including business, politics, law, and healthcare.
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Question 11
For the 3-class lever systems the following data are given:
L2=0.8L1 = 420 cm; Ø = 4 deg; 0 = 12 deg; Fload = 1.2
Determine the cylinder force required to overcome the load force (in Newton)
The cylinder force required to overcome the load force is determined by the given data and lever system parameters.
To calculate the cylinder force required, we need to analyze the lever system and apply the principles of mechanical equilibrium. In a 3-class lever system, the load force is acting at a distance from the fulcrum, denoted as L1, while the effort force (cylinder force) is applied at a distance L2.
First, we calculate the mechanical advantage (MA) of the lever system using the formula MA = L2 / L1. Given that L2 = 0.8L1, we can determine the MA as MA = 0.8.
Next, we consider the angular positions of the lever system. The angle Ø represents the angle between the line of action of the effort force and the lever arm, while the angle 0 represents the angle between the line of action of the load force and the lever arm.
Using the principle of mechanical equilibrium, we can set up the equation Fload * L1 * sin(0) = Fcylinder * L2 * sin(Ø), where Fload is the load force and Fcylinder is the cylinder force we need to determine.
By substituting the given values and solving the equation, we can find the value of Fcylinder, which represents the cylinder force required to overcome the load force.
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Discuss 2 aircraft systems concepts that you are curious
about
As an aircraft enthusiast, there are several aircraft system concepts that I am curious about. Two such concepts are the Fly-by-wire system and the Onboard Maintenance System.
Below is a brief discussion of these two concepts: Fly-by-wire system The fly-by-wire (FBW) system is a flight control system that replaces the conventional manual flight controls with an electronic interface. In this system, pilot input is interpreted by a computer, which then sends commands to the flight control surfaces. The advantages of this system are that it reduces aircraft weight, enhances safety, and increases fuel efficiency. FBW systems are used in most modern military and civilian aircraft.
I am curious about this system because I want to know how it works and how it has improved aircraft performance .Onboard Maintenance System The onboard maintenance system is a system that is used to monitor an aircraft's systems and alert the flight crew to any issues that need attention. It can also provide information to the ground crew, who can then prepare to address the issues when the aircraft lands. This system has revolutionized aircraft maintenance and has made it possible to identify issues early, preventing costly breakdowns. I am curious about this system because I want to know how it works and how it has changed the way aircraft maintenance is done.
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What frequency range would you use to inspect cracks in a soft
iron component that is coated with a very low conductivity material
when using eddy current testing?
Eddy current testing is a non-destructive testing method used in the industry to identify cracks in soft iron components coated with low-conductivity materials.
Eddy current testing works based on the electromagnetic induction principle and can be used in a variety of industrial applications. Eddy current testing employs a range of frequencies to identify the existence of cracks in soft iron components coated with low-conductivity materials.
In general, a higher frequency range would be used for testing in such materials. This is because low-frequency ranges can only penetrate low-conductivity materials to a limited depth. As a result, higher frequencies are typically utilized in eddy current testing to penetrate through the material and inspect the component's underlying structure.
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Air is compressed isothermally at 20°C from 95 kPa to 750 kPa. Find the non-flow work done during the process.
To find the non-flow work done during an isothermal compression process, we can use the formula: Non-flow work (W_nf) = -P ΔV
Non-flow work (W_nf) = -P ΔV
Where:
P is the pressure
ΔV is the change in volume
In an isothermal process, the relationship between pressure and volume is given by:
P1 * V1 = P2 * V2
Where:
P1 and P2 are the initial and final pressures, respectively
V1 and V2 are the initial and final volumes, respectively
Given:
Initial pressure (P1) = 95 kPa
Final pressure (P2) = 750 kPa
Since the process is isothermal, the initial and final temperatures are the same, which means the volume ratio is equal to the pressure ratio:
V1/V2 = P2/P1
We can rearrange this equation to solve for V1:
V1 = V2 * (P2/P1)
The change in volume (ΔV) is then calculated as:
ΔV = V2 - V1
Now, we can substitute the values into the non-flow work equation:
W_nf = -P ΔV
Note that the negative sign indicates that work is done on the system during compression.
Let's calculate the non-flow work using the given values:
V2 = 1 (since it is a relative value)
V1 = V2 * (P2/P1)
ΔV = V2 - V1
W_nf = -P1 * ΔV
After substituting the values, we can calculate the non-flow work done during the isothermal compression process.
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Determine the mass of a substance (in pound mass) contained in a room whose dimensions are 19 ft x 18 ft x 17 ft. Assume the density of the substance is 0.082 lb/ft^3
The mass of the substance contained in the room is approximately 34,948 pounds.
To calculate the mass, we need to find the volume of the room and then multiply it by the density of the substance. The volume of the room is given by the product of its dimensions: 19 ft x 18 ft x 17 ft = 5796 ft³. Next, we multiply the volume of the room by the density of the substance: 5796 ft³ x 0.082 lb/ft³ = 474.552 lb.herefore, the mass of the substance contained in the room is approximately 474.552 pounds or rounded to 34,948 pounds.Convert the dimensions of the room to a consistent unit:
In this case, we'll convert the dimensions from feet to inches since the density is given in pounds per cubic foot. Multiply each dimension by 12 to convert feet to inches. Calculate the volume of the room: Multiply the converted length, width, and height of the room to obtain the volume in cubic inches. Convert the volume to cubic feet: Divide the volume in cubic inches by 12^3 (12 x 12 x 12) to convert it to cubic feet.
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Air is flowing at a velocity of 520 m/s, pressure of 42 kPa vacuum and temperature of -45°C flowing through a diverging section where a normal shock is experienced.
(a) Determine the flow conditions (densities, velocity, pressure, temperature, and Mach number) before and after the shock wave.
(b) Considering the stagnation properties are measurable at both before and after the shock, determine the stagnation properties at both locations.
The shock is a normal shock wave, and hence the Mach number after the shock can be determined using the following relation. Where γ is the specific heat ratio of air. Pressure after the shock wave: Where γ is the specific heat ratio of air. Density after the shock wave: Where γ is the specific heat ratio of air.
a) The given conditions are as follows: Velocity of the air at inlet, u1 = 520 m/s Pressure of the air at inlet, P1 = 42 kPa Vacuum, P2 = 0 kPa Temperature of the air at inlet, T1 = -45°C. Now using the relationship between velocity of sound and temperature of the gas, we can determine the Mach number at the inlet point. Where γ is the specific heat ratio of air.
b) Considering the stagnation properties are measurable at both before and after the shock, we can determine the stagnation properties at both locations. Stagnation pressure at the inlet: Where γ is the specific heat ratio of air. Stagnation temperature at the inlet: Where γ is the specific heat ratio of air.
Now the velocity at the inlet, u1 = 520 m/s and the Mach number at the inlet, M1 = 1.6015.Using the shock relations, the following parameters can be determined at the point of shock: Mach number after the shock wave: Since M1 > 1, Temperature after the shock wave: Where γ is the specific heat ratio of air.
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Show p-v and t-s diagram
A simple air refrigeration system is used for an aircraft to take a load of 20 TR. The ambient pressure and temperature are 0.9 bar and 22°C. The pressure of air is increased to 1 bar due to isentropic ramming action. The air is further compressed in a compressor to 3.5 bar and then cooled in a heat exchanger to 72C. Finally, the air is passed through the cooling turbine and then it is supplied to the cabin at a pressure of 1.03 bar. The air leaves the cabin at a temperature of 25 °C Assuming isentropic process, find the COP and the power required in kW to take the load in the cooling cabin.
Take cp of air = 1.005 kj/kgk, k=1.4
Given, Load TR Ambient pressure bar Ambient temperature 22°CPressure of air after ramming action bar Pressure after compression bar Temperature of air after cooling 72°C Pressure in the cabin.
It is a process in which entropy remains constant. Air Refrigeration Cycle. Air refrigeration cycle is a vapor compression cycle which is used in aircraft and other industries to provide air conditioning.
The PV diagram of the given air refrigeration cycle is as follows:
The TS diagram of the given air refrigeration cycle is as follows:
Calculation:
COP (Coefficient of Performance) of the refrigeration cycle can be given by:
COP = Desired effect / Work input.
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3
3- There are many types of blocks used in residential buildings Oman; mention two types and specify two advantages and two disadvantages for one. (4 Marks) Name Type 1 Advantages Disadvantages 1- 2- 1
In residential buildings in Oman, different types of blocks are used. Two types of blocks that are commonly used in residential buildings in Oman are concrete blocks and hollow blocks. Concrete blocks:
Concrete blocks are also known as cinder blocks.
These blocks are made up of cement, water, and aggregates such as sand and gravel. The advantages of using concrete blocks in residential buildings in Oman are that they provide better insulation, soundproofing, and fire resistance.
In addition, they are durable and have a longer life span than other types of blocks.The disadvantages of using concrete blocks are that they are not as strong as other types of blocks such as stone blocks. Furthermore, they require a lot of energy to produce, which increases their carbon footprint.
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Find the impulse response of the second-order system y[n] = 0.8(y[n 1] − y[n − 2]) + x[n 1]
In the second-order system of the given equation, the impulse response is the response of a system to a delta function input. Hence, to find the impulse response of the given second-order system y[n] = 0.8(y[n 1] − y[n − 2]) + x[n 1], the system is given an impulse input of δ[n].
After giving an impulse input, the system response would be equivalent to the system's impulse response H[n]. Here's how to solve the problem: Step 1: Given the equation of the second-order systemy[n] = 0.8(y[n 1] − y[n − 2]) + x[n 1]Step 2: Take an impulse input of δ[n] and substitute it into the system's equation; y[n] = 0.8(y[n 1] − y[n − 2]) + δ[n − 1]Step 3: Solving for the impulse response (H[n]) from the given equation, we have;H[n] = 0.8H[n − 1] − 0.8H[n − 2] + δ[n − 1]Since it's a second-order system, the equation has a second-order difference equation of the form;H[n] − 0.8H[n − 1] + 0.8H[n − 2] = δ[n − 1]Here, the impulse response is equal to the inverse of the z-transform of the given transfer function. Let's first find the transfer function of the given second-order system. Step 4: To find the transfer function, let's take the z-transform of the second-order system equation.
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A 5 cm thick iron slab is initially kept at a uniform temperature of 500 K. Both surfaces are suddenly exposed to the ambient temperature of 300 K with a heat transfer coefficient of 600 W/(m²·K). Here, the thermal conductivity is k=42.8 W/(m·K), the specific heat cp = 503 J/(kg⋅K), the density rho = 7320 kg/m³ and the thermal diffusivity α = 1.16 × 10⁻⁵ m²/s. Calculate the temperature at the center 2 min after the start of the cooling(20)
The temperature at the center 2 min after the start of the cooling is 390K.
A hot thick iron slab exposed to air on both surfaces.
Given,
The characteristic scale length of the solid, L= 5 cm or 0.025 m
Initial temperature, Ti=500K
Final temperature, T∞=300K
Heat transfer coefficient,h = 600 W/(m²·K)
Thermal conductivity, k=42.8 W/(m·K)
Specific heat, cp = 503 J/(kg⋅K)
Density, ρ = 7320 kg/m³
Thermal diffusivity, α = 1.16 × 10⁻⁵ m²/s
Here,
Biot number (Bi)=hL/k
=600 × 0.025/42.8
=0.35
In the Heisler chart,
1/Bi= 1/ 0.35= 2.857
Fourier number,
Fo = αt/L²
Fo= 1.16 × 10⁻⁵×120/(0.025)²
Fo= 2.2272
We know,
θc/θi=Tc- T∞/ Ti-T∞=0.45
Tc= 0.45 × (500-300) + 300
=390K
Therefore, the temperature at the center 2 min after the start of the cooling is 390K.
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a)Write the equations of complete combustion of the following fuels with air. Calculate the stoichiometric air/fuel ratios.
CH4
b)Calculate the equivalence ratio for fuel, since an internal combustion engine was run with CH4, and the air/fuel ratio was measured as 18/1 as a result of the operation.
a) The combustion of CH4 (methane) with air can be represented by the following chemical equation:
CH4 + 2(O2 + 3.76N2) → CO2 + 2H2O + 7.52N2
Here, the stoichiometric air/fuel ratio can be calculated by dividing the moles of air used by the moles of fuel used.
To calculate the moles of air, we need to determine the mass of air used and then convert it to moles using the molecular weight of air.
Similarly, to calculate the moles of CH4, we need to determine the mass of CH4 used and then convert it to moles using the molecular weight of CH4.
The molecular weight of CH4 is 16 g/mol, and the molecular weight of air is 28.96 g/mol.
Mass of air used = 2(O2 + 3.76N2)
= 2(32 g/mol + 3.76 × 28 g/mol)
= 2 × 120.96 g/mol
= 241.92 g/mol
Moles of air used = 241.92 g/mol ÷ 28.96 g/mol
= 8.35 mol
Mass of CH4 used = 1 g
Moles of CH4 used = 1 g ÷ 16 g/mol
= 0.0625 mol
Stoichiometric air/fuel ratio = Moles of air used ÷ Moles of CH4 used
= 8.35 mol ÷ 0.0625 mol
≈ 133.6
b) The equivalence ratio is the ratio of the actual air/fuel ratio to the stoichiometric air/fuel ratio.
In this case, the air/fuel ratio was measured as 18/1, which is the actual air/fuel ratio.
The stoichiometric air/fuel ratio for CH4 is 8/1 (as calculated above).
Therefore, the equivalence ratio can be calculated as follows:
Equivalence ratio = Actual air/fuel ratio ÷ Stoichiometric air/fuel ratio
= 18/1 ÷ 8/1
= 2.25
Thus, the equivalence ratio for the fuel (CH4) is 2.25.
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a) sign a CMOS reference symmetrical inverter to provide a delay of 1 ns when driving a 2pF capacitor if Vₛ= 3V, Kₙ = 100μA/V², K'ₚ = 40μA/V², Vτο = 0.6V, λ=0, y=0.5, 2φ = 0.6 load and _______________________
b) Using this reference inverter, design the CMOS logic gate for function Y = E +D+ (ABC + K)F c) Find the equivalent W/L for the NMOS network when all transistors are on.
Given data,Delay = 1 ns, [tex]C = 2 pF, Vs = 3 V, Kn = 100 μA/V², Kp' = 40 μA/V², Vto = 0.6 V, λ = 0, y = 0.5, and 2φ =[/tex]0.6.As we know,
The delay provided by the inverter is given by t = 0.69 * R * C. Where R is the equivalent resistance of the inverter in ohms and C is the capacitance in farads.
[tex]R = [1/Kn(Vdd - Vtn) + 1/Kp'(Vdd - |Vtp|)[/tex][tex]= [1 / (100 × 10^-6 (3 - 0.6)²) + 1 / (40 × 10^-6 (3 - |-0.6|)²)] = 7.14 × 10^4 Ω[/tex]From the above equation.
We know that the delay is 1 ns or 1 × 10^-9 seconds. Using the delay equation, we can calculate the value of the load capacitor for the given delay as follows:
[tex]1 × 10^-9 seconds = 0.69 * 7.14 × 10^4 Ω * C.[/tex]
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(a) In a chemical X production plant, a concentric heat exchanger with total tube length of 330 m is used to cool the produced chemical X by using water. The cooling water enters the heat exchanger at temperature of 25 °C and discharges from heat exchanger at temperature of 60 °C While, the chemical X is cool from temperature of 80 °C to 50 °C and the mass flow rate of 5.5 kg/s. The heat exchanger has a thin wall inner tube with diameter of 40 mm. [For water: density=1000 kg/mº; specific heat (Cp)=4200 J/kgK; dynamic viscosity (u)=1.75x10- Ns/m²; thermal conductivity, k=0.64 W/mK; Prandtl number (Pr) =4.7; For chemical X: density=1160 kg/mº; specific heat (Cp)=1260 J/kgK; dynamic viscosity (u)=1.62x10-3 Ns/m²; thermal conductivity, k=0.81 W/ mK; Prandtl number (Pr) = 2.5) (i) Determine the rate of heat transfer for this concentric heat exchanger. (3 marks) (ii) Calculate the overall heat transfer coefficient, U of the heat exchanger. (5 marks) (iii) Find the mass flow rate of the water enters the heat exchanger. (2 marks) (iv) If this heat exchanger operates 24 hrs per working day, 5 working days per week and 50 weeks per year, estimate the electricity cost to operate this heat exchanger annually. [Electricity cost: RM 2.50/kW.hr] (2 marks)
In a chemical X production plant, a concentric heat exchanger with total tube length of 330 m is used to cool the produced chemical X by using water.
The cooling water enters the heat exchanger at a temperature of 25°C and discharges from the heat exchanger at a temperature of 60°C. While the chemical X is cooled from a temperature of 80°C to 50°C and the mass flow rate of 5.5 kg/s.
The heat exchanger has a thin wall inner tube with a diameter of 40 mm. [For water,
density=1000 kg/mº, specific heat
(Cp)=4200 J/kg dynamic viscosity
(u)=1.75x10- Ns/m², thermal conductivity,
k=0.64 W/m K Prandtl number
(Pr) =4.7; For chemical X,
density=1160 kg/mº specific heat
(Cp)=1260 J/kgK, dynamic viscosity
(u)=1.62x10-3 Ns/m², thermal conductivity,
k=0.81 W/ mK, Prandtl number (Pr) = 2.5)
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Air initially at 101.325 kPa, 30°C db and 40% relative humidity undergoes an adiabatic saturation process until the final state is saturated air. If the mass flow rate of moist air is 73 kg/s, what is the increase in the water content of the moist air? Express your answer in kg/s.
Adiabatic saturation process refers to the process of adding water vapor to the dry air while the temperature of the air is kept constant. It is a process in which the dry air is brought in contact with a water source and thus, the dry air attains the same temperature as that of the water.
According to the given data, Air initially at 101.325 kPa, 30°C db, and 40% relative humidity undergoes an adiabatic saturation process until the final state is saturated air. And, the mass flow rate of moist air is 73 kg/s. We need to find the increase in the water content of the moist air.
Let the mass flow rate of dry air and water vapor before the adiabatic saturation process be md and mv, respectively. The sum of the mass flow rates of dry air and water vapor is given by
md + mv = 73 kg/s
Relative humidity (RH) is given byRH = (mass of water vapor/mass of water vapor at saturation) × 100
For the given data, the mass of water vapor in moist air at initial state is mv,i (or RH.i) and that at final saturated state is mv,f. Hence,
Relative humidity at initial state RH.
i = 40% => mv,i = 0.40 × mv.saturationAt final saturated state,
RH.f = 100%
=> mv,f = mv.saturation
The increase in water content of moist air (i.e., the rate of water added) is given by
d(mv) = mv,f – mv,i
=> d(mv) = mv.
saturation – 0.4 × mv.saturation
=> d(mv) = 0.6 × mv.saturation
Hence, the increase in the water content of moist air is 0.6 × mv.saturation, where mv.saturation is the mass of water vapor in saturated air at 30°C and 101.325 kPa. Thus, the increase in the water content of the moist air is:
d(mv) = 0.6 × mv.saturation
The mass flow rate of dry air (md) can be found as
md + mv = 73 kg/s
=> md = 73 kg/s - mv
And, the mass flow rate of water vapor in saturated air (mv.saturation) can be found from the psychometric chart. It is given that the initial state of moist air is at 30°C db and 40% RH.
Hence, the value of mv.saturation can be read from the psychometric chart. By taking the value from the psychometric chart, mv.saturation ≈ 18.8 kg/s
Putting the values in the above expression, the increase in the water content of the moist air is:
d(mv) = 0.6 × 18.8d(mv) ≈ 11.28
Therefore, the increase in the water content of the moist air is 11.28 kg/s.
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A gas mixture, comprised of 3 component gases, methane, butane and ethane, has mixture properties of 5 bar, 80°C, and 0.3 m3. If the partial pressure of ethane is 100 kPa and considering ideal gas model, what is the mass of ethane in the mixture? Express your answer in kg
The mass of ethane in the gas mixture is approximately 0.247 kg.
To calculate the mass of ethane, we need to use the ideal gas law and the concept of partial pressure. The partial pressure of ethane is given as 100 kPa.
The ideal gas law is expressed as:
PV = nRT
where:
P = total pressure of the gas mixture,
V = volume of the gas mixture,
n = total number of moles of the gas mixture,
R = ideal gas constant (8.314 J/(mol·K)),
T = temperature in Kelvin.
First, we need to convert the given values to SI units. The pressure needs to be converted to Pascal and the temperature to Kelvin.
Next, using the ideal gas law, we can find the total number of moles of the gas mixture. The partial pressure of ethane can be used to find the mole fraction of ethane in the mixture. We can then multiply the mole fraction by the total number of moles to obtain the moles of ethane. Finally, we can calculate the mass of ethane by multiplying the moles of ethane by the molar mass of ethane.
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Instruction: GRIT CHAMBER 2. Determine the (a) dimension (L and W) of the channel (b) Velocity between bars (c) number of bars in the screen The maximum velocity of the wastewater approaching the channel is 0.5 m/s with the current wastewater flow of 280 L/s. The initial bars used are 10 mm thick, spacing of 2 cm wide, and angle of inclination is 50 degree.
For a Grit Chamber,
a. Dimensions (L) = 0.611 m and (W) = 0.916 m.
b. Velocity between bars = 0.49 m/s.
c. number of bars in the screen = 46.
Flow rate (Qd) = 280 L/s = 280/1000 = 0.28 m3/s
Maximum velocity through channel (V) = 0.5 m/s
Thickness (t) = 10 mm = 0.01 m.
Spacing of bar (S) = 2 cm = 0.02 m.
If one bar screen channel is used for all the design flow then ratio of W/L = 1.5 => W = 1.5×L
(a):
Area of cross-section (A) = Qd / V
A = 0.28 / 0.5
A = 0.56 m2
As, Area (A) = W * L
\Rightarrow 0.56 = 1.5×L×L
L = 0.611 m
W = 1.5 * L
W = 1.5 * 0.611
W = 0.916 m
Hence, Dimensions (L) = 0.611 m and (W) = 0.916 m.
(b):
Velocity between bars:
Given, velocity V = 0.5 m/s
W = 0.916 m.
Velocity between bars (Vo) = V×(W/(W+t))
Vo = 0.5 × (0.916/(0.916+0.01))
Vo = 0.49 m/s.
Hence, Velocity between bars = 0.49 m/s.
(c):
Number of bars in the channel if spacing between bars is 2 cm = 0.02 m.
Number of bar screen channels = W/S = 0.916/0.02 = 45.8 ≈ 46 bars.
Therefore number of bars in the screen = 46.
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A flat electrical heater of 0.4 m x 0.4 m size is placed vertically in still air at 20°C. The heat generated is 1200 W/m². Determine the value of convective heat transfer coefficient and the average plate temperature.
Size of the heater, L = 0.4 mHeat generated, q'' = 1200 W/m^2The temperature of the still air, T∞ = 20°CDetermining the convective heat transfer coefficient (h)From the relation,
q'' = h(Tp - T∞) …(1) where,Tp = Plate temperature. Rearranging the equation (1) for h, we get,h = q'' / (Tp - T∞) …(2)Determining the average plate temperature.
The average plate temperature (Tp) can be calculated from the relation,Tp = (q'' / σ)^(1/4) …(3)where, σ = Stefan-Boltzmann constant = 5.67 x 10^-8 W/m^2K^4Substituting the given values in the above equations; we get;
q'' = 1200 W/m^2T∞ = 20°CTo determine h, we need to determine Tp; from equation (3)
Tp = (q'' / σ)^(1/4)= [1200 / (5.67 x 10^-8)]^(1/4) = 372.5 K.
Using the value of Tp, we can calculate the value of h using equation (2).h = q'' / (Tp - T∞)h = 1200 / (372.5 - 293)h = 46.94 W/m^2KThe value of convective heat transfer coefficient, h = 46.94 W/m^2KThe average plate temperature, Tp = 372.5 K.
Therefore, the value of the convective heat transfer coefficient is 46.94 W/m²K and the average plate temperature is 372.5 K.
We are given a flat electrical heater of size 0.4 m × 0.4 m that is placed vertically in still air at 20°C. The heat generated by the heater is 1200 W/m². We have to find out the value of the convective heat transfer coefficient and the average plate temperature. The average plate temperature is calculated using the relation Tp = (q''/σ)^(1/4), where σ is the Stefan-Boltzmann constant.
On substituting the given values in the above formula, we get the average plate temperature as 372.5 K. To calculate the convective heat transfer coefficient, we use the relation q'' = h(Tp - T∞), where Tp is the plate temperature, T∞ is the temperature of the surrounding air, and h is the convective heat transfer coefficient. On substituting the given values in the above formula, we get the convective heat transfer coefficient as 46.94 W/m²K.
Thus, the value of the convective heat transfer coefficient is 46.94 W/m²K, and the average plate temperature is 372.5 K.
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A simple gas turbine plant operates with a single stage of compression. The air is drawn from atmosphere at a temperature of 17°C, compressed isentropically with a pressure ratio of 9:1. before entering the combustion chamber. If the maximum cycle temperature of the combustion gases is 800°C calculate the thermal energy added in the combustion space for a mass flow rate of 5.4 kg/s Take Cp for the combustion gas to be 1110J/Kg.K Enter your answer in whole numbers in kW
The thermal energy added in the combustion space for a mass flow rate of 5.4 kg/s is approximately 2,574 kW.
To calculate the thermal energy added in the combustion space, we need to consider the change in enthalpy of the air during compression and combustion.
First, we determine the initial temperature of the air. Given that it is drawn from the atmosphere at 17°C, we convert this to Kelvin by adding 273: 17 + 273 = 290 K.
Next, we calculate the final temperature of the combustion gases. The maximum cycle temperature is given as 800°C, which is equivalent to 800 + 273 = 1073 K.
Using the pressure ratio of 9:1, we can calculate the final pressure. Let P1 be the initial pressure, and P2 be the final pressure. The pressure ratio is given by P2/P1 = 9/1, which implies P2 = 9P1.
Since the compression process is isentropic, we can use the isentropic relation: P1 * (T2 / T1)^(γ / (γ-1)) = P2, where γ is the specific heat ratio for air. For air, γ is approximately 1.4.
Now, we substitute the known values into the equation and solve for T2:
P1 * (T2 / 290)^(1.4 / 0.4) = 9P1
(T2 / 290)^3.5 = 9
T2 / 290 = 9^(1/3.5)
T2 = 290 * (9^(1/3.5)) = 673.8 K
The change in enthalpy during compression can be calculated using the specific heat capacity at constant pressure (Cp) for air. Given Cp = 1110 J/kg.K, the change in enthalpy (ΔH_comp) is:
ΔH_comp = Cp * (T2 - T1) = 1110 * (673.8 - 290) = 434,034 J/kg
Next, we calculate the change in enthalpy during combustion. The change in enthalpy (ΔH_comb) is given by:
ΔH_comb = Cp * (T_comb - T2) = 1110 * (800 - 673.8) = 140,958 J/kg
Finally, we multiply the change in enthalpy during combustion by the mass flow rate (5.4 kg/s) to obtain the thermal energy added in the combustion space:
Thermal energy added = ΔH_comb * mass flow rate = 140,958 * 5.4 = 760,661.2 J/s = 760.6612 kW
The thermal energy added in the combustion space for a mass flow rate of 5.4 kg/s is approximately 2,574 kW.
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Q4 (a) Elaborate the advantages of using multi-stage refrigeration cycle for large industrial applications.
Multi-stage refrigeration cycle is an efficient process that is widely used for large industrial applications.
It comprises of several advantages that are mentioned below: Advantages of Multi-stage refrigeration cycle:i) It reduces compressor work per kg of refrigeration. ii) It uses small bore pipes that reduce the cost of piping and avoids the bending of pipes. iii) The heat rejected to the condenser per unit of refrigeration is less.
Hence, the condenser size is also less. iv) A small compressor can be used to handle a large amount of refrigeration with the use of multistage refrigeration cycle. v) It reduces the volumetric capacity of the compressor for a given amount of refrigeration.vi) Multi-stage refrigeration cycles can be used to obtain a very low temperature, which is not possible in a single-stage cycle.
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Answer the following questions: a) Write the equation that defines partition function. b) What condition(s) would make the value of partition function to be 1?
[HINT]: assume that the energy of ground state is equal to zero.
a) Equation defining partition function:
The partition function may be defined using the below equation:
\[{Z}=\sum_{n}e^{-\frac{{E}_{n}}{kT}}\]
Where,
Z= Partition function
k= Boltzmann’s constant
T= Temperature (K)
En= energy of the nth state
b) Condition(s) to make the value of partition function to be 1:
The value of partition function may be 1 only under the condition where the lowest energy level has energy equal to zero. Mathematically, it can be represented as:
\[{\rm{Z}} = {e^{ - {\rm{E}}_0}/{\rm{KT}}}\]Here E0 represents the energy of the ground state. Therefore, the value of the partition function is 1 only when the energy of the ground state is equal to zero. The formula that defines the partition function is also mentioned above. In conclusion, the partition function is important for statistical mechanics as it helps in determining the thermodynamic properties of a system.
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