A split-phase AC induction motor is a type of single-phase motor that utilizes two windings, a main or running winding and an auxiliary or starting winding, to create a rotating magnetic field.
The main winding is designed to carry the majority of the motor's current and is responsible for producing the majority of the motor's torque. The auxiliary winding, on the other hand, is only used during the starting period to provide additional starting torque. During the starting period, a capacitor is connected in series with the auxiliary winding. The capacitor creates a phase shift between the currents in the main and auxiliary windings, resulting in a rotating magnetic field. This rotating magnetic field causes the rotor to start rotating.
At the instant of starting, the main and auxiliary winding currents are not in quadrature (90 degrees apart) due to the presence of the starting capacitor. However, as the motor speeds up, the relative speed between the main and auxiliary windings decreases, and the current in the auxiliary winding decreases. At a certain speed called the split-phase speed, the auxiliary winding current becomes negligible, and the motor runs solely on the main winding. The speed-torque characteristics of a split-phase motor are such that it has high starting torque but relatively low running torque compared to other types of motors.
Learn more about induction motors here:
https://brainly.com/question/32808730
#SPJ11
What is the relationship between green building and self-interest? (Select all that apply.)
Green building is burdensome but has advantages in terms of public image.
Green building should be considered when necessary resources are in short supply.
Green building practices can lead to planning and budget efficiencies in general.
Green building is attractive because of its long-term growth potential as a market.
The relationship between green building and self-interest include the following:
Green building is burdensome but has advantages in terms of public imageGreen building is attractive because of its long-term growth potential as a market.What is Green building?This is the process of reducing the environmental impact of buildings. This therefore leads to enhancement of the health of people.
Its relationship with self interest can seen listed above as the most appropriate choice.
Read more about Green building here https://brainly.com/question/9779427
#SPJ1
What is a transition? A. An animation that happens on a single slide B. An outline format that uses roman numerals C. An image file imported to a title slide D. An effect that happens between slides Please select the best answer from the choices provided A B C D
Answer:
its c
Explanation:
which of the following correctly describes a type of data mart? more than one answer may be correct.
Sometimes necessary, dependent data marts take data from a data warehouse. Data from a data warehouse and various gathering systems are combined in hybrid data marts.
Hybrid data warehouse: What is it?Businesses may combine the strength of cloud storage with their present on-premise data systems in a hybrid data warehouse, as the name suggests. With a hybrid platform, companies can take advantage of the newest innovations and improve efficiency without having to lose the money they have already invested in their present installations.
What drawbacks does the hybrid database model have?There are a few difficulties in creating a hybrid model, such as the absence of a single access point for several heterogeneous databases. The second need is that programmers master several query languages.
To know more about Hybrid data marts visit:
https://brainly.com/question/25885061
#SPJ4
When a licensed engineer or land surveyor testifies as an expert in an iowa court, the licensee's testimony cannot be challenged by the opposing attorney
In Iowa courts, the testimony of a licensed engineer or land surveyor, when presented as an expert witness, can be challenged by the opposing attorney.
The opposing attorney has the right to cross-examine the expert witness and challenge their testimony through questioning and presenting counterarguments or conflicting evidence. This is a fundamental aspect of the legal process that allows for the exploration of different perspectives and the evaluation of the credibility and accuracy of expert testimony. By challenging the testimony, the opposing attorney aims to test the expert's qualifications, methods, reasoning, and conclusions to present a comprehensive and well-rounded view to the court. It is through the adversarial process that the court can weigh the evidence and make an informed decision. Therefore, in Iowa courts, the testimony of a licensed engineer or land surveyor, like any other expert witness, can be subject to challenge by the opposing attorney.
Learn more about engineer here
https://brainly.com/question/28717367
#SPJ11
If the unit sales price is $10 and variable costs are $6, how many units have to be sold to earn a profit of $2,400 if fixed costs equal $6,000
The contribution margin per unit is the selling price per unit minus the variable cost per unit. In this case , it would be:Contribution margin per unit = Selling price per unit - Variable cost per unit= $10 - $6 = $4
Next, we can calculate the breakeven point in units using the following formula:Breakeven point (in units) = Fixed costs / Contribution margin per unitGiven that the fixed costs are $6,000 and the contribution margin per unit is $4, we can calculate the breakeven point: Breakeven point (in units) = $6,000 / $4 = 1,500 unitsTherefore, to earn a profit of $2,400, the number of units that need to be sold would be the breakeven point plus the desired profit: Total units sold = Breakeven point + Desired profit = 1,500 + ($2,400 / $4) = 1,500 + 600 = 2,100 units variable Therefore, 2,100 units would need to be sold to earn a profit of $2,400 with a unit sales price of $10, costs of $6, and fixed costs of $6,000.
learn more about contribution here :
https://brainly.com/question/31546435
#SPJ11
State kirchoffs laws
Explanation:
Kirchhoffs Voltage Law or KVL, states that “in any closed loop network, the total voltage around the loop is equal to the sum of all the voltage drops within the same loop” which is also equal to zero. In other words the algebraic sum of all voltages within the loop must be equal to zero.
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASEWhich 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.”
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.
Read more on machine learning here: brainly.com/question/25523571
#SPJ1
Re armature of a 4 pole DC generator is required to generate an emf of 520v on open circuit when revolving at a speed of 660rpm. Calculate the magnetic flux per pole required if the armature has 144 slots with 2 coil sides per slot each coil consisting of 3 turns. The armature is wave wound.
Since the armature is wave wound, the magnetic flux per pole is 0.0274 Weber.
Given the following data:
Emf = 520 VoltsSpeed = 660 r.p.mNumber of armature conductors = 144 slotsNumber of poles = 4 polesNumber of parallel paths = 2To find the magnetic flux per pole:
Mathematically, the emf generated by a DC generator is given by the formula;
\(E = \frac{\theta ZN}{60}\) × \(\frac{P}{A}\)
Where:
E is the electromotive force in the DC generator.Z is the total number of armature conductors.N is the speed or armature rotation in r.p.m.P is the number of poles.A is the number of parallel paths in armature.Ф is the magnetic flux.First of all, we would determine the total number of armature conductors:
\(Z = 144\) × \(2\) × \(3\)
Z = 864
Substituting the given parameters into the formula, we have;
\(520 = \frac{\theta (864)(660)}{60}\) × \(\frac{4}{2}\)
\(520 = \theta (864)(11)\) × \(2\)
\(520 = 19008 \theta \\\\\Theta = \frac{520}{19008}\)
Magnetic flux = 0.0274 Weber.
Therefore, the magnetic flux per pole is 0.0274 Weber.
Read more: https://brainly.com/question/15449812?referrer=searchResults
FILL IN THE BLANK. ____is the order in which waveforms from each phase (A,B, and C) cross zero. (Current crest rotation; Harmonic sequence; Phasor rotation ; Harmonic degree)
Phasor rotation is the order in which waveforms from each phase (A, B, and C) cross zero.
In a three-phase electrical system, the voltage and current waveforms of each phase are offset by a specific angle from each other. This angle is called the phase angle, and it determines the relationship between the waveforms. The phasor rotation is the order in which the voltage or current waveforms from each phase (A, B, and C) cross the zero axis, which is also known as the reference or neutral line.
In a three-phase electrical system, the waveform of each phase completes one full cycle (360 degrees or 2π radians) within a given time period. The phasor rotation refers to the order in which each waveform completes this cycle, starting from the point where it crosses the zero axis.
For example, in a three-phase system, the voltage waveforms for each phase (A, B, and C) may be offset by 120 degrees from each other. This means that each waveform crosses the zero axis at a different time relative to the other waveforms. The phasor rotation refers to the order in which these waveforms cross the zero axis, as they complete one full cycle.
To learn more about waveforms, click here:
https://brainly.com/question/30054547
#SPJ4
A 60 mm radium drum is rigidly attached to a 100 mm radius drum as shown. One of the drum rolls without sliding on the surface shown, and a cord is wound around the other drum. Knowing that end D of the cord
is pulled to the left with a velocity of 160 mm/s and acceleration of 600 mm/s?, both directed to the left, determine the acceleration of points A, B, and C of the drum.
The acceleration at points A, B and C are respectively; 960 mm²/s, 1600 mm²/s and 600 mm²/s
What is the acceleration?The drum rolls without sliding and as such its' instantaneous center will lie at B. Thus;
V_d = V_c = 160 mm/s
Also, a_d = a_c = 600 mm²/s
Now, formula for velocity at A is;
V_a = r_ab * ω
where ω = 160/(100 - 60)
ω = 4 rad/s
V_a = 60 * 4
V_a = 240 mm/s
Acceleration at A = V_a²/r_ab
Acceleration at A = 240²/60 = 960 mm²/s
Now, V_b = 100 * 4 = 400 mm/s
Acceleration at B = 400²/100 = 1600 mm²/s
Read more about Acceleration at; https://brainly.com/question/14344386
After cutting a PVC pipe you should use a
to debure the pipe
Answer:
Deburring Tool
Explanation:
A deburring tool is used in order to debur the PVC pipes. They are mostly used for the plastic pipes.
After the PVC pipes are cut, there are burrs on the pipe surface. To remove these burrs, a deburring tool is used. It removes the burrs form the edges of the PVC pipes that results from grinding, cutting, milling, drilling, etc.
The deburring tools are made from high speed steels.
Consider the following lines of Python:
>>> x = input()
>? 12
>>> x + “abc”
What is the output?
Answer:
I don't know
............................
The output will be an error message since the input() function in Python always takes input as a string, even if the entered value is an integer like 12.
Here,
It cannot directly concatenate a string with an integer.
In order to fix this, we need to convert the input string into an integer using the int() function,
```
x = int(input())
x = x + "abc" # this will give an error message
```If we fix the code, the correct output will be:
`>>> x = int(input())`
`12`
`>>> x + "abc"`
`TypeError: unsupported operand type(s) for +: 'int' and 'str'`
Know more about python,
https://brainly.com/question/11288191
#SPJ4
___________________ is the primary classification trait used to explain how scientists divide rocks into the three classification groups.
answer choices
- Composition
- Formation
- Location
- Texture
a tensile member in a truss frame is subjected to a load that varies from 0 to 6500 lb as a traveling crane moves across the frame. design the tensile member.
To design the tensile member for the truss frame, select a material with sufficient strength and durability to withstand the varying load of 0 to 6500 lb.
The tensile member in a truss frame plays a crucial role in withstanding the loads imposed on the structure. In this case, the load varies from 0 to 6500 lb as a traveling crane moves across the frame. To design the tensile member, several considerations need to be taken into account.
Firstly, the material selection is critical. It is important to choose a material with high tensile strength to ensure that it can withstand the maximum load of 6500 lb without experiencing permanent deformation or failure. Common materials used for tensile members include steel alloys, such as carbon steel or stainless steel, which possess excellent tensile properties.
Secondly, the cross-sectional area of the tensile member needs to be determined based on the anticipated load. By calculating the maximum tensile stress experienced by the member using the formula stress = force / area, the required cross-sectional area can be obtained. It is advisable to include a safety factor in the design to account for potential variations in the load or unexpected dynamic effects.
Lastly, the overall design and connection details of the tensile member should be carefully considered. The member should be securely attached to the truss frame to prevent any slippage or displacement under load. Proper fasteners, such as bolts or welds, should be used to ensure a robust and reliable connection.
In summary, the tensile member for the truss frame subjected to a varying load from 0 to 6500 lb should be designed by selecting a material with high tensile strength, determining the appropriate cross-sectional area, and ensuring secure connections. These considerations will help to ensure the structural integrity and safe operation of the truss frame.
Learn more about tensile members
brainly.com/question/31043645
#SPJ11
recall from the video that the field diameter for one objective lens can be used to calculate the field diameters of the other objective lenses of a parfocal microscope. using the diameter of the scanning field, calculate the approximate field diameters of the low power, high power, and oil immersion objectives. drag the correct measurements to complete the table.
The approximate field diameters of the low power, high power, and oil immersion objectives can be calculated using the diameter of the scanning field.
How to calculate the approximate field diameters of the different objectives of a parfocal microscope?To calculate the approximate field diameters of the low power, high power, and oil immersion objectives, we can use the concept of parfocality. Parfocality means that when one objective lens is in focus, the other objective lenses should also be nearly in focus.
The field diameter is defined as the diameter of the circular area visible through the microscope. Since the objective lenses are parfocal, the ratio of the field diameters is equal to the ratio of the objective lens magnifications.
Let's assume the diameter of the scanning field is D_scanning. If the magnification of the scanning objective lens is M_scanning, and the magnifications of the low power, high power, and oil immersion objective lenses are M_low, M_high, and M_oil, respectively, then we can calculate the approximate field diameters as follows:
D_low = (M_low / M_scanning) * D_scanning
D_high = (M_high / M_scanning) * D_scanning
D_oil = (M_oil / M_scanning) * D_scanning
Learn more about: field diameters
brainly.com/question/33814029
#SPJ11
All of the following methods have proven to be useful techniques to help project teams identify the risks that might impact the project EXCEPT:a) reviewing project documents; b) documenting lessons learned; c) interviewing stakeholders; d) brainstorming among team members and subject matter experts
All the following methods have proven to be useful techniques to help project teams identify the risks that might impact the project, except documenting lessons learned.
What techniques do you use to identify project risks?The unexpected can happen regardless of how thoroughly you prepare your project and throw you entirely off track. Before the project begins, potential risks should be identified to assist mitigate some effects of unanticipated events. These risk identification methods can also be employed as a project progresses to make sure that any additional risks are taken into account.To find hazards in a project, project managers have a variety of methods at their disposal. They include expert judgment techniques, documentation reviews, information collecting, brainstorming, checklist analysis, assumption analysis, diagramming, and SWOT analysis.Reviewing project documentation for discrepancies entails looking over items including project plans, resource schedules, scoping documents, and requirement documents.To learn more about project, refer to
https://brainly.com/question/27995740
#SPJ4
A low-altitude meteorological research balloon, temperature sensor, and radio transmitter together weigh 2.5 lb. When inflated with helium, the balloon is spherical with a diameter of 4 ft. The volume of the transmitter can be neglected when compared to the balloon's size. The balloon is released from ground level and quickly reaches its terminal ascent velocity. Neglecting variations in the atmosphere's density, how long does it take the balloon to reach an altitude of 1000 ft?
Answer:
12 mins
Explanation:
The summation of the forces in vertical direction
= Fb - Fd - w = 0 ∴ Fd = Fb - w ----- ( 1 )
Fb ( buoyant force ) = Pair * g * Vballoon ------- ( 2 )
Pair = air density , Vballoon = volume of balloon
Vballoon = \(\frac{\pi D^3}{6}\) , where D = 4 ∴ Vballoon = 33.51 ft^3
g = 32.2 ft/s^2
From property tables
Pair = 2.33 * 10^-3 slug/ft^3
μ ( dynamic viscosity ) = 3.8 * 10^-7 slug/ft.s
Insert values into equation 2
Fb = ( 2.33 * 10^-3 ) * ( 32.2 ) *( 33.51 ) = 2.514 Ib
∴ Fd = 2.514 - 2.5 = 0.014 Ib ( equation 1 )
Assuming that flow is Laminar and RE < 1
Re = (Pair * vd) / μair -------- ( 3 )
where: Pair = 2.33 * 10^-3 slug/ft^3 , vd = ( 987 * 4 ) ft^2/s , μair = 3.8 * 10^-7 slug/ft.s
Insert values into equation 3
Re = 2.4 * 10^7 ( this means that the assumption above is wrong )
Hence we will use drag force law
Assume Cd = 0.5
Express Fd using the relation below
Fd = 1/2* Cd * Pair * AV^2
therefore V = 1.39 ft/s
Recalculate Reynold's number using v = 1.39 ft/s
Re = 34091
from the figure Cd ≈ 0.5 at Re = 34091
Finally calculate the rise time ( time taken to reach an altitude of 1000 ft )
t = h/v
= 1000 / 1.39 = 719 seconds ≈ 12 mins
What is the purpose of a gusset or gusset plate used in the construction and repair of aircraft structures?
Answer:
To join and reinforce intersecting structural members
Explanation:
The purpose of a gusset or gusset plate used in the construction and repair of aircraft structures is to join and reinforce intersecting structural members
New tie rod ends are being installed. Technician A says it is a good idea to replace the cotter pin. Technician B says to tighten the retaining nut to the low side of the torque spec then further tighten to align the cotter key hole. Which technician is correct
Answer:
technician b?
Explanation:
2. Discuss the reengineering process in your own words and provide an example.
Reengineering is the process of redesigning and improving business processes to achieve significant performance improvements. It involves challenging traditional methods and leveraging technology for transformative change.
Reengineering is the process of fundamentally redesigning and improving business processes to achieve significant improvements in performance, efficiency, and effectiveness. It involves a holistic approach that rethinks and restructures existing processes, often leveraging technology and innovation to drive transformative change. Reengineering aims to break away from traditional ways of operating and create new, streamlined processes that align with organizational goals and deliver value to customers.
Example: One example of reengineering is the transformation of a traditional paper-based invoicing process into an automated electronic invoicing system. In the traditional process, invoices would be generated manually, printed, and sent through the mail, resulting in delays, errors, and inefficiencies. Through reengineering, the process can be redesigned to leverage electronic invoicing software, where invoices are generated electronically, sent via email or a digital platform, and seamlessly integrated with the organization's accounting systems. This reengineering effort eliminates manual steps, reduces processing time, improves accuracy, and enhances customer satisfaction through faster invoice delivery and streamlined payment processes. The focus is on reimagining the entire invoicing process, identifying pain points, and implementing technological solutions to drive efficiency and effectiveness.
Reengineering projects can vary in scope and scale, but they all involve a critical examination of existing processes, identifying bottlenecks, and finding innovative ways to streamline operations. The goal is to achieve radical improvements in performance and outcomes by challenging traditional assumptions and embracing new approaches to work.
To learn more about Reengineering Click Here: brainly.com/question/28902509
#SPJ11
What quantity measures the effect of change?
control variable
independent variable
relative variable
dependent variable
Answer:
The Dependent Variable is the Effect, Its value depends on changes from the Independent Variable
Hope this Helps
A machine used to lift motorcycles consists of an electric winch pulling on one supporting cable of a block and tackle system. The winch can pull with a force of 75 lb. If the system can lift a maximum weight of 860 lb, what is the minimum number of supporting strands for this block and tackle system?
Answer: So you are dealing with maximum and minimum weights and you want to know what MINIMUM number of supporting strands for this block and tackle system are needed I believe. If so you are dealing with economic imbalances Though we are not worrying about money Right? Right we need physics which Physics study matter and how it moves You would need 8 STRANDS
Explanation: Step By Step
A pequin walks 10 feet in six second how far does the pequin wals in 45 seconds
Answer:
7.5 feet
Explanation:
45 divided by 6 is 7.5
Answer:
7.5 feet
Explanation:
45 divided by 6 is 7.5
a commercial refrigerator with r-134a as the working fluid is used to keep the refrigerated space at -35 c by rejecting waste heat to cooling water that enters the condenser at 18 c at a rate of 0.25 kg/s and leaves at 26 c. the refrigerant enters the condenser at 1.2 mpa and 50 c and leaves at the same pressure subcooled by 6 c. if the compressor consumes 3.3 kw of power , determine (a) the mass flow rate of the refrigerant, b) the refrigerant load, c) the cop, and d) the minimum power input to the compressor for the same refrigeration load.
At 1.2mpa pressure and 50c
What is pressure?
By pressing a knife against some fruit, one can see a straightforward illustration of pressure. The surface won't be cut if you press the flat part of the knife against the fruit. The force is dispersed over a wide area (low pressure).
a)Mass flow rate of the refrigerant
Therefore h1= condenser inlet enthalpy =278.28KJ/Kg
saturation temperature at 1.2mpa is 46.29C
Therefore the temperature of the condenser
T2 = 46.29C - 5
T2 = 41.29C
Now,
d)power consumed by compressor W = 3.3KW
Q4 = QL + w = Q4
QL = mR(h1-h2)-W
= 0.0498 x (278.26 - 110.19)-3.3
=5.074KW
Hence refrigerator load is 5.74Kg
(COP)r = 238/53
(Cop) = 4.490
Therefore the above values are the (a) mass flow rate of the refrigerant, b) the refrigerant load, c) the cop, and d) the minimum power input to the compressor for the same refrigeration load.
To learn more about pressure
https://brainly.com/question/13717268
#SPJ4
Draw the megnetization current or circut of generatpr characterstistics and explian the shape
46.5 kg (102.3 lb) of fine aggregate is mixed with 72.3 kg (159.1 lb) of coarse aggregate. the fine aggregate has a moisture content of 2.0% and absorption of 3.4%, whereas the coarse aggregate has a moisture content of 1.3% and absorption of 3.8%. what is the amount of water required to increase the moisture contents of both fine and coarse aggregates to reach absorption?
The amount of water required to increase the moisture contents of both fine and coarse aggregates to reach absorption 2.418 kg total 0.638kg fine 1.78 kg coarse.
What are coarse aggregates?Coarse aggregates are any particles greater than 0.19 inch, but generally range between 3/8 and 1.5 inches in diameter. Gravels constitute the majority of coarse aggregate used in concrete with crushed stone making up most of the remainder.
What is an example of coarse aggregate?Coarse aggregates are a construction component made of rock quarried from ground deposits. Examples of these kinds of ground deposits include river gravel, crushed stone from rock quarries, and previously used concrete.
To know more about Coarse aggregates visit:
https://brainly.com/question/28964237
#SPJ4
Identify the action and reaction forces of a rocket blasting off.
Answer: ( give brainliest)
Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. ... A rocket engine produces thrust through action and reaction. The engine produces hot exhaust gases which flow out of the back of the engine. In reaction, a thrusting force is produced in the opposite reaction.
Explanation:
The force that the rocket's engines exert on the exhaust gases is known as the "action force." The rocket experiences an upward thrust as the engines burn fuel and release exhaust gases at high velocity downward.
Thus, The rocket's force on the exhaust gases is referred to as the response force.
The rocket experiences an equal and opposite reaction force in response to the action force, which causes it to be propelled upward into the sky.
For every action, there is an equal and opposite response, states Newton's third rule of motion. The forces involved in a rocket's propulsion during takeoff make this principle clear.
Thus, The force that the rocket's engines exert on the exhaust gases is known as the "action force." The rocket experiences an upward thrust as the engines burn fuel and release exhaust gases at high velocity downward.
Learn more about Force, refer to the link:
https://brainly.com/question/13191643
#SPJ3
A battery consists of
solution.
and an electrolyte, wh
Select one:
O a. Two dissimilar metals
b. An insulator material separating the metals
c. Both A and B
O d. Neither A nor B
Clear my choice
Answer:
c
Explanation:
positive charge and negative charge but cant touch
What is the tenacity in gf/den of a 3.2 tex fiber that ruptures under a load of 94.8 gf ? Provide your answer with two decimal positions and no unit. Answer:
The tenacity of the fiber is 3.29 gf/den.
Explanation:
To calculate the tenacity of a fiber, we need to know the load at which the fiber ruptures and its linear density. Linear density is usually given in tex, which is the weight in grams of 1,000 meters of fiber.
The formula for tenacity is:
Tenacity = Load / Linear density
To use this formula, we first need to convert the linear density from tex to denier, which is another common unit for linear density. The conversion factor is 1 tex = 9 denier.
So, for a fiber with a linear density of 3.2 tex, we can convert it to denier as follows:
Linear density in denier = 3.2 tex * 9 denier/tex = 28.8 denier
Now we have both the load and the linear density in the appropriate units to calculate the tenacity:
Tenacity = Load / Linear density
Substituting the given values, we get:
Tenacity = 94.8 gf / 28.8 den = 3.29 gf/den
Therefore, the tenacity of the fiber is 3.29 gf/den.
Know more about the linear density click here:
https://brainly.com/question/30929692
#SPJ11
Consider the following hypothetical scenario for Jordan Lake, NC. In a given year, the average watershed inflow to the lake is 900 cfs. Precipitation over the lake is 32 inches/year and evaporation over the lake is 55 inches/year; the area of the lake is 47,000 ac. If an average flow of 300 cfs must be released from the dam for the benefit of fish and downstream water users, calculate the amount of water that can be withdrawn from the lake to provide water supply for the Triangle area. Assume any other source/sink of water (such as groundwater), is negligible.
Answer:
The lake can withdraw a maximum of \(1.464\times 10^{10}\) cubic feet per year to provide water supply for the Triangle area.
Explanation:
The maximum amount of water that can be withdrawn from the lake is represented by the following formula:
\(V = V_{in}+V_{p}-V_{e}-V_{out}\) (Eq. 1)
Where:
\(V\) - Available amount of water for water supply in the Triangle area, measured in cubic feet per year.
\(V_{in}\) - Inflow amount of water, measured in cubic feet per year.
\(V_{out}\) - Amount of water released for the benefit of fish and downstream water users, measured in cubic feet per year.
\(V_{p}\) - Amount of water due to precipitation, measured in cubic feet per year.
\(V_{e}\) - Amount of evaporated water, measured in cubic feet per year.
Then, we can expand this expression as follows:
\(V = f_{in}\cdot \Delta t+h_{p}\cdot A_{l}-h_{e}\cdot A_{l}-f_{out}\cdot \Delta t\)
\(V = (f_{in}-f_{out})\cdot \Delta t +(h_{p}-h_{e})\cdot A_{l}\) (Eq. 2)
Where:
\(f_{in}\) - Average watershed inflow, measured in cubic feet per second.
\(f_{out}\) - Average flow to be released, measured in cubic feet per second.
\(\Delta t\) - Yearly time, measured in seconds per year.
\(h_{p}\) - Change in lake height due to precipitation, measured in feet per year.
\(h_{e}\) - Change in lake height due to evaporation, measured in feet per year.
\(A_{l}\) - Surface area of the lake, measured in square feet.
If we know that \(f_{in} = 900\,\frac{ft^{3}}{s}\), \(f_{out} = 300\,\frac{ft^{3}}{s}\), \(\Delta t = 31,536,000\,\frac{second}{yr}\), \(h_{p} = 32\,\frac{in}{yr}\), \(h_{e} = 55\,\frac{in}{yr}\) and \(A_{l} = 47,000\,acres\), the available amount of water for supply purposes in the Triangle area is:
\(V = \left(900\,\frac{ft^{2}}{s}-300\,\frac{ft^{3}}{s} \right)\cdot \left(31,536,000\,\frac{s}{yr} \right) +\left(32\,\frac{in}{yr}-55\,\frac{in}{yr} \right)\cdot \left(\frac{1}{12}\,\frac{ft}{in}\right)\cdot (47000\,acres)\cdot \left(43560\,\frac{ft^{2}}{acre} \right)\)\(V = 1.464\times 10^{10}\,\frac{ft^{3}}{yr}\)
The lake can withdraw a maximum of \(1.464\times 10^{10}\) cubic feet per year to provide water supply for the Triangle area.