By dimensional analysis, determine the pi -groups for the change in pressure that occurs when water or oil flows through a horizontal pipe with an abrupt contraction as shown. Express your answer in the functional form delta pd^4/pQ^2 = f (pi _1, pi _2)

Answers

Answer 1

The pi-groups for the change in pressure that occurs when water or oil flows through a horizontal pipe with an abrupt contraction can be expressed in the functional form of delta

pd^4/pQ^2 = f(pi_1, pi_2),

where pi_1 and pi_2 are the dimensionless parameters that represent the relevant physical properties of the system.

The Buckingham Pi theorem states that any physical relationship involving a certain number of variables can be expressed in terms of dimensionless parameters known as pi-groups. These pi-groups can be determined through dimensional analysis, which involves identifying the fundamental dimensions (such as mass, length, and time) and using them to form dimensionless groups.

For this problem, the relevant variables include the change in pressure (delta p), the diameter of the pipe (d), the flow rate (Q), and the properties of the fluid (such as density and viscosity). Using dimensional analysis, we can determine that the following dimensionless parameters are relevant to the problem:

Reynolds number (Re): This represents the ratio of inertial forces to viscous forces in the fluid and is given by Re = rhoVd/mu, where rho is the density of the fluid, V is the velocity of the fluid, mu is the dynamic viscosity of the fluid, and d is the diameter of the pipe.

Expansion factor (beta): This represents the change in the cross-sectional area of the pipe at the point of contraction, and is given by beta = A_2/A_1, where A_1 and A_2 are the cross-sectional areas of the pipe before and after the contraction, respectively.

Using these two dimensionless parameters, we can express the relationship between the change in pressure (delta p), the diameter of the pipe (d), the flow rate (Q), and the properties of the fluid as a function of pi_1 and pi_2 in the form of delta pd^4/pQ^2 = f(pi_1, pi_2).

The specific form of the function f(pi_1, pi_2) will depend on the exact nature of the system and the flow conditions and can be determined through experimental data or theoretical modeling.

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Related Questions

Shops should avoid purchasing any material sold in ____________.

Answers

Answer: Aerosol Cans

Explanation: I just did the quiz

What long shaft a tool works in a combination with a impact wrench air to install Lugnuts on wheels

Answers

I guess a Torque wrench?

convert the following decimal number to octal number and the to binary .58​

Answers

Answer:

21/2 we get remainder 1

10/2 we get remainder 0

5/2 we get remainder 1

2/2 we get remainder 0

1. Now take the 1

The answer to the question is

(21)10=(10101)2

contrast moral and immoral creativity and innovation

Answers

Moral creativity and innovation are based on original discoveries,  whereas immoral innovation is based on unscrupulous actions.

What is innovation?

Innovation refers to the practices aimed at developing new products and services for the well-being of society.

Moral innovation is an expression generally used to describe technological advancements based on intellectual property rights.

In conclusion, moral creativity and innovation are based on original discoveries,  whereas immoral innovation is based on unscrupulous actions.

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9. The highest voltage typically encountered on the job by a residential electrician is
volts.
A. 120
B. 600
C. 240
D. 480

Answers

Answer:

240

Explanation:

9. The highest voltage typically encountered on the job by a residential electrician isvolts.A. 120B.

The highest voltage typically encountered on the job by a residential electrician is C. 240 volts.

What is voltage?

Voltage is the measure of the difference in electrical power between two points in a circuit.

It is like the force that pushes electric charges in a circuit and is measured in volts (V) and affects how strong the electric current flows in a wire.

In many countries, the United States included, residential electrical systems often use a split-phase setup with a voltage of 120/240 volts.

This voltage is widely used for things like household appliances, lights, and other electrical needs in homes.

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the wooden framework built to support and arch during construction is called

Answers

The wooden framework built to support an arch during construction is called a "centering" or "formwork."

Centering refers to the temporary structure that is made of wooden beams and planks that are used to support the weight of the arch and any construction materials until the arch is completed and can support itself.

The centering provides stability and helps maintain the shape of the arch during the construction process. Once the arch is fully constructed and set, the centering is removed. The careful placement and alignment of the centering are crucial to ensure the accurate and precise construction of the arch.

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F= 10kN
G= 20kN
member lengths are 4m

F= 10kNG= 20kNmember lengths are 4m

Answers

2.1) The support reactions are calculated now: \(A_{x} = 10\,kN\), \(A_{y} = -10\,kN\), \(B_{y} = 30\,kN\).

2.2) The member CD is on tensile load and the member BC is on compressive load. \(F_{BC} \approx 28.284\,kN\), \(F_{CD} = 20\,kN\)

How to analyze a system in static condition

The dynamic situation of a mechanical system whose geometry cannot be neglected is described by Newton's laws and D'Alembert's principle. A planar system in equilibrium is described by the following formulae:

\(\sum F_{x} = 0\)     (1)

\(\sum F_{y} = 0\)     (2)

\(\sum M = 0\)     (3)

2.1) The support reactions can be found by assuming that the truss is a rigid solid:

\(\sum F_{x} = A_{x} - F = 0\)    (4)

\(A_{x} = F\)

\(A_{x} = 10\,kN\)

\(\sum M_{A} = F\cdot r_{BD} - G \cdot (r_{AB}+r_{CD}) + B_{y}\cdot r_{AB} = 0\)     (5)

\(B_{y} = \frac{G\cdot (r_{AB}+r_{CD})-F\cdot r_{BD}}{r_{AB}}\)

\(B_{y} =\frac{(20\,kN)\cdot (8\,m)-(10\,kN)\cdot (4\,m)}{4 \,m}\)

\(B_{y} = 30\,kN\)

\(\sum F_{y} = A_{y} + B_{y} - G = 0\)     (6)

\(A_{y} = G - B_{y}\)

\(A_{y} = 20\,kN - 30\,kN\)

\(A_{y} = -10\,kN\)

Note - The negative sign means that the real direction of the component is antiparallel to the assumed one.

2.2) If the entire system is at equilibrium, then every part of the system must be also at equilibrium. The joint is considered a particle and thus the D'Alembert's principle is not necessary. The member CD is on tensile load and the member BC is on compressive load.

\(\sum F_{x} = F_{BC} \cdot \cos 45^{\circ} - F_{CD} = 0\)     (7)

\(\sum F_{y} = -G + F_{BC}\cdot \sin 45^{\circ} = 0\)     (8)

By (8):

\(F_{BC} = \frac{G}{\sin 45^{\circ}}\)

\(F_{BC} \approx 28.284\,kN\)

By (7):

\(F_{CD} = F_{BC}\cdot \cos 45^{\circ}\)

\(F_{CD} = 20\,kN\)

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F= 10kNG= 20kNmember lengths are 4m
F= 10kNG= 20kNmember lengths are 4m

Explain how optimising the use of energy in an industrial
process is a step toward sustainable engineering

Answers

Optimizing the use of energy in an industrial process is a step toward sustainable engineering because it helps to reduce the carbon footprint and conserve natural resources.

This can be achieved by adopting various energy-efficient measures such as reducing energy consumption, using renewable energy sources, and recycling waste products.Increasing the efficiency of the industrial process not only saves energy but also reduces costs, increases productivity, and enhances the competitiveness of the business.

It also helps to minimize the impact of industrial activities on the environment by reducing the amount of greenhouse gases released into the atmosphere.Optimizing energy usage involves making use of cutting-edge technologies that allow for more efficient usage of energy.

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Which of the following terms describes the path from an electrical source to a switch or plug?
transmitter
circuit breaker
raceway
breaker panel

Answers

Answer:

transmitter hope thus helped!

Explanation:

Raceway is the answer

"A raceway is an enclosed conduit that forms a physical pathway for electrical wiring."

helppppppp plssss Identifying job responsibilities for staff members is an example of which section of the project charter?


project requirements

project objectives

project team

project description

Answers

The correct answer is project team.

what does si stand for in the national electrical code

Answers

In the context of the National Electrical Code (NEC), "SI" stands for the International System of Units, also known as the metric system.

The NEC is a standard for electrical installations, adopted in the United States, and it includes provisions for electrical safety, wiring, and other aspects related to electrical systems.

The SI units are widely used in scientific, engineering, and technical fields globally, providing a standardized and coherent system of measurement.

The NEC references SI units for various electrical quantities, such as voltage (volts), current (amperes), resistance (ohms), power (watts), and others.

By adopting SI units, the NEC aligns with international standards and promotes consistency and compatibility in electrical installations.

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All behavior has
A) A good reason
B) Ethical endangerment
C) Danger
D) Consequences

Answers

Answer: d consequences

Explanation:

Professor Gordon Holloway and his students at the University of New Brunswick went to a fast-food emporium and tried to drink chocolate shakes (p ~ 1200 kg/m', u ~ 6 kg/m-s) through fat straws 8 mm in diameter and 30 cm long. (a) Verify that their human lungs, which can develop approximately 3000 Pa of vacuum pressure, would be unable to drink the milkshake through the vertical straw. (b) A student cut 15 cm from his straw and proceeded to drink happily. What rate of milkshake flow was produced by this strategy?

Answers

The pressure drop across the straw is greater than the maximum vacuum pressure the lungs can produce, so, the students would be unable to drink the milkshake.

Can students drink the shakes through fat straw?

The pressure drop across the straw can be calculated using the Hagen-Poiseuille equation which is ΔP = (8μLQ)/(πr⁴)

ΔP = pressure drop

μ = viscosity of the shake

L = length of the straw

Q = flow rate

r = radius of the straw.

Substituting the values, we get:

ΔP = (8 x 6 x 0.3 x Q)/(π x (8 x 10^-3)⁴)

ΔP = 1181103.52Q

The maximum vacuum pressure the human lungs can develop is 3000 Pa. Converting to Pascals, we get:

3000 Pa = 3000 N/m²

So, the pressure drop across the straw is greater than the maximum vacuum pressure the lungs can produce.

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4.
Describe the correct use of any equipment used to protect the health and safety of themselves and
their colleagues

Answers

Items such as gloves, safety goggles, shoes, earplugs, respirators, hard hats, coveralls, vests, and full body suits are examples of personal protection equipment.

What equipment is used for safety and protection?

Wearing a safety helmet when using a power tool, donning the proper protective clothing when working with chemicals, and taking all necessary safety precautions when operating machinery are all examples of how to use equipment correctly to safeguard their own health and the health and safety of their coworkers.

Healthcare Facilities Using PPE Gloves shield the hands; gowns or aprons shield the skin or clothing; masks and respirators shield the mouth and nose; goggles shield the eyes; and face shields shield the full face. consisting of goggles, gloves, gowns, shoe covers, head coverings, masks, and respiratory equipment.

PPE, or personal protective equipment, is gear that shields users from harm to their health or the danger of accidents. It may consist of equipment like safety harnesses, gloves, eye protection, high-visibility clothes, safety footwear, and respiratory protective equipment (RPE).

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Imagine a cantilever beam fixed at one end with a mass = m and a length = L. If this beam is subject to an inertial force and a uniformly distributed load = w, what is the moment present at a length of L/4?

Answers

Answer:

jsow

hfhcffnbxhdhdhdhdhdhdddhdhdgdhdhdhdhdhdhhhdhdjsksmalalaksjdhfgrgubfghhhhhhh

Explanation:

j

grudb

a 6-in.-diameter concrete test cylinder is loaded with a compressive force of 113.1 kips, as shown. determine the stress in the cylinder.

Answers

The stress in a concrete test cylinder can be determined by calculating the compressive force acting on the cylinder and dividing it by the cross-sectional area of the cylinder.

The cross-sectional area of the 6-in.-diameter cylinder can be calculated as follows:

A = π * r^2

where r is the radius of the cylinder, given as r = 6 in. / 2 = 3 in.

A = π * 3^2 = 28.26 in.^2

The compressive force acting on the cylinder can be determined from the given value of 113.1 kips.

The stress in the cylinder can be calculated by dividing the compressive force by the cross-sectional area:

σ = F / A = 113.1 kips / 28.26 in.^2 = 4 ksi

This stress is the average normal stress acting on the cylinder. It represents the force per unit area acting on the cylinder due to the applied compressive load.

In conclusion, the stress in a concrete test cylinder can be determined by calculating the compressive force acting on the cylinder and dividing it by the cross-sectional area of the cylinder. In the case of the 6-in.-diameter cylinder loaded with 113.1 kips, the stress was calculated to be 4 ksi. This stress is the average normal stress acting on the cylinder.

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Which step in the reverse-engineering process involves the identification of subsystems and their relationship to one another?

Answers

The answer is analyze

The starting device usually used on single phase, fractional horsepower motors requiring low starting torque is the

Answers

The starting device usually used on single-phase, fractional horsepower motors requiring low starting torque is the current relay.

How tons cutting-edge relay is wanted energized?

This is the minimal cutting-edge, the relay expects to float thru the now shorted contacts whilst the relay is became on (forty mA). The load may be much less than that too however relay won't stay sufficient for range of cycles of operation referred to withinside the information sheet. The minimum running voltage to your precise relay is 3. seventy-five V.

A cutting-edge relay is a kind of electromagnetic transfer used as a part of the manipulating structures for electric equipment. These relays are generally used as sensors (cutting-edge sensor/tracking relays) to screen cutting-edge float inside the business and different safety-touchy equipment current beginning relays are used on single-phase, fractional horsepower cars requiring low beginning torque.

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what is the most common type of suspensions system used on body over frame vehicles?

Answers

Answer:

Engine

Explanation:

Semi-independent suspension is the most common type of suspension system used on body over frame vehicles.

What is a Semi-independent suspension?

Semi-independent suspension give the front wheels some individual movement.

This suspension only used in rear wheels.

Thus, the correct option is Semi-independent suspension

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The scale of the blueprint tells us the
of drawing to real space?

Answers

Answer:

yes

Explanation:

blueprint of the construction is a prediction of project its is slightly auto cad

Large electrical currents are often carried in aluminum conductors. Consider a long, 2-cm-diameter cable covered by insulation 2 mm thick. For a particular application, the outside insulation temperature is limited to 35 °C, and none of the insulation can exceed 50 °C. The cable is in an environment in which the convective heat transfer coefficient is 25 W/m^2.K, the air temperature is 24°C, the insulation thermal conductivity is 0.10 W/m·K, and the electrical resistance per unit length of the wire is 3.9 x 10^-4 Ω/m. Determine the maximum current allowed (in A).

Answers

The maximum current allowed in the long, 2-cm-diameter cable covered by insulation 2 mm thick is approximately 1300 A. To determine the maximum current allowed, we need to consider the heat generated by the electrical current and its effect on the insulation temperature.

The heat generated per unit length of the wire can be calculated using the formula: \(heat = I^2 R\), where I is the current and R is the electrical resistance per unit length. In this case,\(heat = (I^2) (3.9 \times 10^{-4} \Omega/m)\). The heat generated must be dissipated through convection from the cable's surface. The rate of heat dissipation can be calculated using the formula: \(Q = hA(T_s - T_a)\), where Q is the heat dissipation rate, h is the convective heat transfer coefficient, A is the surface area of the cable, Ts is the surface temperature of the insulation, and Ta is the air temperature.

By equating the heat generated to the heat dissipation rate, we can solve for the maximum current allowed. Considering the cable's diameter and insulation thickness, we can calculate the surface area of the cable. By substituting the given values, including the temperature limits, we find that the maximum current allowed is approximately 1300 A.

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An AC bridge has 4 arms. In arm AB, a 120 kilo-ohm resistor and a 47 microfarads capacitor are connected in parallel while arm BC has 330 microfarads capacitor. If arm AD has a 330 kilo-ohm resistor, calculate the value of the unknown capacitor and resistor in arm CD connected in series. (AC power is supplied through A and C while the detector is connected across BD)

Answers

The unknown capacitor in arm CD must have a value of 330 microfarads, and the unknown resistor must have a value of 100 kilo-ohms.

To solve the problem, use the following formula:
Cseries = C1 x C2 / (C1 + C2)

Where C1 is the value of the capacitor in arm AB (47 microfarads) and C2 is the value of the capacitor in arm BC (330 microfarads).

Therefore, Cseries = 330 microfarads.

Also, the total resistance of arms CD is the sum of the resistance of the resistor (R) and the reciprocal of the capacitive reactance of the capacitor (1/Xc).

Using the following formula:
Rtotal = R + 1/Xc

Where Xc = 1/2πfC,

f is the frequency and C is the capacitance.

For this problem,

Xc = 1/2π(50)(330 x 10-6)

=> 100 kilo-ohm.

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a special construct used in a shell script to alter the flow of the program based on the outcome of a command or contents of a variable. common decision constructs include if, case, &, and ||.

Answers

We are referring to is "Conditional Statements" or "Decision Constructs" in shell scripting. Conditional statements are used to alter the flow of a program based on certain conditions or the outcome of a command or the contents of a variable.

The common decision constructs in shell scripting include:

if statement: The if statement allows you to execute a block of code if a certain condition is true. It has the following syntax:

if condition

then

   # code to be executed if condition is true

else

   # code to be executed if condition is false

fi

case statement: The case statement is used to match the value of a variable against multiple patterns and execute corresponding code blocks. It has the following syntax:

css

case variable in

   pattern1)

       # code to be executed if pattern1 matches

       ;;

   pattern2)

       # code to be executed if pattern2 matches

       ;;

   ...

   *)

       # code to be executed if no pattern matches

       ;;

esac

logical operators: The logical operators && (AND) and || (OR) are used to combine multiple conditions and control the flow of the program based on the outcome. For example:

command1 && command2

The command2 is executed only if command1 succeeds (returns an exit status of 0).

command1 || command2

The command2 is executed only if command1 fails (returns a non-zero exit status).

These decision constructs provide flexibility in controlling the program flow and allow you to handle different scenarios based on conditions and variables.

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How many times will be body of the FOR loop execute. (note the semicolon at the end of FOR statement
for (int i=0; i<20;i++);
{
//body of for loop
}
O Syntax error
O 20
O 21
O Infinite Loop
will save this response

Answers

Answer:

Explanation:

code in the curly braces is treated as regular body and will be executed normally

A. A solidified lava flow containing zircon mineral crystals is present in a sequence of rock layers that are exposed in a hillside.A mass spectrometer analysis was used to count the atoms of uranium-235 and lead-207 isotopes in zircon samples from thelava flow. The analysis revealed that 71% of the atoms were uranium-235, and 29% of the atoms were lead-207. Refer toFIGURE 8.11 to help you answer the following questions.1. About how many half-lives of the uranium-235to lead-207 decay pair have elapsed in the zircon crystals? ______________2. What is the absolute age of the lava flow based onits zircon crystals? Show your calculations.3. What is the age of the rocklayers above the lava flow? _______________4. What is the age of the rocklayers beneath the lava flow? _______________B. Astronomers think that Earth probably formed at the same time as

Answers

Answer:

1. 0.494

2. = 352.299 million years

3. It is between 0 years to 352.299 million years

4. greater than the 352.299 million years.

Explanation:

Given

Uranium 235 ———— lead 207( zircon sample)

t= 0 100%. 0%

t= t. 71%. 29%

1)- half lives elapsed = n

(1/2)n = 0.71

By taking log and solving n = 0.494

No of half lives = 0.494

2) Calculating the age of the larva

- age of lava flow = half life of uranium 235 x n

= 713 x 0.494

= 352.299 million years

3)- The rock layers was created above this lava flow is of later occurrence so the age will be lower than that of the age of the lava flow so the age of rock over the lava flow will lower than the 352.299 million years it will be in between 0 years to 352.299 million years.

4)- The rock layers created underneath this lava flow is of earlier occurrence so its age is more than that of the age of the lava flow so the age of rock will more than the lava flow is greater than the 352.299 million years.

B. The astronomers think the earth was created as all of the other rock materials in our solar system, including the oldest meteorites. The oldest meteorites ever found on Earth contain nearly equal amounts of both Uranium-238 and Lead-206.

The number of half-lives of the uranium-235to lead-207 decay pair have elapsed in the zircon crystals is; 0.494

What is the number of half lives?

We are given;

The atoms of Uranium-235 and lead-207 which made up the zircon sample.

At t = 0; Uranium-235 is 100% while lead-207 is 0%

At t = t;  Uranium-235 is 71% while lead-207 is 29%

1) Let the half lives that elapsed be n. Thus;

(¹/₂)ⁿ = 0.71

n*log0.5 = log 0.71

n = (log 0.71)/(log 0.5)

n = 0.494

Thus;

Number of half lives = 0.494

2) Formula to get the absolute age of the larva is;

Absolute age age of lava flow = half life of uranium-235 * n

The half life of uranium-235 is 713 million years. Thus;

Absolute age age of lava flow  = 713 * 0.494

Absolute age of lava flow = 352.22 million years

3) The rock layers above the lava flow were created after the lava flow and so the age will be lower than that of the age of the lava flow. Thus, it's age will be between 0 years and 352.299 million years.

4) A: The rock layers beneath the lava flow were in existence earlier than the lava flow and as such, the age of rock layers beneath the lava flow will be greater than 352.22 million years.

B; The astronomers think the earth was created as all of the other rock materials in our solar system.

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differential manometer is used to measure the pressure change caused by a flow constriction in a piping system as shown. determine the pressure difference between points aand bin psi. which section has the higher pressure?

Answers

The pressure drop between heated air and cold water can be measured with differential manometers.

What is the differential manometer's working principle?

A manometer works by connecting one end to a gas that is sealed to measure the source of pressure. However, its opposite end is exposed to the earth's atmospheric pressure. It is more sensitive. It is accurate well. The design and operation of it are straightforward. The pressure difference can be calculated based on basic principles and does not need to be calibrated against any standard. As particles flow through orifices and filters, differential pressure is used to determine if a pipeline has any clogs or contaminants. A change in pressure, which results in an increase or decrease in differential pressure, will occur if a portion of the pipe becomes blocked.

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Masking decisions are made when developing a refinishing plan.

True

O False

Table of Contents

Answers

Masking decisions are made when developing a refinishing plan: True.

What is a refinishing plan?

A refinishing plan can be defined as a process through which automobile vehicles or other mobile equipment are coated with a paint and masking tape during repair, so as to beautify them and give it a new look.

This ultimately implies that, masking decisions are made by an engineer when developing a refinishing plan.

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Which statement best describes how power and work are related?
O A. Power is the ability to do more work with less force.
O B. Power is a measure of how quickly work is done.
O C. Power and work have the same unit of measurement
O D. Power is the amount of work needed to overcome friction.
Pls answer quick

Answers

B

a jsdnjwevhfgruewbkuwygru

A shaft of a circular cross section is supported by two housings at B and C. The shaft
is subjected to static loads: concentrated force N applied by gear D and an applied torque T. The yielding strength of the shaft is Sy, and the diameter of the shaft is d. For circular cross sections, | = nd*/64, J = md*/32. The length of the shaft is L. Transverse shear stress is ignored here.

1) Draw the bending moment diagram of the shaft. Specify the location of the weakest (most dangerous) cross section A on bending moment diagram.

2) Draw the weakest point(s) on cross section A.

3) Determine the von-Mises stress at the weakest point(s).

4) Determine the factor of safety n based on Distortion Energy Theory.

A shaft of a circular cross section is supported by two housings at B and C. The shaftis subjected to

Answers

Answer:

1) The bending moment diagram of the shaft is shown in Figure 1. The weakest cross section A is located at the point where the bending moment is maximum.

2) The weakest point on cross section A is located at the point where the bending moment is maximum.

3) The von-Mises stress at the weakest point is given by:

σ = M/I

where M is the bending moment and I is the moment of inertia of the cross section.

4) The factor of safety n is given by:

n = Sy/σ

where Sy is the yield strength of the shaft and σ is the von-Mises stress at the weakest point.

Explanation:

Hope this helps!

A hydrogenation catalyst is prepared by soaking alumina particles (100-150 mesh size) in aqueous NiNO3 solution. After drying and reduction, the particles contain about 7 wt% NiO. This catalyst is then made into large cylindrical pellets for rate studies. The gross measurements for one pellet are: Mass, g 3.15 Diameter, mm 25 Thickness, mm 6 Volume, cm3 3.22 The alumina particles contain micropores, and the pelleting process introduces macropores surrounding the particles. If the macropore volume of the pellet is 0.645 cm3 and the micropore volume is 0.40 cm3 /g of particles, determine: i] The density of the pellet ii] The macropore volume in cm3 /g iii] The macropore void fraction in the pellet iv] The micropore void fraction in the pellet v] The solid fraction vi] The density of the particles

Answers

i] The density of the pellet is 0.977 g/cm^{3}. ii] The macropore volume in cm^{3}/g is 0.205 cm^{3}/g. iii] The macropore void fraction in the pellet is 25.1%.iv] The micropore void fraction in the pellet is 49.0%. v] The solid fraction of the pellet is 25.9%. vi] The density of the particles is 1.222 g/cm^{3}.

i] To determine the density of the pellet, we can use the formula:

Density = Mass / Volume

Given that the mass of the pellet is 3.15 g and the volume is 3.22cm^{3}, we can calculate the density as follows:

Density = 3.15 g / 3.22 cm^{3}≈ 0.977 \(g/cm^{3\)

ii] The macropore volume in cm3/g can be calculated by dividing the macropore volume of the pellet (0.645 cm3) by the mass of the pellet (3.15 g):

Macropore volume = 0.645 cm^{3} / 3.15 g ≈ 0.205 \(cm^{3} /g\)

iii] The macropore void fraction in the pellet can be calculated using the formula:

Macropore void fraction = Macropore volume / Total volume of the pellet

Total volume of the pellet = Volume - Macropore volume = 3.22 cm^{3}- 0.645 cm^{3} = 2.575 cm^{3}

Macropore void fraction = 0.645 cm^{3} / 2.575 \(cm^{3}\)≈ 0.251 or 25.1%

iv] The micropore void fraction in the pellet can be calculated using the given micropore volume of the particles (0.40 cm^{3} /g) and the mass of the pellet (3.15 g):

Micropore volume in the pellet = Micropore volume/g x Mass

Micropore volume in the pellet = 0.40 \(cm^{3} /g\) x 3.15 g = 1.26 cm3

Micropore void fraction = Micropore volume in the pellet / Total volume of the pellet

Micropore void fraction = 1.26 \(cm^{3}\) / 2.575 \(cm^{3}\) ≈ 0.490 or 49.0%

v] The solid fraction of the pellet can be calculated by subtracting the sum of macropore and micropore void fractions from 1:

Solid fraction = 1 - (Macropore void fraction + Micropore void fraction)

Solid fraction = 1 - (0.251 + 0.490) ≈ 0.259 or 25.9%

vi] The density of the particles can be determined using the mass of the pellet (3.15 g) and the total volume of the particles:

Total volume of the particles = Volume - Macropore volume = 3.22 \(cm^{3}\)- 0.645 \(cm^{3}\) = 2.575\(cm^{3}\)

Density of the particles = Mass / Total volume of the particles

Density of the particles = 3.15 g / 2.575\(cm^{3}\) ≈ 1.222 \(g/cm^{3}\)

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