Answer:
If the graph is sparse.
When the graph has a large number of vertices but only a small number of edges, the adjacency matrix representation can still be efficient in terms of memory and lookup times. The space complexity of an adjacency matrix is O(n^2), where n is the number of vertices. Therefore, if the graph is sparse, it means that a significant amount of memory is being wasted on representing non-existent edges in a matrix. In such cases, an adjacency list would be a better choice since it only represents actual edges, saving a lot of memory.
Explanation:
When you park on a hill,the direction your __are pointed determines which direction your car will roll if the breaks fail
Answer:
Tires or wheels? I think this is the answer. ^_^
Explanation:
John plans to deposit $1000 at the end of next year into an account that earns 10% year. Further, he estimates that his deposits will increase by $100 per year for only 10 years thereafter, then cease. The closest equivalent present worth is: less than $8,000 between $8,000−8,300 Between $8,300−$8,600 Higher than $8,600
The closest equivalent present worth of John's deposits is less than $8,000.
To determine the closest equivalent present worth of John's deposits, we need to calculate the present value of the cash flows he will make.
The deposit of $1000 at the end of the next year can be considered a future value (FV). We need to calculate its present value (PV) using the formula:
PV = FV / (1 + r)^n
Where:
FV = $1000
r = interest rate = 10% = 0.10
n = number of years = 1
PV = $1000 / (1 + 0.10)^1 = $909.09
Next, we calculate the present value of the increasing deposits of $100 per year for 10 years. These cash flows form an arithmetic progression with a common difference of $100.
Using the formula for the sum of an arithmetic progression, we can find the present value of these cash flows:
PV = (n/2) * (2a + (n-1)d)
Where:
n = number of terms = 10
a = first term = $100
d = common difference = $100
PV = (10/2) * (2*100 + (10-1)*100) = 5 * (200 + 9 * 100) = $5,500
Now, we can sum up the present values of both cash flows:
PV = $909.09 + $5,500 = $6,409.09
The closest equivalent present worth is between $8,000 - $8,300. Since the calculated present value is lower than $8,000, the closest equivalent present worth is less than $8,000.
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Underground water is to be pumped by a 78% efficient 5- kW submerged pump to a pool whose free surface is 30 m above the underground water level. The diameter of the pipe is 7 cm on the intake side and 5 cm on the discharge side. Determine (a) the maximum flow rate of water (5-point) and (b) the pressure difference across the pump (5-point). Assume the elevation difference between the pump inlet and the outlet and the effect of the kinetic energy correction factors to be negligible
Answer:
a) The maximum flowrate of the pump is approximately 13,305.22 cm³/s
b) The pressure difference across the pump is approximately 293.118 kPa
Explanation:
The efficiency of the pump = 78%
The power of the pump = 5 -kW
The height of the pool above the underground water, h = 30 m
The diameter of the pipe on the intake side = 7 cm
The diameter of the pipe on the discharge side = 5 cm
a) The maximum flowrate of the pump is given as follows;
\(P = \dfrac{Q \cdot \rho \cdot g\cdot h}{\eta_t}\)
Where;
P = The power of the pump
Q = The flowrate of the pump
ρ = The density of the fluid = 997 kg/m³
h = The head of the pump = 30 m
g = The acceleration due to gravity ≈ 9.8 m/s²
\(\eta_t\) = The efficiency of the pump = 78%
\(\therefore Q_{max} = \dfrac{P \cdot \eta_t}{\rho \cdot g\cdot h}\)
\(Q_{max}\) = 5,000 × 0.78/(997 × 9.8 × 30) ≈ 0.0133 m³/s
The maximum flowrate of the pump \(Q_{max}\) ≈ 0.013305 m³/s = 13,305.22 cm³/s
b) The pressure difference across the pump, ΔP = ρ·g·h
∴ ΔP = 997 kg/m³ × 9.8 m/s² × 30 m = 293.118 kPa
The pressure difference across the pump, ΔP ≈ 293.118 kPa
Bi servers use ________ to determine what results to send to which users and on which schedule.
Bi servers use matadata to determine what results to send to which users and on which schedule.
Metadata, also known as data that describes other data, is organized reference material that aids in classifying and identifying characteristics of the data it describes. John W. Warren refers to metadata as "both a cosmos and DNA" in Zen and the Art of Metadata Maintenance.
In most applications of information technology, the prefix "meta" denotes "an underlying definition or description." Basic data information is summarized in metadata, which can make it simpler to locate, utilize, and reuse specific instances of data.
Simple document file metadata includes things like author, date created, date edited, and file size. Finding a given document is made considerably simpler when one has the option to search for a specific aspect (or elements) of that metadata.
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which of the following is the correct formula for the unweighted center of gravity method for evaluating location alternatives?
X-bar = sigma(Xi) / n, Y-bar = sigma(Yi) / n.
A center de gravity method is what?The center of gravity approach is a way to choose a distribution center where the cost of distribution is kept to a minimum.It is a technique for locating a facility such that transportation expenses or transit time to different locations are kept to a minimum.Clustering is the term used to describe when businesses locate close to other comparable businesses.
How is the centre of gravity is the point determined?The gravity center is determined by adding the weight/volume average value times this same distance times that volume segment multiplied by the weight.
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If it is an animal then it is an organism convert it in first order logic
Answer:
This is not an engineering question.
Explanation:
A mass of 5 kg of saturated liquid-vapor mixture of water is contained in a piston-cylinder device at 125 kPa. Initially, 2 kg of the water is in the liquid phase and the rest is in the vapor phase. Heat is now transferred to the water, and the piston, which is resting on a set of stops, starts moving when the pressure inside reaches 300 kPa. Heat transfer continues until the total volume increases by 20 percent.
Determine:
(a) the initial and final temperatures,
(b) the mass of liquid water when the piston first start moving
a) The initial and final temprature are 99.61°C and T3 = 259.07°C
b) The mass of liquid water when the piston first start moving is 0g
Using the data provided:
Initial Pressure = P1 = 125kPa
Mass of Saturated Vapor Liquid = m = 5kg
Initial Mass of Liquid water = mf = 2kg
Initial Mass of Vapor = mg = 3kg
The temperature for a mixture of liquid steam saturated with water according to the thermodynamic table is:
T₁ = 99.61°C
The specific volume is:
vf = 0.001043m³/kg
And the saturated volume is:
vg = 1.6941m³/kg
Therefore, the volume in state 1 will be equal to:
V1 = mfvf + mgvg
V1 = (2kg)(0.001043m³/kg) + (3kg)(1.6941m³/kg)
V1 = 5.084m³
In state 3 then the volume will be equal to:
V3 = 1.2V1
V3 = 1.2(5.084m³)
V3 = 6.1008m³
Then the specific volume will be equal to:
v3 = V₃/m
v3 = 6.1008m³/5kg
v3 = 1.2202m³/kg
For a pressure of 300 kPa and the previous specific volume found through the thermodynamic table, the value of the temperature is:
T3 = 259.07°C
Question b) When the piston first stats moving at P₂ = 300kPa and V₂ = V₁ = 5.084m³
v₂ =V₂/m
v₂ = 5.084m³/5kg
v2 = 1.0168m³/kg
While at 300 kPa the value of the vapor saturated vg = 0.88578m³/kg This implies that the condition is met:
v2 > vg
Therefore, no liquid is there in-cylinder when piston stats moving, mf = 0kg
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Instructions Create an app using a math solver to solve a type of math question using Java. Create an application with a GUI to perform one small, useful task for any type of math question. be You will create a develop the software, documentation, Junit testing, and training material, and close the project.
Checklist:
Software attached (zip your whole project and attach a jar file)
Documentation
Junit testing
Training material (how to file or help file)
and close the project (attach updated Gantt chart).
In the software development life cycle (SDLC), software development is the first step. It includes software design, software implementation, testing, and documentation. Java is a common programming language for developing software since it is object-oriented, platform-independent, and stable.
A math solver can solve a wide range of math problems using Java. Here are the instructions to create an app using a math solver to solve a type of math question using Java:
Step 1: Select a Math Problem There are a variety of math problems that you may solve with a math solver.
In this step, you must choose a math problem to solve with a math solver. Make sure that the math problem you've chosen is difficult enough to demonstrate the effectiveness of the math solver.
Step 2: Create a GUI Application for the Math Solver In this phase, you'll need to create a GUI application that can receive input data from the user and pass it to the math solver
. Furthermore, the GUI application should be able to display the outcomes of the math solver.
Step 3: Develop the Software In this stage, you'll need to create the math solver using Java.
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Because tires do not come perfectly round and balanced, most tire manufacturers indicate
the tire's highest point with a dot and the tire's lightest point with a dot.
I'm not sure if this is a question to answer or...I dont know lol. Sorry if I couldn't answer this but yeah-
the importance of reading a circuit diagram to interpret a wiring diagram?
Answer:
The ability to read electrical schematics is a really useful skill to have. To start developing your schematic reading abilities, it's important to memorize the most common schematic symbols. ... You should also be able to get a rough idea of how the circuit works, just by looking at the schematic.
Explanation:
Plumbing
The should indicate the materials, fixtures, and faucets to be
used.
A. specifications
B. plumbing code
C. mechanical code
D. plumbing instructor
Answer:
B....................
Which company produces comprehensive patch management software?
Quest
Motorola
Apple
Sony
Fluid flows past the two-dimensional bar shown. The pressures on the ends of the bar are as shown and the average shear stress on the top and bottom of the bar is avg. The drag due to pressure is equal to viscous effects width = h 】Oh Determine (a) ravg in terms of the dynamic pressure pu2 (Ans:Tavg 0.06 pu2) (b) the drag coefficient of the bar. (Ans: CD = 2.40)
The average shear stress, Tavg, is equal to 0.06 pu2., Solving for the drag coefficient of the bar, CD, yields: 2.40.
What is shear stress?
An object experiences deformation whenever an external force acts upon it. if the force's direction is parallel to the object's plane. Along that plane, there will be a deformation. The object in this instance is under shear or tangential stress. It happens so when force vector components that are perpendicular to the material's cross-sectional area. The force vectors for normal/longitudinal stress will be parallel to the cross-sectional area that it affects.
(a) The average shear stress, Tavg, is equal to the dynamic pressure pu2 divided by the width of the bar, h. Therefore,
Tavg = pu2/h
Rearranging for the dynamic pressure pu2 yields:
pu2 = Tavg h
Substituting the given value of Tavg as 0.06 pu2 gives:
pu2 = 0.06 pu2 x h
Solving for h yields:
h = pu2/0.06 pu2
Therefore, the average shear stress, Tavg, is equal to 0.06 pu2.
(b) The drag coefficient of the bar, CD, is equal to the drag force (Fd) divided by the dynamic pressure (pu2) times the area (A) of the bar. Therefore,
CD = Fd/(pu2 x A)
Rearranging for Fd yields:
Fd = CD x pu2 x A
Substituting the given values for CD, pu2, and A gives:
Fd = 2.40 x pu2 x (h x L)
Solving for the drag coefficient of the bar, CD, yields:
CD = Fd/(pu2 x A) = 2.40
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Which workplaces are common to both the Engineering and Technology pathway and the Science and Math pathway?
a) laboratories and ships
b) parks and radio stations
c) construction sites and zoos
d) offices and weather stations
The common workplace for both science and math pathways, with engineering and technology in laboratories and ships. Thus, option A is correct.
What is a workplace?A workplace is given as the location or the place at which the employee are performing their jobs and tasks.
The science or technology-mediated employees are related to research where they perform the tests in laboratories, as well as the ships are the location for the engineering and the math candidates for the analysis of the studies and to perform the job.
Hence, the location in the workplace common for both engineering and technology candidates has been the laboratories and the ships. Thus, option A is correct.
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______________ measures how well a window allows heat from the sunlight
Solar heat gain coefficient (SHGC) measures how well a window allows heat from the sunlight to pass through it.
The solar heat gain coefficient (SHGC) is a value that represents the amount of solar radiation, in the form of heat, that can pass through a window or glazing system. It measures the ability of the window to transmit solar energy from the sunlight into the interior space. A higher SHGC indicates that the window allows more solar heat to pass through, which can contribute to increased solar heat gain and potentially higher cooling loads. On the other hand, a lower SHGC indicates that the window has better heat-blocking properties, reducing the amount of solar heat entering the building and potentially lowering cooling needs. The SHGC is an important factor to consider when selecting windows for energy efficiency and managing indoor thermal comfort.
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1. Describe an occasion in which an explanatory sketch would be used.
the end user how
Answer:
building a bridge
Explanation:
you would have to sketch ideas to see what the bridge would look like and you need to know what to add to it to enhance the percentage of it working. if you sketch it you would have an idea of the process also
Building a bridge is an occasion in which an explanatory sketch would be used.
What is meant by explanatory sketch ?Sketches of explanations are created to demonstrate form, structure, and function. They accurately and objectively communicate a design, placing more emphasis on explanation than pitch. Outside of the design team, explanation sketches must be understandable.
Exploratory sketches, often referred to as thinking drawings, are a type of personal communication that frequently serve as the starting point for brand-new product concepts.
During a brainstorming session or for personal usage in a design notebook, these quick sketches are meant to quickly capture ideas. Exploratory research aims to study the important aspects of a topic that hasn't gotten much attention.
Thus, it is Building a bridge.
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NatGas Corporation obtains a federal license to operate a gas pipeline through a certain area of Oregon. The Oregon state legislature enacts a law that bans gas pipelines in that area. Most likely, the state law violates:________
a. the due process clause.
b. the supremacy clause.
c. the U.S. Constitution.
d. the commerce clause.
Answer:
c. the U.S. Constitution.
Explanation:
A Constitution refers to a set of written laws and principles which is typically used to determine the power and authority of the government, as well as guarantee the fundamental rights of its citizens.
Basically, the Constitution accords powers to the national or federal government and these includes; enumerated or delegated, reflected, and concurrent powers. Therefore, base on the US Constitution, any law, act, or license issued and approved by the federal government supercedes or overrides any state law.
In this scenario, NatGas Corporation obtains a federal license to operate a gas pipeline through a certain area of Oregon. The Oregon state legislature enacts a law that bans gas pipelines in that area. Most likely, the state law violates the U.S. Constitution because a federal law is supreme.
A digital filter is given by the following difference equationy[n] = x[n] − x[n − 2] −1/4y[n − 2].(a) Find the transfer function of the filter.(b) Find the poles and zeros of the filter and sketch them in the z-plane.(c) Is the filter stable? Justify your answer based on the pole-zero plot.(d) Determine the filter type (i.e. HP, LP, BP or BS) based on the pole-zeroplot.
Answer:
\(y(z) = x(z) - x(z) {z}^{ - 2} - \frac{1}{4} y(z) {z}^{ - 2} \\ y(z) + \frac{1}{4} y(z) {z}^{ - 2} = x(z) - x(z) {z}^{ - 2} \\ y(z) (1 + \frac{1}{4}{z}^{ - 2}) = x(z)(1 - {z}^{ - 2}) \\ h(z) = \frac{y(z)}{x(z)} = \frac{(1 + \frac{1}{4}{z}^{ - 2})}{(1 - {z}^{ - 2})} \)
The rest is straightforward...
for a 10-ton-capacity refrigeration system, the pressure of refrigerant in the evaporator is 210 kpa, whereas in the condenser it is 750 kpa. if ammonia (r-717) is used under saturated conditions, calculate the theoretical power required to operate the compressor.
To calculate the theoretical power required to operate the compressor in a 10-ton-capacity refrigeration system using ammonia (r-717) under saturated conditions, we can use the following formula:Power = mass flow rate x specific enthalpy changeFirst, we need to determine the mass flow rate of the refrigerant. We can do this using the following formula:
Mass flow rate = refrigeration capacity / (specific enthalpy change x refrigerant density)
Since the refrigeration capacity is given as 10 tons, we need to convert this to kilowatts (kW) by multiplying by 3.517:
Refrigeration capacity = 10 tons x 3.517 kW/ton = 35.17 kW
Next, we need to determine the specific enthalpy change of the refrigerant. This can be found by subtracting the specific enthalpy of the refrigerant in the evaporator from the specific enthalpy of the refrigerant in the cSpecific enthalpy change = h2 - h1
To find the specific enthalpies, we can use a refrigerant table. For ammonia (r-717) at 210 kPa, the specific enthalpy in the evaporator (h1) is 349.7 kJ/kg, and at 750 kPa, the specific enthalpy in the condenser (h2) is 400.8 kJ/kg.Substituting these values into the formula, we get:Specific enthalpy change = 400.8 - 349.7 = 51.1 kJ/kg
Finally, we need to determine the refrigerant density. At 210 kPa, the density of ammonia (r-717) under saturated conditions is 480 kg/m³.Substituting all of these values into the mass flow rate formula, we get:
Mass flow rate = 35.17 kW / (51.1 kJ/kg x 480 kg/m³) = 1.007 kg/s
Now we can use the power formula to calculate the theoretical power required to operate the compressor:Power = 1.007 kg/s x 51.1 kJ/kg = 51.48 kWTherefore, the theoretical power required to operate the compressor in a 10-ton-capacity refrigeration system using ammonia (r-717) under saturated conditions is approximately 51.48 kW.
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create a visual studio console application create a class called fruit create two properties to store the values from weight and color create a constructor that takes 2 parameters int weight and string color set these two values on the properties create a method that prints the weight and the color of the fruit you are free to create more methods as you see fit. it's up to you on your main program instantiate 3 objects of the fruit class the first object will have color red and weight 10 for the second object, you can freely choose any color an any weight there's no right/wrong choices for each of the objects you created, call the print method
A visual studio console application create a class will be:
using System;
public class Fruit
{
int weight;
string color;
public Fruit(int weight, string color)
{
this.weight = weight;
this.color = color;
}
public void PrintFruit()
{
Console.WriteLine($"Weight: {weight}, Color: {color}");
}
}
class Program
{
static void Main(string[] args)
{
Fruit fruit1 = new Fruit(10, "red");
Fruit fruit2 = new Fruit(12, "green");
Fruit fruit3 = new Fruit(14, "blue");
fruit1.PrintFruit();
fruit2.PrintFruit();
fruit3.PrintFruit();
}
}
What is visual studio?
Visual Studio is a suite of development tools for creating software applications. It is developed and published by Microsoft and is the current version of their Visual Studio product line. Visual Studio provides a comprehensive set of tools and services for developing, debugging, and testing applications for various platforms, including Windows, the web, and cloud. It also supports various programming languages such as C# and Visual Basic.
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What can you determine about the feasibility of a reaction if the enthalpy is positive and the entropy is negative?.
The right answer is B. The reaction will never be possible since the Gibbs energy will always be positive.
Gibbs free energy, G, enthalpy, H, and entropy, S are related as follows:
ΔG = ΔH - TΔS
We will always have a positive value for the Gibbs free energy if enthalpy is positive and entropy is negative.
This means that choice B is the best one. A reaction will always be possible if it is exothermic (H is negative), has a positive entropy change (S is positive), and G is always negative. The sign of G determines whether a response (or other physical change) is possible. The reaction cannot take place if G is positive.
The complete question is- What can you determine about the feasibility of a reaction if the enthalpy is positive and the entropy is positive?
A. The Gibbs energy will always be positive, and the reaction will never be feasible.
B. The Gibbs energy will always be negative, and the reaction will always be feasible.
OC. The reaction could be feasible above a certain temperature.
D. The reaction will usually occur because it is unlikely the entropy will be greater than the enthalpy.
Reset Selection
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computer system analyst advantage
Answer:
They help an organization realize the maximum benefit from its investment in equipment, personnel, and business processes. They use and analyze systems, interpret data, and customize systems to better meet the organization's needs.
Explanation:
brainliest plz
Answer:
ục tiêu của pháp y máy tính là kiểm tra phương tiện kỹ thuật số theo cách thức pháp y với mục đích xác định, bảo tồn, phục hồi, phân tích và trình bày các sự kiện và ý kiến về thông tin kỹ thuật số
Explanation:
An automobile travels along a straight road at 15.65 m/s through a 11.18 m/s speed zone. A police car observed the automobile. At the instant that the two vehicles are abreast of each other, the police car starts to pursue the automobile at a constant acceleration of 1.96 m/s2. The motorist noticed the police car in his rear view mirror 12 s after the police car started the pursuit and applied his brakes and decelerates at 3.05 m/s2. (Hint: The police will not go against the law.) a) Find the total time required for the police car to overtake the automobile. (12 marks) b) Find the total distance travelled by the police car while overtaking the automobile. (2 marks) c) Find the speed of the police car at the time it overtakes the automobile
Answer:
A.) Time = 17.13 seconds
B.) Distance = 31.9 m
C.) V = 11.18 m/s
D.) V = 7.1 m/s
Explanation:
The initial velocity U of the automobile is 15.65 m/s.
At the instant that the two vehicles are abreast of each other, the police car starts to pursue the automobile with initial velocity U = 0 at a constant acceleration of 1.96 m/s². Because the police is starting from rest.
For the automobile, let us use first equation of motion
V = U - at.
Acceleration a is negative since it is decelerating with a = 3.05 m/s² . And
V = 0.
Substitute U and a into the formula
0 = 15.65 - 3.05t
15.65 = 3.05t
t = 15.65/3.05
t = 5.13 seconds
But the motorist noticed the police car in his rear view mirror 12 s after the police car started the pursuit and applied his brakes and decelerates at 3.05 m/s².
The total time required for the police car to overtake the automobile will be
12 + 5.13 = 17.13 seconds.
b.) Using the third equation of motion formula for the police car at V = 11.18 m/s and a = 1.96 m/s²
V^2 = U^2 + 2aS
Where S = distance travelled.
Substitute V and a into the formula
11.18^2 = 0 + 2 × 1.96 ×S
124.99 = 3.92S
S = 124.99/3.92
S = 31.88 m
c.) The speed of the police car at the time it overtakes the automobile will be in line with the speed zone which is 11.18 m/s
d.) That will be the final velocity V of the automobile car.
We will use third equation of motion to solve that.
V^2 = U^2 + 2as
V^2 = 15.65^2 - 2 × 3.05 × 31.88
V^2 = 244.9225 - 194.468
V = sqrt( 50.4545)
V = 7.1 m/s
Which tool is used to protect a hose line that is being hoisted over a sharp edge?
Answer:
A hose roller
Explanation:
On a typical 120 volt circuit in your home, you may have a 15 ampere fuse or circuit breaker. What is the maximum power (watts) that this circuit can handle? How many 10 Watt light bulbs could you turn on without blowing the fuse?
Answer:
Maximum power is
P = V × I
P = 120 × 15
P = 1800 watt
Please help with these circuit questions
A 2 in. sch 40 pipe carries an oil at 50°F (SG = 0.85, μ= 15 cP). The flow rate is measured by an orifice meter, which has a diameter of 1.5 in. The pressure drop across the orifice plate is measured by a water manometer connected to flange taps.
To calculate the flow rate of the oil through the 2-inch schedule 40 pipe using an orifice meter and a water manometer, we need to apply the principles of fluid mechanics and orifice meter equations.
Pipe diameter (D) = 2 inches
Pipe schedule (sch) = 40
Oil temperature (T) = 50°F
Specific gravity of oil (SG) = 0.85
Viscosity of oil (μ) = 15 cP
Orifice diameter (d) = 1.5 inches
First, we need to convert the units of diameter and temperature to a consistent system. Let's use SI units (meters and Kelvin) for calculations.
1 inch = 0.0254 meters
2 inches = 2 * 0.0254 meters = 0.0508 meters
1.5 inches = 1.5 * 0.0254 meters = 0.0381 meters
50°F = (50 - 32) × 5/9 = 10°C = 283.15 K
Now, we can calculate the flow rate using the orifice meter equation:
Q = Cd * A * sqrt(2 * ΔP / ρ)
Where:
Q = Flow rate
Cd = Discharge coefficient (depends on the orifice plate design, typically around 0.6-0.8)
A = Cross-sectional area of the orifice (π * (d/2)^2)
ΔP = Pressure drop across the orifice
ρ = Density of the fluid
First, let's calculate the density of the oil:
ρ = SG * ρwater (ρwater = 1000 kg/m^3)
ρ = 0.85 * 1000 kg/m^3 = 850 kg/m^3
Next, let's calculate the cross-sectional area of the orifice:
A = π * (d/2)^2 = π * (0.0381/2)^2
A = 0.0011375 m^2
We need the pressure drop across the orifice to calculate the flow rate. The pressure drop can be measured by the water manometer. However, the details about the specific water manometer setup are not provided in the question. We need the height difference or pressure difference measured by the water manometer to proceed further. Please provide the necessary information regarding the water manometer setup or the pressure difference so that we can calculate the flow rate accurately.
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A pool of contaminated water is lined with a 40 cm thick containment barrier. The contaminant in the pit has a concentration of 1.5 mol/L, while the groundwater circulating around the pit flows fast enough that the contaminate concentration remains 0. There is initially no contaminant in the barrier material at the time of installation. The governing second order, partial differential equation for diffusion of the contaminant through the barrier is: dC
This question is incomplete, the complete question is;
A pool of contaminated water is lined with a 40 cm thick containment barrier. The contaminant in the pit has a concentration of 1.5 mol/L, while the groundwater circulating around the pit flows fast enough that the contaminate concentration remains 0. There is initially no contaminant in the barrier material at the time of installation. The governing second order, partial differential equation for diffusion of the contaminant through the barrier is:
dC/dt = D( d²C / dz²)
where c(z,t) represent the concentration of containment of any depth into the barrier at anytime and D is the diffusion coefficient (a constant) for the containment in the barrier material.
a) write all boundary and initial conditions needed to solve this equation for C(z, t)
b) Find the steady state solution (infinite time) for C(z)
Answer:
a) At t = 0, z= 0, c = 1.5 mol/L
at t =0, z = 0.4m, c = 0 mol/L
b) C(z) = z² - 4.15z + 1.5
Explanation:
a)
The boundary and initial conditions are as follows
At t = 0, z= 0, c = 1.5 mol/L
at t =0, z = 0.4m, c = 0 mol/L
b)
The governing second order, partial differential equation for diffusion of the contaminant through the barrier is :
(dC/dt) = D*(d²C/dz²) ..............equ(1)
For steady state, above equation becomes,
(d²C/dz²) =0
Integrating above equation,
(dC/dz) = Z + C1 { where C1 is integration constant) }
again integrating above equation,
C = z² + C1*z + C2 ...................equ(2)
applying boundary condition : at t =0, z= 0, c = 1.5 mol/L, to above equation
C = z² + C1*z + C2
1.5 = 0 + 0*0 + c2
C2 = 1.5
applying boundary condition : at t =0, z= 0.4m, c = 0 mol/L, to equation (2) ,
0 = 0.4² + C1*0.4 + 1.5
0 = 0.16 + 0.4C1 + 1.5
0.4C1 = - 1.66
C1 = -1.66/0.4
C1 = -4.15
So, the steady state solution for C(z) is:
C(z) = z² - 4.15z + 1.5
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Answer:
C. WordArt
Explanation:
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