5.] Wave Mechanics a. Show that the addition of an imaginary part to the potential in the quantal wave equation describes the presence of sources or sinks of probability. (Work out the appropriate continuity equation.) 8 points b. Solve the wave equation for a potential of the form V=−Vo(1+iζ), where Vo and ζ are positive constants. 7 points c. If ζ<<1, show that there are stationary state solutions that represent plane waves with exponentially attenuated amplitude, describing absorption of the waves. 5 points d. Calculate the absorption coefficient. 5 points
Answers
a. The continuity equation for a wave function in three dimensions is given by the following:
∇·J + ∂ρ/∂t = 0
where, ∇ is the gradient operator, J is the current density of the wave function, ρ is the probability density of the wave function, and ∂/∂t is the partial derivative of time.
In quantum mechanics, the probability density of the wave function is given by the product of the complex conjugate of the wave function and the wave function itself.
In this case, ρ = Ψ*Ψ, where Ψ is the wave function.
When an imaginary part is added to the potential in the wave equation, it implies that there is a loss or gain of probability density. This change in probability density is referred to as sources or sinks.
The continuity equation can be modified as follows:
∇·J - αρ + ∂ρ/∂t = 0
where α is a positive constant that denotes the absorption coefficient. The addition of the imaginary part to the potential causes the value of α to increase.
b. The wave equation for a potential of the form V=−Vo(1+iζ) is given by the following:
Ψ''(x) + 2iζΨ'(x) + k²Ψ(x) = 0
where, Ψ(x) is the wave function, k is the wave number, and Vo and ζ are positive constants.
The solution to the wave equation can be obtained using the following characteristic equation:
r² + 2iζr + k² = 0where r = dΨ(x)/dx
The roots of the characteristic equation are given by:
r = -iζ ± √(ζ² - k²)
Thus, the wave function is given by the following:
Ψ(x) = Ae^(r1x) + Be^(r2x)
where A and B are constants and r1 and r2 are the roots of the characteristic equation.
c. When ζ<<1, the roots of the characteristic equation can be approximated as:
r1 ≈ -ik and r2 ≈ -iζ
The wave function can be written as follows:
Ψ(x) = Ae^(-ikx) + Be^(-iζx)
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Related Questions
rosbel or Janette lol baakkaaa
Answers
Answer:
t5g5gtttttttttttttttttttttttttttttttttttttttttttt
Explanation:gt555555555555555555555555555555555555555555555555
Answer:
dawbkjbjwwjhjfbfjewfaekfhawkjndwkja
Explanation: dum*as*
An electronics engineer is interested in the effect on tube conductivity of five different types of coating for cathode ray tubes in a telecommunications system display device. The following conductivity data are obtained. Coating type | Conductivity 1 143 141 150 146
2 152 149 137 143
3 134 133 132 127
4 129 127 132 129
5 147 148 144 142
Is there any difference in conductivity due to coating type? Use a = 0.01. Approximate your answer up to 2 decimal places. F0 = ___
Answers
The sum of squares of error, treatment, within and between four painters are: 330, 692, 110 and 43.25.
What data provides?The data has been provided has for the dying time of four different types of paint. One-way ANOVA can be used to determine whether all the four paints have the same drying time.
Use Excel in order to perform the one-way ANOVA.
Go to Data → Data Analysis → Anova: Single Factor
A dialog box will open. Select the data. Select "Grouping" as Columns.
Press OK.
The output is attached below.
The required values are as follows:
(1) Sum of Squares of Treatment (Between Subjects):
SST = 330
(2) Sum of Squares of Error (Within Subjects):
SSE = 692
(3) Mean Squares Treatment (Between Subjects):
MST = 110
(4) Mean Squares Error (Within Subjects):
MSE = 43.25
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In which model of the system, the change in order is generated depending on the system activities. *
Static Model
Dynamic Model
Analytical Model
Numerical Model
Answers
Answer:
Static Model
Explanation:
Liquid water flows isothermally at 20°C through a one-inlet, one-exit duct operating at steady state. The duct’s inlet and exit diameters are 0.02 m and 0.1 m, respectively. At the inlet, the velocity is 10 m/s and pressure is 1 bar. At the exit, determine the mass flow rate, in kg/s, and velocity, in m/s.
Answers
The continuity equation allows finding the results for the speed and flow of the outlet pipe are:
Q = 3.14 kg / s v₂ = 0.4 m / s
Fluid mechanics studies the movement and fluid dynamics, it is described by two fundamental relationships:
The Bernoulli equation that an expression of the energy conservation\(P_1 + \frac{1}{2} \rho v_1^2 + \rho g y_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g y_2\)
Where P is the pressure, v the velocity, y the height, the subscripts are two selected points of interest in the pipe.
The continuity equation which is an expression that our principle of mass conservation for fluids
\(A_1v_1 = A_2 v_2\)
Where A₁ and A₂ is the area of the inlet and outlet pipes and v₁ and v₂ are the velocities of the fluid at the inlet and outlet
They indicate the inlet and outlet diameters of the pipe are d₁ = 0.02 m and d₂ = 0.1 m, the inlet velocity v₁ = 10 m / s, with the continuity equation let's find the outlet velocity
\(v_2 = ( \frac{A_1}{A_2} )^2 \ v_1\)
the cross section of the tavern is
A = \(\pi r^2 = \pi \ d^2/4\)
Where r is the radius and d is the diameter
Let's substitutes
\(v_2 = (\frac{d_1}{d_2} )^2 \ v_1\)
\(v_2 = (\frac{0.02}{0.1} )^2 \ 10\)
v₂ = 0.4 m / s
The flow (Q) is defined as the amount of liquid that passes through the section of the pipe per unit of time, we can see that this is the same conservation of mass, therefore
Q = A v
Q = \(\pi \frac{d_2^2}{4} \ v_2\)π d2 ^ 2 v2
Q = \(\pi \ \frac{0.1^2}{4} \ 0.4\)
Q = 3.14 10⁻³ m ^ 3 / s
As the transported liquid is water
1 liter water = 1 kg
Consequently
1 m³ = 1000 liter = 1000 kg of water
Let's reduce the flow
Q = 3.14 10⁻³ m³/s ( \(\frac{10^3 kg}{1 m^3}\) )
Q = 3.14 kg / s
In conclusion using the continuity equation we can find the results for the speed and flow of the outlet pipe are:
v₂ = 0.4 m / s Q = 3.14 kg / s
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Draw an ERD for each of the following situations. (If you believe that you need to make additional assumptions, clearly state them for each situation.) Draw the same situation using the tool you have been told to use in the course. a. A company has a number of employees. The attributes of EMPLOYEE include Employee ID (identifier), Name, Address, and Birthdate. The company also has several projects. Attributes of PROJECT include Project ID (identifier), Project Name, and Start Date. Each employee may be assigned to one or more projects or may not be assigned to a project. A project must have at least one employee assigned and may have any number of employees assigned. An employee's billing rate may vary by project, and the company wishes to record the applicable billing rate (Billing Rate) for each employee when assigned to a particular project. Do the attribute names in this description follow the guidelines for naming attributes? If not, suggest better names. Do you have any associative entities on your ERD? If so, what are the identifiers for those associative entities? Does your ERD allow a project to be created before it has any employees assigned to it? Explain. How would you change your ERD if the Billing Rate could change in the middle of a project? b. A laboratory has several chemists who work on one or more projects. Chemists also may use certain kinds of equipment on each project. Attributes of CHEMIST include Employee ID (identifier), Name, and Phone No. Attributes of PROJECT include Project ID (identifier) and Start Date. Attributes of EQUIPMENT include Serial No and Cost The organization wishes to record Assign Date—that is, the date when a given equipment item was assigned to a particular chemist working on a specified project A chemist must be assigned to at least one project and one equipment item. A given equipment item need not be assigned, and a given project need not be assigned either a chemist or an equipment item. Provide good definitions for all of the relationships in this situation. c. A college course may have one or more scheduled sections or may not have a scheduled section. Attributes of COURSE include Course ID, Course Name, and Units. Attributes of SECTION include Section Number and Semester ID. Semester ID is composed of two parts: Semester and Year. Section Number is an integer (such as 1 or 2) that distinguishes one section from another for the same course but does not uniquely identify a section. How did you model SECTION? Why did you choose this way versus alternative ways to model SECTION? d. A hospital has a large number of registered physicians. Attributes of PHYSICIAN include Physician ID (the identifier) and Specialty. Patients are admitted to the hospital by physicians. Attributes of PATIENT include Patient ID (the identifier) and Patient Name. Any patient who is admitted must have exactly one admitting physician. A physician may optionally admit any number of patients. Once admitted, a given patient must be treated by at least one physician. A particular physician may treat any number of patients, or may not treat any patient& Whenever a patient is treated by a physician, the hospital wishes to record the details of the treatment (Treatment Detail). Components of Treatment Detail include Date, Time, and Results. Did you draw more than one relationship between physician and patient? Why or why not? Did you include hncnithi ac an antitv type? Why or why not?
Answers
Answer:
it wqas red
Explanation:
red
a load of 12tonnes is put along a horizontal plane by a force at 30°to and above the flat. if the coefficient of sliding friction is 0.2 find the frictional force
Answers
Answer:
20368.917N
Explanation:
Frictional force (F) is the product of the Coefficient of friction and the normal reaction.
F = μN
Coefficient of friction, μ = 0.2
Normal reaction = MgCosθ
Mass, m = 12 tonnes = 12 * 1000 = 12000 kg
N = 12000 * 9.8 * cos30
N = 101844.58
F = 0.2 * 101844.58
F = 20368.917N
People tend to self-disclose to others that are in age, social status, religion, and personality.
Answers
Answer:people tend to do this when they are in a different environment they lose something or just have something going on in their life
Explanation:
Which of the following is false about most machine learning models?
They require numbers or collections of numbers as input.
They are flexible enough to handle all issues you might see in your dataset (lack of data, incorrect data, etc)
They are trained by iteratively adjusting their parameters to minimize a loss function.
Once trained, their model parameters can be used to make new predictions in a process called a “model inference algorithm.”
Answers
The false statement about most machine learning models is that: B. they are flexible enough to handle all issues you might see in your dataset (lack of data, incorrect data, etc).
What is machine learning?Machine learning (ML) is also referred to as deep learning or artificial intelligence (AI) and it can be defined as a subfield in computer science which is typically focused on the use of data-driven techniques (methods), computer algorithms, and technologies to develop a smart computer-controlled robot with an ability to automatically perform and manage tasks that are exclusively meant for humans or solved by using human intelligence.
Generally speaking, machine learning models are designed and developed to accept numerical data (numbers) or collections of numerical data (numbers) as an input.
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what is the function of filters in communication system ?
Answers
In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist.
Explanation:
Electrically heated draw batch furnaces are commonly used in the heat treatment industry. Consider a draw batch furnace front made of a 20-mm thick steel plate with a thermal conductivity of 25 W/m·K. The furnace is situated in a room with surrounding air temperature of 20°C and an average convection heat transfer coefficient of 10 W/m2·K. If the inside surface of the furnace front is subjected to uniform heat flux of 5 kW/m2 and the outer surface has an emissivity of 0.30, determine the inside surface temperature of the furnace front in K. (Round your answer up to 2 decimal places.)
Answers
Answer:idek
Explanation:u
Use the HELPrct data from the mosaicData to calculate the mean of all numeric variables (be sure to exclude missing values)
Answers
To calculate the mean of all numeric variables in the HELPrct data from the mosaicData package, we can use the colMeans() function in R. This function calculates the mean of each column in a data frame.
However, it only works on numeric columns, so we need to first remove any non-numeric columns or missing values.
To do this, we can use the select_if() function from the dplyr package to only select columns that are numeric. Then, we can use the na.omit() function to remove any rows with missing values. Finally, we can use the colMeans() function to calculate the mean of each column.
Here's the code:
library(mosaicData)
library(dplyr)
# Select only numeric columns
numeric_cols <- select_if(HELPrct, is.numeric)
# Remove rows with missing values
numeric_cols <- na.omit(numeric_cols)
# Calculate column means
means <- colMeans(numeric_cols)
# Print the result
print(means)
This will give us the mean of each numeric column in the HELPrct data, excluding any missing values.
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Quadrilateral ABCD is a rectangle.
If m ZADB = 7k + 60 and mZCDB = -5k + 40, find mZCBD.
Answers
Hope this helps...........
a 400 l tank initially contains water at 200 kpa and a quality of 1%. heat is transferred to the tank by a burner, thereby raising the temperature and pressure of the water. at a pressure of 3 mpa, a valve opens and saturated vapor at 2 mpa flows out. the burner remains on, maintaining a pressure of 3 mpa inside the tank, until the quality of the tank is 90%, after which it shuts off
Answers
To prevent a waterlogged tank or surging at the faucets, you must keep air in the bladder of bladder-type pressure tanks. First, look at the pressure gauge to determine the pressure at which your well pump activates and deactivates.
The difference in pressure between turning on and turning off is typically 20 psi. our pipes, fittings, and switches may become damaged by pressures more than 60 psi. Plumbing failure and expensive leaks could result from this damage. It's probable that the pump won't be able to achieve the cut-off pressure if the pressure is set at 80 psi. The bladder could be torn or holed if tank pressure lowers. If a tank is totally filled with water or has too much water for it to function properly, it is said to be waterlogged.
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For fire alarm cable to be effective the _______ wire must be grounded.
Answers
Answer:
the ground wire must be grounded.
Explanation:
For fire alarm cable to be effective, the ground wire must be grounded. This is because grounding the wire helps to ensure that the fire alarm system is properly connected to the earth, which can help to protect against electrical surges and other issues that could interfere with the proper functioning of the system. Additionally, grounding the wire can help to prevent the build-up of static electricity, which can damage the cable or the fire alarm system itself.
What is the purpose of water tanks?
Answers
A water storehouse tank's primary function is to hold water before it's employed for drinking, washing, cleaning, and other purposes. nonetheless, numerous storehouse tanks are trickier than they appear.
Water tank storehouse is a system of storing water that can be applied to home, marketable, and artificial settings. Depending on how the tank will be used, water storehouse tanks come in a variety of accoutrements , shapes, and sizes. Water Well Pressure Tanks In structures that acquire their water from a well force, well pressure tanks are installed. The well-conditioned pump's lifetime is increased by a well-conditioned pressure tank, which maintains water pressure and stops it from turning on and off all day. Before the well-conditioned pump, the tank fills with a constant inflow of water that's transferred to appliances.
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A robot with artificial intelligence would best be suited for
Answers
________ refers to detection and treatment of equipment or facilities.
Answers
Maintenance refers to detection and treatment of equipment or facilities. In simple terms, it refers to taking care of things. Whether it is about your house, car, or any other equipment that you possess, maintenance plays a vital role in keeping things operational and working efficiently.
The same is true when it comes to industrial equipment or facilities. Maintenance is essential for the smooth running of operations and prolonging the life of assets.Maintenance can be categorized into three different types; preventive, corrective, and predictive maintenance. Preventive maintenance is a strategy for maintaining equipment that is done on a set schedule. This helps to avoid any unscheduled breakdowns and downtime, which can be costly. Corrective maintenance is the type of maintenance done after a failure has occurred.
It includes any repairs and replacement of faulty parts. Predictive maintenance uses data analytics and condition-based monitoring to predict when maintenance will be needed before failure occurs. This type of maintenance is useful in minimizing downtime, increasing efficiency, and reducing repair costs.In conclusion, maintenance is essential in keeping equipment and facilities operational, efficient, and cost-effective. It is a preventative measure that can be done in different ways, depending on the nature of the equipment and facility. Preventive, corrective, and predictive maintenance strategies are all necessary to ensure that operations run smoothly and to minimize downtime.
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Determine numerical values for each of the three mesh currents as labeled in
the circuit diagram of Fig. 4.58.
Answers
The numerical values for the mesh currents that we have in the question are given as:
1i = 0.9892 = 0.9892 amperei2 = 0.1501 amperei3 = 0.1570 ampereHow to solve for the values of the mesh currentWe first have to write the KVL
2 - 1(i₁ - i₂) + 3 - 5(i₁ - i₃) = 0
We have to expand the equation that we have above
2 - i₁ + i₂ + 3 - 5i₁ + 5i₃ = 0
take like terms
-i₁ - 5i₁ i₂ + 5i₃ = 5
= 6i₁ - i₂ - 5i₃ = 5
-1(i₂ - i₁) - 6 i₂ - 9(i₃ - i2) = 0
after expanding we would have
i₁ - 16i₂ + 9i₃ = 0------- equation 2
-5 (i3 - i1) - 3 - 9(i3 - i2) - 7i3 = 0
5i1 + 9i2 - 2i3 = 3 ------ equation 3
From the equations that we have in 1, 2 and 3, we would solve the system of equations to get
1i = 0.9892 = 0.9892 ampere
i2 = 0.1501 ampere
i3 = 0.1570 ampere
These are the mesh current that are in the labeled diagram.
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A steel cylindrical pressure vessel has an inside diameter of 2m and a wall thickness of 2cm. If the steel has a yield stress Y= 425 MPa, calculate the tank pressure that would just cause yielding of the tank material:
Answers
Answer:
The pressure that will cause yielding in the tank in the longitudinal direction is 1.7 Mpa
Explanation:
We are dealing with a thin-walled pressure vessel here.
the formula for calculating the hoops stress of this pressure vessel is \(\sigma =P d/4t\)
\(\sigma Y =\) longitudinal yield stress = \(425 \times 10^{6} Pa\)
Thickness = 2/1000 =0.002m
Outside diameter = inside siameter + thickness = 2m + 0.002m= 2.002m
Dm = Mean diameter = Outside diameter - thickness = 2.002 - 0.002 = 2m
\(P= 425 \times 10^{6} \times 4 \times 0.002 /2=1.7 Mpa\)
A society can rise no higher than the individual values of its citizens. Driving can get no better than the
values of the drivers?
Answers
It is TRUE to state that A society can rise no higher than the individual values of its citizens. Driving can get no better than the values of the drivers.
What is the import of the above statement?The above statement infers that to have better drivers on the road, the government must be intentional about the quality of training and standards imposed on drivers and or would-be drivers.
Thus, the higher the training and standards, the better the quality of driving on our roads, and less vehicular accidents.
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A student lives in an apartment with a floor area of 60 m2 and ceiling height of 1.8 m. The apartment has a fresh (outdoor) air exchange rate of 0.5/hr. The stove in the apartment heats by natural gas. The student cooks a meal using two gas burners that each emit carbon monoxide (CO) at a rate of 100 mg/hr. The outdoor CO concentration can be assumed to be negligible (0 ppm). The initial (time = 0) indoor CO concentration can be assumed to be 0 ppm (except for problem 4). Carbon monoxide can be considered as an inert gas, i.e., it does not stick to or react with any surfaces or other gases in air.
1. Assume that the student cooks for a long enough period of time to achieve a steady-state CO concentration in the apartment. What is that concentration in ppb?
2. Assume that the student cooks for only 45 minutes and turns off both burners at that time. What is the CO concentration in ppb at the end of 45 minutes?
3. Repeat problem 2 for air exchange rates that vary from 0.1 to 1/hr and plot the concentration at 45 minutes (in ppb) versus air exchange rate.
4. Assume that for the conditions of problem 2, the student waits 25 minutes after turning the burners off and then starts cooking again with two burners on. How long will it take to reach a concentration that is 95% of steady-state under this condition?
Note that you can actually address this question with an eloquent mathematical derivation (preferred) or simply by crunching the concentration profile in a spreadsheet.
What is the concentration at 95% of steady-state?
Compare your result with the time that would be required to reach 95% of steady-state had the initial indoor CO concentration been 0 ppm.
Answers
Answer:
4
Explanation:
when there are requirements to the manner and look of a contract, it is considered a(n) _____
Answers
When there are requirements to the form and appearance of a contract, it is considered a formal contract. Formal contracts have specific requirements and must follow certain legal formalities to be valid and enforceable. This may include the presence of witnesses, the signature of all parties involved, and the inclusion of specific clauses and terms.
It is important to note that a formal contract is not always the best option, and that there are situations where an informal contract may be more appropriate. Informal contracts can be equally valid and enforceable, although they may be more difficult to prove in case of disputes or breach.
In general, the choice between a formal or informal contract will depend on the specific circumstances of the agreement and the needs of the parties involved. If it is a complex or high-risk agreement, or if the agreement is expected to be of long duration, it may be more appropriate to opt for a formal contract to ensure greater legal protection.
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What does efficiency measure?
Answers
Answer:
Efficiency is defined as any performance that uses the fewest number of inputs to produce the greatest number of outputs. Simply put, you're efficient if you get more out of less.
Explanation:
Determine the length of welds required to transmit a load 54.5 KN between 12.7mm. thick plates, when the plates are to be joined by 1) Two parallel fillet welds. 2) Two transverse fillet welds.
Answers
For the parallel fillet weld, the length required is 24.52mm and for transverse fillet welds, the longer fillet weld required is 24.39 mm and the length of the shorter fillet weld required is 6.13 mm.
What is the length to transmit the loadThe length of weld required to transmit a load between two plates depends on the type of weld used and the strength of the material being welded. For the given scenario:
Two parallel fillet welds:
The length of each fillet weld required can be calculated using the following formula:
L = (2 x F x P) / (0.7 x T)
where L is the length of each fillet weld, F is the applied force (54.5 KN), P is the perimeter of the weld (2 x length of the joint), T is the thickness of the plate (12.7 mm), and 0.7 is a constant. Substituting the values, we get:
L = (2 x 54.5 x 2) / (0.7 x 12.7) = 24.52 mm
Therefore, the length of each fillet weld required is 24.52 mm.
Two transverse fillet welds:
The length of each fillet weld required in this case can be calculated using the same formula as above, but with the perimeter of the weld being the sum of the lengths of the two sides being welded. Since the two fillet welds are transverse, their lengths will be different. Assuming one fillet weld is longer than the other, we can calculate their lengths as follows:
L1 = (F x P1) / (0.7 x T)
L2 = (F x P2) / (0.7 x T)
where L1 and L2 are the lengths of the two fillet welds, P1 and P2 are the perimeters of the two sides being welded, and all other variables are the same as before. We can assume that the longer fillet weld is on the side with the higher applied force, so we have:
P1 = 2 x length of joint
P2 = length of joint
Substituting the values, we get:
L1 = (54.5 x 2 x 2) / (0.7 x 12.7) = 24.39 mm
L2 = (54.5 x 1) / (0.7 x 12.7) = 6.13 mm
Therefore, the length of the longer fillet weld required is 24.39 mm and the length of the shorter fillet weld required is 6.13 mm.
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URGENT NEED HELP BY AN HOUR
C++ ONLY
Given a line of text as input: (1) output the number of characters excluding the three characters commonly used for end-of-sentence punctuation( period, exclamation point, and question mark), (2) then output the number of end-of-sentence punctuation characters that were found. You can just do (1) to pass the first few test cases for partial credit, then do (2) for full credit.
Ex: If the input is "Listen, Sam! Calm down. Please.", the output is:
28
3
Ex: If the input is "What time is it? Time to get a watch! O.K., bye now.", the output is:
43
5
Answers
Using the knowledge in computational language in python it is possible to write a code that output the number of characters excluding the three characters commonly used for end-of-sentence punctuation.
Writting the code:import re
def check_sentence(text):
result = re.search(r"^[A-Z][A-Za-z\s]*[\.\?!]$", text)
return result != None
print(check_sentence("Is this is a sentence?")) # True
print(check_sentence("is this is a sentence?")) # False
print(check_sentence("Hello")) # False
print(check_sentence("1-2-3-GO!")) # False
print(check_sentence("A star is born.")) # True
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Which sentence from the passage uses passive voice?
Question 9 options:
a)
E-books also make reading easier for people with disabilities. (paragraph 12)
b)
M.K. sees it another way. (paragraph 16)
c)
In one year, e-reader production released 2350 million kilograms of carbon dioxide into the atmosphere. (paragraph 8)
d)
The Diamond Sutra was printed in China in 868 AD. (p
Answers
Answer:
"The Diamond Sutra was printed in China in 868 AD." (paragraph 4)
Explanation:
I took the test
Air is kept in a tank at pressure Po = 689 KPa abs and temperature To = 17°C. If one allows the air to issue out in a one-dimensional isentropic flow, the flow per unit area at the exit of the nozzle where P = 101.325 KPa is ____ kg/m²-s. For air, Use R = 287 J/kg-K and Mol. Wt. = 29.1 *Express your answers in whole significant figure without decimal value and without unit*
Answers
Given conditions are,Initial pressure of the tank, Po = 689 KPa Temperature of the tank, To = 17°C Pressure at nozzle exit, P = 101.325 KPa Molecular weight of air, Mol. Wt. = 29.1 Gas constant, R = 287 J/kg-K We have to calculate the flow per unit area at the exit of the nozzle where P = 101.325 KPa.
As the flow process is isentropic, the equation for the isentropic flow is given as,Where, A1 is the cross-sectional area of the tank opening (m²), and A2 is the cross-sectional area of the nozzle exit (m²).By simplifying the equation, we getρ1A1V1 = ρ2A2V2ρ1 = density of air in the tank = P1/RT1ρ2 = density of air in the nozzle exit = P2/RT2T1 = To + 273 = 290 K (temperature of the tank)T2 = T1 (isentropic flow)∴
\(ρ1/ρ2 = T2/T1P1V1 = P2V2\)(from the equation of state for isentropic flow)∴ \(V2/V1 = (P1/P2)^(1/γ)\)
Here,γ = cp/cv = 1.4 (for air)P1 = Po = 689 KPa (pressure in the tank)P2 = P = 101.325 KPa (pressure at the nozzle exit)
\(∴ V2/V1 = (689/101.325)^(1/1.4) = 2.1628\)As mass flow rate, dm/dt = ρ A V (from the continuity equation)∴ \(dm/dt = ρ1 A1 V1 = ρ2 A2 V2ρ1 = P1/RT1 = 689000/(287 × 290) = 85.615 kg/m³\\∴ dm/dt = ρ1 A1 V1 = 85.615 × 1 × 2.1628 = 185.101 kg/m²-s\)Therefore, the flow per unit area at the exit of the nozzle where P = 101.325 KPa is 185 kg/m²-s (approximately).Thus, the required answer is 185.
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Hey guys can anyone list chemical engineering advancement that has been discovered within the past 20 years
Answers
Nanopesticides. The world population keeps growing. ...
Enantio selective organocatalysis. ...
Solid-state batteries. ...
Flow Chemistry. ...
Porous material for Water Harvesting. ...
Directed evolution of selective enzymes. ...
From plastics to monomers. ...
3. Give an example of a visual or graphic representation of information that has
more impact than an explanation of the information in text.
Answers
An example of a visual or graphic representation of information that has more impact than an explanation of the information in text is a pie chart (graph).
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
The types of graph.In Science, there are different types of graph and these include the following:
Scatter plotBar graphPie chartDot graphLine graphHistogramWhat is a pie chart?A pie chart can be defined as a type of graph that is typically used for the graphical representation of the relationship between each part (unit) to a whole, especially by dividing a circle into various sectors.
In this context, we can reasonably infer and logically deduce that an example of a visual or graphic representation of information that has more impact than an explanation of the information in text is a pie chart (graph).
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Most of the work that engineers do with fluids occurs in nature. True False
Answers
Answer:
It's False
Explanation:
I did the assignment