A cylindrical space capsule lands in the ocean. This capsule is 2.44 m long, 1.10 m in diameter, and weighted at one end so that it floats with its long central axis vertical and 0.820 m of its length above the water surface. The mass density of sea water is 1025 kg/m3.What is the magnitude of the buoyant force exerted on the capsule?

Answers

Answer 1

Answer:

The correct answer is "15456.8 N".

Explanation:

According to the question,

The inside volume will be:

= \(3.14\times (\frac{1.1}{2} )^2\times (2.44-0.82)\)

= \(3.14\times \frac{1.21}{4}\times 1.62\)

= \(3.14\times 03025\times 1.62\)

= \(1.538757 \ m^3\)

hence,

The buoyant force will be:

= \(V\times Pw\times g\)

= \(1.538757\times 1025\times 9.8\)

= \(15456.8 \ N\)


Related Questions

both the pokerhand and blackjackhand classes must override which member functions? several answers may be correct.

Answers

In both the `PokerHand` and `BlackjackHand` classes, the following member functions must be overridden:

1. `getValue()` or `getScore()`: This function calculates and returns the value or score of the hand in the respective game (poker or blackjack).

2. `isBust()`: This function determines whether the hand has exceeded the maximum allowable value in blackjack (typically 21) and returns a boolean indicating if the hand is bust.

3. `isWinningHand()`: This function evaluates whether the hand is a winning hand based on the game rules and returns a boolean indicating the result.

These member functions need to be overridden in both classes to provide the specific behavior and logic required for each game.

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Which of the following are the main psychological domains?

Answers

Answer:

Domain 1: Biological (includes neuroscience, consciousness, and sensation) Domain 2: Cognitive (includes the study of perception, cognition, memory, and intelligence) Domain 3: Development (includes learning and conditioning, lifespan development, and language) i hope this helps you.

Hey everyone!

This question is hard.
What specific fluid goes in the windshield wipers? (I never drove a car before)
And how much to put in fluid ounces? (So you don't blow a car up)

Answers

Hello!
I’ve never driven either. But I’m pretty sure there is not really specific fluid you have to use. Just to name a few are Rain-X Bug Remover Windshield Washer Fluid, Prestone AS657 Deluxe 3-in-1 Windshield Washer Fluid.
For how much, there should be a little line or 3/4th of the way full.

Hope this helps!

Answer:

What specific fluid goes in the windshield wipers.

Distilled water

How much to put in fluid ounces?

There should be a tiny bit more than 3/4 of the way full.

The current standard for recovery only equipment is sae

Answers

Explanation:

I think is SAE standard J2810

Which stages occur during incomplete metamorphosis?
ASAP


A. Adult, larva, and pupa

B. Egg, nymph, and adult

C. Larva, nymph, and egg

D. Pupa, egg, and nymph


NO LINKS PLEASE

Answers

Answer:

The answer is B

Explanation: Hope this helps:)

Utility company power lines carry what kind of current?

Answers

Answer:

Alternating

Explanation:

providing the three principal stresses of a point are 10mpa, 2mpa, -4mpa, what is the equivalent stress at that point?

Answers

When three principal stresses are given, the equivalent stress at the point can be calculated using the following formula:σe = [(σ1-σ2)² + (σ2-σ3)² + (σ3-σ1)²]^(1/2)where,σ1, σ2, and σ3 are the principal stresses.

In this case, the given principal stresses are 10MPa, 2MPa, and -4MPa. Therefore,σ1

\(= 10MPaσ2 = 2MPaσ3 = -4MPaSubstituting these values in the above formula, we get:σe = [(10-2)² + (2-(-4))² + (-4-10)²]^(1/2)= [(8)² + (6)² + (14)²]^(1/2)= [64 + 36 + 196]^(1/2)= [296]^(1/2)≈ 17.2\) MPaTherefore, the equivalent stress at the point is approximately 17.2 MPa.

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20. A spur gear pinion and gear shown on a drawing have a diametral pitch of 12. The pitch radius of the pinion is 1.500 inches and the gear ratio is
specified to be 1:3. On the print, you would expect the pitch diameter of the gear to be
OA. 9.00 inches.

Answers

On the print you would expect the pitch diameter of the gear to be 9.00 inches. Option A is right.

How to solve for the diameter

Gear ratio = 1/3

This is solved as number of teeth on pinion / teeth on gear

= Np/Ng

The pitch diameter = 1.5 x 2

= 3

Diametral pitch = 12

NP = 3 x 12 = 36

This is the teeth on piston

Ng = 3NP

Ng = 3 * 36

= 108

Hence pitch diameter = 108/12 = 9

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all electrical service distribution equipment is labeled with its maximum voltage and current ratings . select one: a. true b. false

Answers

The voltage range and current consumption at which an electrical device is intended to function are both disclosed in its rating. Normally, a rating plate that is attached to the device displays these figures, such as 230 volts, 3 amps.

Explain about the maximum voltage and current ratings?

For products lacking a protective element at the VCC side, voltages up to the absolute maximum rated supply voltage (i.e., VEE+36V) can be delivered, independent of supply voltage. In general, the absolute maximum common-mode voltage is VEE-0.3V and VCC+0.3V.

The chip's maximum ratings are the harsh conditions to which it can be subjected for a brief period of time without suffering long-term harm. Long-term exposure to absolute maximum ratings may have an impact on a device's dependability.

(Krnt Rest) (Electrical engineering: Circuits, Electrical power) The greatest current that a fuse is rated to carry for an infinite duration without significantly degrading the fuse element is known as the current rating.

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what do find interesting about engineering

Answers

A career in engineering is interesting and fun. It involves a lifetime of continuous learning to adapt to changes in society and the natural world. It often involves working in multi-disciplinary, multi-cultural, multi-site teams.

That you can invent something that doesn’t already exist

I really need help on this!
Which of the following is a term for a comparison between product metrics and values to industry standards and competitions metrics and values?
A: ideal value
B: competitive analysis
C: benchmark
D: marginally accepted value

Answers

C: benchmark because I have done this before
The answer is D!
Plz mark brainliest

Polarization: Unpolarized light passes through three ideal polarizing filters. The first filter is oriented with a horizontal transmission axis, the second one has its transmission axis at 30° from the horizontal, and the third filter has a vertical transmission axis. What percent of the light gets through this combination?

Answers

Answer:

the percentage of light that gets through this combination is 9.38

Explanation:

Given the data in the question;

Let us represent the incident unpolarized light with \(I_0\).

So, the amount of light intensity passing through the first polarizer will be;

\(I_1\) = \(I_0\) / 2 ------ let this be equation 1

An the amount of light intensity passing through the second polarizer will be;

\(I_2\) = \(I_1\)cos²θ

given that; the second one has its transmission axis at 30°

so, we substitute;

\(I_2\) = \(I_1\) × cos²( 30° )

\(I_2\) = \(I_1\) × 0.75

\(I_2\) = 0.75\(I_1\)

from equation; \(I_1\) = \(I_0\) / 2

\(I_2\) = 0.75( \(I_0\) / 2 )

\(I_2\) = 0.375\(I_0\) .

Now, the amount of light intensity passing through the third polarizer will be;

\(I_3\) = \(I_2\)cos² ( 90° - 30° )

\(I_3\) = \(I_2\) × cos²( 60° )

\(I_3\) = \(I_2\)  × 0.25

we substitute

\(I_3\) = 0.375\(I_0\)  × 0.25

\(I_3\) = 0.09375\(I_0\)

∴ \(I_3\)/\(I_0\) × 100 = 0.09375 × 100

9.38%

Therefore, the percentage of light that gets through this combination is 9.38

What is the relationship between mechanical stress inside of a cylindrical part with a given force applied to it

Answers

The relationship between mechanical stress inside of a cylindrical part with a given force applied to it is stress = force/area.

How is pressure associated with strain?

The utility of pressure offers upward thrust to strain, however now no longer the opposite manner around. A pressure is a push or pull upon an item attributable to the item's interplay with some other item while Stress is an inner resistance to supplied through the frame itself each time it's far beneath a few type of deformation.

Stress is denoted through σ. It is represented as N/m2. Stress formulation is made use of to locate carried out on any given frame if pressure and region on which pressure is exerted is given withinside the problem.

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Treatment Theory The following (one option only) is an example of source reduction in the 'Pollution Prevention Hierarchy' for air pollution control. Select one: a. Turning off appliances and lighting when not in use. b. Desulfur fuel before power generation c. Install electrostatic precipitators to remove particulate matter at all coal fired power stations. d. Switching from coal fired power generation to renewable energy.

Answers

The correct option that represents source reduction in the 'Pollution Prevention Hierarchy' for air pollution control is:

a. Turning off appliances and lighting when not in use.

Source reduction focuses on minimizing or eliminating the generation of pollutants at their source, thereby reducing the need for pollution control measures. By turning off appliances and lighting when not in use, energy consumption is reduced, resulting in lower emissions from power generation sources. This action helps prevent air pollution by reducing the release of pollutants associated with electricity production.

Desulfurizing fuel before power generation (option b) is an example of pollution control rather than source reduction. It aims to reduce the emissions of sulfur dioxide (SO2) during the combustion of fossil fuels, but it does not eliminate the generation of pollutants at the source.

Installing electrostatic precipitators (option c) is also a pollution control measure rather than source reduction. It aims to capture and remove particulate matter emitted from coal-fired power stations but does not address the root cause of pollution.

Switching from coal-fired power generation to renewable energy (option d) is an example of a more sustainable and environmentally friendly approach. It represents a shift away from a pollutant-intensive energy source to one that generates cleaner energy. However, it is not specifically classified as source reduction within the given options.

Therefore, the correct option representing source reduction in the context of the 'Pollution Prevention Hierarchy' for air pollution control is a. Turning off appliances and lighting when not in use.

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technician a says that two diodes are required for each stator winding lead. technician b says that diodes change alternating current into direct current. which technician is correct?

Answers

Technician B is incorrect, and Technician A is also likely incorrect.

Technician A's statement about using two diodes for each stator winding lead is unclear without additional context about the specific system being discussed.

In general, a diode can be used to rectify AC voltage into DC voltage, but it is not always necessary to use two diodes. Some rectifiers use a single diode, while others use multiple diodes in a configuration called a bridge rectifier.

Technician B's statement is incorrect. Diodes can be used to rectify AC voltage, but they do not change AC into DC. Instead, they allow the positive portion of the AC voltage to pass through while blocking the negative portion, resulting in a DC voltage with a pulsating waveform.

In summary, both technicians' statements are either unclear or incorrect.

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The _____ controls the opening of engine’s valves.

(A) camshaft

(B) crankshaft

(C) valve springs

(D) combustion chamber

Answers

A) The Camshaft Controls The Opening of The Engines Valves

We have a program with 30 billion instructions that takes 45 seconds to run on a 2GHz machine. It is given that the program consists of 25% branch instructions, and the CPI of branch instructions is 4. The average CPI is 3.0.
Using a newly developed compiler, the recompiled program now uses 20 billion instructions. It is still composed 25% branch instructions, but the CPI of the branch instructions has been reduced by a factor of 2. What is the expected speedup of the new program over the original program?

Answers

The expected speedup of the new program over the original program is approximately 2.25 times faster. This means that the recompiled program is expected to run in approximately 20 seconds, compared to the original program's runtime of 45 seconds. The original program has 30 billion instructions and an average CPI of 3.0.

This gives us the total number of cycles required to execute the program as (30 billion instructions) x (3.0 CPI) = 90 billion cycles. Since the machine has a clock rate of 2 GHz, the time taken to execute the program is (90 billion cycles) / (2 GHz) = 45 seconds.

In the recompiled program, the number of instructions has been reduced to 20 billion, while still maintaining a 25% branch instruction composition. The CPI of the branch instructions has been reduced by a factor of 2, which means the new CPI is 4 / 2 = 2.0. Using the same calculation, the total number of cycles required to execute the recompiled program is (20 billion instructions) x (2.0 CPI) = 40 billion cycles. With the same clock rate of 2 GHz, the expected runtime of the recompiled program is (40 billion cycles) / (2 GHz) = 20 seconds.

Comparing the runtimes of the original and recompiled programs, we can calculate the speedup as (original runtime) / (recompiled runtime) = 45 seconds / 20 seconds ≈ 2.25. Therefore, the expected speedup of the new program over the original program is approximately 2.25 times faster.

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The expected speedup of the new program over the original program is 1.8x.

1. Calculate the total number of branch instructions in the original program:

  Total branch instructions = 30 billion instructions * 25% = 7.5 billion instructions

2. Calculate the total number of non-branch instructions in the original program:

  Total non-branch instructions = 30 billion instructions - 7.5 billion instructions = 22.5 billion instructions

3. Calculate the average CPI of the original program:

  Average CPI = (CPI of branch instructions * percentage of branch instructions) + (CPI of non-branch instructions * percentage of non-branch instructions)

  Average CPI = (4 * 25%) + (1 * 75%) = 1 + 0.75 = 1.75

4. Calculate the execution time of the original program:

  Execution time = Total instructions / (Clock rate * CPI)

  Execution time = 30 billion instructions / (2 GHz * 1.75) = 8.5714 seconds

5. Calculate the total number of branch instructions in the recompiled program:

  Total branch instructions = 20 billion instructions * 25% = 5 billion instructions

6. Calculate the total number of non-branch instructions in the recompiled program:

  Total non-branch instructions = 20 billion instructions - 5 billion instructions = 15 billion instructions

7. Calculate the CPI of the branch instructions in the recompiled program:

  CPI of branch instructions = CPI of original branch instructions / Reduction factor = 4 / 2 = 2

8. Calculate the average CPI of the recompiled program:

  Average CPI = (CPI of branch instructions * percentage of branch instructions) + (CPI of non-branch instructions * percentage of non-branch instructions)

  Average CPI = (2 * 25%) + (1 * 75%) = 0.5 + 0.75 = 1.25

9. Calculate the execution time of the recompiled program:

  Execution time = Total instructions / (Clock rate * CPI)

  Execution time = 20 billion instructions / (2 GHz * 1.25) = 8 seconds

10. Calculate the expected speedup of the new program over the original program:

   Speedup = Execution time of original program / Execution time of new program

   Speedup = 8.5714 seconds / 8 seconds = 1.0714

11. Round the speedup value to two decimal places:

   Speedup = 1.07

Therefore, the expected speedup of the new program over the original program is 1.8x.

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what component allows ics to determine whether or not a signal on a data line is a 0, a 1, or undetermined?

Answers

A comparator compares two voltages and produces an output signal based on the comparison. If the voltage on the data line is higher than the reference voltage, the comparator will output a 1.

What is Voltages?

Voltage is the electrical force or pressure that causes electrons to move in a circuit. It is measured in volts, and is the difference in electric potential energy between two points in a circuit. Voltage is generated in a circuit when a battery or other power source is connected.

If the voltage on the data line is lower than the reference voltage, the comparator will output a 0; if the voltage on the data line is equal to the reference voltage, the comparator will output an undetermined signal.

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Jay decides to walk home from school today. He lives 3 miles from school and can walk home in 45 minutes. At what rate is Jay traveling?

Answers

Answer: jay is traveling at 4 miles per hour :)

Explanation:

What role do nongovernmental organizations playin emergency planning?

Answers

Answer:

they play a huge role

Explanation:

took the test

The role Nongovernmental organizations (NGOs) play in emergency planning IS :NGOs' only role is providing volunteers during an emergency. This response has been verified as correct and useful.

Team communication is often more formal than other types of group communication.
True
False

Answers

Answer:

True

Explanation:

True I think it’s true

A stone with a mass of 0.600 kg is attached to one end of a string 0.800 m long. The string will break if its tension exceeds 55.0 N. The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed. Find the maximum speed the stone can attain without breaking the string.

Answers

To find the maximum speed the stone can attain without breaking the string, we need to determine the maximum tension the string can withstand.

We know that the tension in the string is equal to the centripetal force required to keep the stone moving in a circular path:

Tension = centripetal force = (mass x velocity^2) / radius

where the radius is the length of the string, 0.800 m.

If we rearrange the equation to solve for velocity, we get:

velocity = sqrt((Tension x radius) / mass)

Now we can substitute the given values:

Tension = 55.0 N (the maximum tension the string can withstand)
radius = 0.800 m
mass = 0.600 kg

Plugging these values into the equation, we get:

velocity = sqrt((55.0 N x 0.800 m) / 0.600 kg)
velocity = 3.31 m/s

Therefore, the maximum speed the stone can attain without breaking the string is 3.31 m/s.

calculate the sum of squares of given input of numbers

Answers

Answer:

Here is a Python function to calculate the sum of squares of a list of numbers:

python

Copy code

def sum_of_squares(numbers):

 return sum([x**2 for x in numbers])

You can use this function by passing a list of numbers as an argument:

scss

Copy code

numbers = [1, 2, 3, 4, 5]

result = sum_of_squares(numbers)

print(result) # Output: 55 (1^2 + 2^2 + 3^2 + 4^2 + 5^2)

Explanation:

For a bronze alloy, the stress at which plastic deformation begins is 284 MPa and the modulus of elasticity is 106 GPa. (a) What is the maximum load that can be applied to a specimen having a cross-sectional area of 310 mm2 without plastic deformation? (b) If the original specimen length is 120 mm, what is the maximum length to which it may be stretched without causing plastic deformation?

Answers

Answer:

a) the maximum load is 88,040 N

b)

the maximum length to which the specimen may be stretched is 0.12032148 mm

Explanation:

Given the data in the question;

the stress at which plastic deformation begins σ = 284 MPa = 2.84 × 10⁸ Pa

modulus of elasticity E = 106 GPa = 1.06 × 10¹¹ Pa

a)

Area A = 310 mm² = 310 × 10⁻⁶ m ( without plastic deformation )

now, lets consider the equation relating to stress and cross sectional area.

σ = F / A₀

hence, maximum load F = σA₀  

so we substitute

F = (2.84 × 10⁸) × (310 × 10⁻⁶)

F = 88,040 N

Therefore, the maximum load is 88,040 N

b)

Initial length specimen l₀ = 120 mm  = 120 × 10⁻³ m

using engineering strain, ε = (l₁ - l₀)/l₀

Also from Hooke's law, σ = Eε

so from the equation above;

l₁ = l₀( ε + 1 )

l₁ = l₀( σ/E + 1 )

so we substitute

l₁ = (120 × 10⁻³)( (2.84 × 10⁸)/(1.06 × 10¹¹)) + 1 )

l₁ = (120 × 10⁻³) ( 1.002679 )

l₁ = 0.12032148 mm

Therefore, the maximum length to which the specimen may be stretched is 0.12032148 mm

This agency develops standards for pressure vessels and pressure relief valves, as well as the design, welding, and materials that may be used in pipeline construction.
Select one:
a. American Petroleum Institute
b. American Society of Mechanical Engineers
c. American Gas Association
d. National Fire Protection Association

Answers

Answer:

b. American Society of Mechanical Engineers

Explanation:

The "American Society of Mechanical Engineers" (ASME) is an organization that ensures the development of engineering fields. It is an accreditation organization that ensures parties will comply to the ASME Boiler and Pressure Vessel Code or BPVC.

The BPVC is a standard being followed by ASME in order to regulate the different pressure vessels and valves. Such standard prevents boiler explosion incidents.

Can somebody help me with that

Can somebody help me with that

Answers

Answer:

I think it's 23 ohms.

Explanation:

Not entirely sure about it.

hope this helps

A rocket is launched from rest with a constant upwards acceleration of 18 m/s2. Determine its velocity after 25 seconds

Answers

Answer:

The final velocity of the rocket is 450 m/s.

Explanation:

Given;

initial velocity of the rocket, u = 0

constant upward acceleration of the rocket, a = 18 m/s²

time of motion of the rocket, t = 25 s

The final velocity of the rocket is calculated with the following kinematic equation;

v = u + at

where;

v is the final velocity of the rocket after 25 s

Substitute the given values in the equation above;

v = 0 + 18 x 25

v = 450 m/s

Therefore, the final velocity of the rocket is 450 m/s.

Please help me solve Problem 21.2

Please help me solve Problem 21.2

Answers

__________________________________________________________

Hello! In this question, we are trying to find the maximum value of shear flow in the web of the wing spar. Note that we are trying to find this with a section that is 1 meter away from the free end of the beam.
__________________________________________________________

Explanation:

In this problem, we know that:

the web has a thickness of 2 mm.Fully effective in resisting direct stress

This information should be kept in mind and can help us solve our problem.

__________________________________________________________

Solve:

Let us begin to solve the problem.

Since we're analyzing the moment in one section, in this case, we can note this as "section 1", we can use this formula to determine the moment in this section:

\(M_{1}=\frac{wl^2}2}\)
Whereas:

w = distributed load (15 kN/m)l = length of beam (1 m)

Plug in the values into the equation and solve:

\(M_{1}=\frac{15*1^2}2}=7.5\text{kN-m}\)
Now, let us find the moment of inertia of the beam in our 1st section. We'll use the formula:

\(I_{xx}=\frac{BD^3}{12} +2Ah^2\)

Whereas:

B = width (2 mm)D = depth (300 mm)A = area (500 mm²)h = centroid of this section (150 mm)

Plug in the values into the equation and solve:

\(I_{xx}=\frac{2(300)^3}{12} +2(500)(150)^2=2.7\times10^7\:\text{mm}^4\)
Now knowing our moment and inertia, we can solve our direct distress in the z direction of our flanges using the following formula:

\(\sigma_{z,U} = -\sigma_{z,L}=\frac{M_{1}}{I_{xx}}y\)
We know:

\(M_{1}=7.5\text{kN-m}\)\(I_{xx}=2.7\times10^7\:\text{mm}^4\)y = 150mm

Plug the values into the equation and solve. (Note that unit conversion was done for M1):

\(\sigma_{z,U} = -\sigma_{z,L}=\frac{7.5\text{kN-m}*(\frac{1000 N}{1kN})(\frac{1000mm}{1m} )}{2.7\times10^7}(150mm)=-41.7\:\text{N/mm}^2\)
Since we now know what our direct distress is, we can find the bending moment resultant with the formula:

\(P_{z,U}=\sigma_{z,U}\times A\)

We know:

\(\sigma_{z,U} = -\sigma_{z,L}=-41.7\:\text{N/mm}^2\)A = 500 mm² (according to our wing spar given in our problem)

Plug in the values to our equation and solve:

\(P_{z,U}=-41.7\:\text{N/mm}^2\times 500\:mm^2=-20850\:N\)
Now knowing our bending moment resultant, we can now find our flange load of the web section. Note that our flange load is uniformly distributed. We will use the formula:

\(P_{U}=\sqrt{P_{z,U}^2+P_{y,U}^2}}\)
We know that:

\(P_{z,U}^2= -20850\:N\)\(P_{y,U}^2=0\)

Plug in the values into the equation and solve:
\(P_{U}=\sqrt{(-20850)^2+0^2}}=20850\:N\)
Please note that the answer we calculated above is our tension (T).

Let's now calculate our bending moment resultant using:

\(P_{y,L}=P_{z,L}\times\frac{\delta{y}^2}{\delta_{z}}\)

We know:

\(P_{z,L}=-20850\:N\)\(\delta{y}^2=100\:mm\)\(\delta_{z}=1\:m\)

Plug in the values and solve. To make things go faster, I included the unit conversion for our denominator value:

\(P_{y,L}=-20850\:N\times\frac{100\:mm}{(1\:m\times\frac{1000\:mm}{1\:m} )}=-2085\:kN=2085\:kN\)
Please note that the above calculation would be our compression value.

Let's calculate our shear force in the web in our 1st section using a known relationship:

\(S_{y}=-W\times\delta_{z}+P_{y,L}\)
We know:

W = 15 kN/m\(\delta_z=1\:m\)\(P_{y,L}=2085\:N\)

Plug in our known values and solve:

\(S_{y}=-15\times(1\:m\times\frac{1000\:mm}{1\:m} )+2085=-12915\:N\)

In order to figure out what our shear flow is (note that our shear flow is represented as q), we will use the relationship:

\(q=\frac{S_y}{I_{xx}} [\int_{0}^{s}2(150-s)ds+500\times(\frac{300}{2} )]\)

We know:

\(S_{y}=-12915\:N = 12915\:N\)\(I_{xx}=2.7\times10^7\:mm\)

Plugging in the values, we will get:

\(q=\frac{12915}{2.7\times10^7\:mm} [\int_{0}^{s}2(150-s)ds+500\times(\frac{300}{2} )]\)

Simplify the equation:

\(q=4.78\times10^{-4} [\int_{0}^{s}(300-s)ds+75000]\)
Integrate the equation:

\(q=4.78\times10^{-4} [\int_{0}^{s}(300-s)ds+75000]\\\\q=4.78\times10^{-4} ((300s-\frac{2s^2}{2} +[0])+75000)\\\\q=4.78\times10^{-4} ((300s-s^2 )+75000)\)

We now have our equation for the shear flow. We know that the max value of shear flow will happen when s equals 150 mm, so let's plug in the value 150 mm into "s" in our "q" equation and solve:

\(q=4.78\times10^{-4} ((300(150)-150^2 )+75000)=\boxed{46.8\:N/mm}\)

__________________________________________________________

Answer:

The max value of shear flow in the web in the 1st section of the beam is:

\(q=\boxed{46.8\:N/mm}\)

__________________________________________________________

Problems 1. Calculate the power in MW's of a pump moving liquid water with a mass flow rate of 3kg/s going from a pressure of 20kPa to 5 MPa at a temperature of 50°C. (10 points) Refer to page 449 for eq-n 8.7b and refer to example 8.1 for help

Answers

The power of the pump in MW is 4.509 MW. The power required by the pump can be calculated using the following formula:

`P = Δp * Q / η`

where `P` is the power required in watts, `Δp` is the pressure difference in Pascals, `Q` is the flow rate in cubic meters per second, and `η` is the pump efficiency.

From the problem,

- The mass flow rate of water, `m` = 3 kg/s

- The initial pressure of the water, `p1` = 20 kPa (converted to Pascals, `Pa`)

- The final pressure of the water, `p2` = 5 MPa (converted to Pascals, `Pa`)

- The temperature of the water, `T` = 50°C

First, we need to calculate the specific volume, `v`, of water at the given conditions. Using the steam tables, we find that the specific volume of water at 50°C is 0.001041 m³/kg.

Next, we can calculate the volume flow rate, `Qv`, from the mass flow rate and specific volume:

`Qv = m / v = 3 / 0.001041 = 2883.5 m³/s`

We can then convert the volume flow rate to cubic meters per second:

`Q = Qv / 1000 = 2.8835 m³/s`

The pressure difference, `Δp`, is given by:

`Δp = p2 - p1 = 5e6 - 20e3 = 4.98e6 Pa`

According to Example 8.1, we can assume the pump efficiency `η` to be `0.7`.

Substituting the values, we get:

`P = Δp * Q / η = 4.98e6 * 2.8835 / 0.7 = 20.632 MW`

Therefore, the power required by the pump is `20.632 MW`.

However, this is the power required by the pump. The power of the pump (or the power output) is less due to the inefficiencies of the pump. Hence, we need to multiply the above power by the pump efficiency to find the actual power output from the pump.

Therefore, the power output of the pump is:

`Power output = Pump efficiency * Power required = 0.7 * 20.632 MW = 4.509 MW`

The power output of the pump moving liquid water with a mass flow rate of 3 kg/s, from a pressure of 20 kPa to 5 MPa at 50°C, is 4.509 MW.

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b) A vapor compression refrigerator uses methyl chloride and works in the pressure range of 1.19 bar and 5.67 bar. At the beginning of compression, the refrigerant is 0.96 dry and the end of isentropic compression its temperature is 55 °c. The refrigerant liquid leaving the condenser is saturated.

If the mass flow of refrigerant is 1.8 kg/min.​

Answers

The calculation of the coefficient of performance, the rise in temperature of condenser cooling water, and the ice produced in the evaporator can be done using the energy balance equations for the refrigeration cycle.

How can we use energy balance equations for the refrigeration cycle to determine the values?

(i) Co-efficient of Performance (COP):

COP is defined as the ratio of the cooling capacity to the power required for refrigeration.

COP = Cooling capacity / Power required for refrigeration

The cooling capacity can be determined using the energy balance on the evaporator, which states that the heat absorbed by the refrigerant in the evaporator is equal to the heat rejected by the condenser.

Cooling capacity = m_ref * (h2 - h1)

where

m_ref = 1.8 kg/min, mass flow rate of refrigerant

h2 = enthalpy of refrigerant at the end of isentropic compression, 55°C

h1 = enthalpy of refrigerant at the beginning of the compression, 0.96 dry

The power required for refrigeration can be calculated as the work done on the refrigerant during the isentropic compression process.

Power required for refrigeration = m_ref * (h2 - h1)

Now we can calculate the COP using the above equations.

(ii) Rise in temperature of condenser cooling water:

The rise in temperature of condenser cooling water can be calculated using the energy balance on the condenser. The heat rejected by the refrigerant in the condenser is equal to the heat absorbed by the condenser cooling water.

Q_rejected = m_cw * Cp * (T_out - T_in)

where

m_cw = 16 kg/min, mass flow rate of condenser cooling water

Cp = 4.187 kJ/kg, specific heat of water

T_out = Final temperature of cooling water

T_in = Initial temperature of cooling water

We can solve for the rise in temperature (T_out - T_in) using the above equation.

(iii) Ice produced in the evaporator:

The ice produced in the evaporator can be calculated using the energy balance on the evaporator and the latent heat of fusion of ice.

Q_absorbed = m_ice * hf

where

m_ice = Mass of ice produced

hf = 336 kJ/kg, specific enthalpy of fusion of ice

We can solve for the mass of ice produced (m_ice) using the above equation.

Note: The above calculations require the enthalpies of the refrigerant at various states, which can be obtained from thermodynamic tables.

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The complete question goes thus:

A vapour compression refrigerator uses methyl chloride and works in the pressure range of 1.19 bar and

5.67 bar. At the beginning of the compression, the refrigerant is 0.96 dry and at the end of isentropic

compression, it has a temperature of 55°C. The refrigerant liquid leaving the condenser is saturated. If the

mass flow of refrigerant is 1.8 kg/min. Determine :

(i) Co-efficient of performance.

(ii) The rise in temperature of condenser cooling water if the water flow rate is 16 kg/min.

(iii) The ice produced in the evaporator in kg/hour from water at 15°C and ice at 0°C. Take : Specific enthalpy of fusion of ice = 336 kJ/kg

Specific heat of water = 4.187 kJ/kg.

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