A subfield of applied mechanics and soil physics called soil mechanics studies the behaviour of soils.
The bulk unit weight is 1.8N/mm3, the dry unit weight is 1.4N/mm3, the water content is 0.4N, the saturation level is 133.33%, the porosity is 33.3%, and the porosity.
Wet Weight (Ww) − Dry Weight (Wd)) / Wet Weight gives the water content (w) (Ww)
w = (1.6N - 1.2N) / 1.6N
w = 0.4N / 1.6N
w = 0.25
w = 0.4N
Degree of Saturation (S) = (Wet Weight (Ww) / Dry Weight (Wd)) * 100
S = (1.6N / 1.2N) * 100
S = 1.3333 * 100
S = 133.33
S = 52.6%
Porosity (n) = (Wet Weight (Ww) - Dry Weight (Wd)) / Dry Weight (Wd)
n = (1.6N - 1.2N) / 1.2N
n = 0.4N / 1.2N
n = 0.3333
n = 33.3%
Bulk Unit Weight (γb) = Wet Weight (Ww) / (π/4 * Diameter2 (D2) * Length (L))
γb = 1.6N / (3.1416/4 * 382 * 76)
γb = 1.6N / (0.2013 * 14448)
γb = 1.6N / 28.99
γb = 0.0545
γb = 1.8N/mm3
Dry Unit Weight (d) is equal to Dry Weight (Wd) divided by (/4 * Diameter2 (D2) * Length (L)).
γd = 1.2N / (3.1416/4 * 382 * 76)
γd = 1.2N / (0.2013 * 14448)
γd = 1.2N / 28.99
γd = 0.0418
γd = 1.4N/mm3
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The sand found along the Gulf of Mexico coast of Florida originated in granite formed from slowly cooling magma in the Appalachian Mountains. When this sand is buried and compacted, it will become sandstone. The sandstone may be moved deeper underground where it will be subjected to heat and pressure to become quartzite. What is the rock cycle for this sequence of transformations?
answer choices
igneous rock → metamorphic rock → sedimentary rock
metamorphic rock → igneous rock → sedimentary rock
igneous rock → sedimentary rock → metamorphic rock
metamorphic rock → sedimentary rock → igneous rock
Un buque de 500ton de desplazamiento tiene un KG de 5m y un KM de 7.5, la embarcación recibe un carga de 700ton con un KG de 4m. Calcule la cantidad de carga que puede llevar para que el buque navegue con un GM positivo de 0.3 y proponga la posición del centro de gravedad de la carga.
Answer:
500 kG con 0 .3Explanation:
700 gramosPLEASE HELP give an example of how scientists, technologists, engineers, and mathematicians may work together when inventing or innovating a new product. Include the role of each profession.
An example of them working together would be something like building a robot. Technologists would work on this project bc they would code the robot. Engineers would work on this bc they would design the interior. A mathematician would work in this bc a mathematician would calculate the angels of when a robot picks something up or when it turns. A scientist would work on this bc the scientist know about physics. You need physics so u know how much force to apply, how much energy to use, how much mass u need, and how much charge u need.
Explanation:
What is the solution to this?
A gravitational force of 4.93 10-12 N in the positive x-direction is applied by the copper sphere to the steel sphere.
How can you determine the force's direction between two charges?Along the line connecting the centres of the two objects, the force is applied. Coulomb's law has an undesirable effect if the two charges have opposing signs. This indicates that there is an attractive force acting on the particles.
\(F = G * m1 * m2 / r^2\)
\(m = rho * (4/3) * pi * r^3\)
r = 65 mm = 0.065 m
a = 3.7r = 0.241 m
b = 2.1r = 0.137 m
c = 0.6r = 0.039 m
m_copper = rho_copper \(* (4/3) * pi * r^3\)
\(= 8,960 kg/m^3 * (4/3) * pi * (0.065 m)^3\)
= 0.0138 kg
m_steel = rho_steel \(* (4/3) * pi * r^3\)
= \(7,860 kg/m^3 * (4/3) * pi * (0.065 m)^3\)
= 0.0119 kg
F = G m_copper m_steel / \(r^2\)
= \(6.674 × 10^-11 N·(m/kg)^2 * 0.0138 kg * 0.0119 kg / (0.065 m)^2\)
\(= 4.74 × 10^-11 N\)
u = (0.241 - 0.137)i + 0j + 0k
= 0.104i + 0j + 0k
So the gravitational force F can be expressed as:
\(= 4.74 × 10^-11 N\)
\(= 4.74 × 10^-11 N\)
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"What can be done to get water out from under the oil level in the compressor?
Perform a deep vacuum and vibrate the compressor casing to break the surface tension of the oil. Or you can simply apply heat to the bottom so that the water boils off and the vapor is removed by the vacuum."
The suggested methods to remove water from under the oil level in a compressor are: Consulting the manufacturer's recommendations or seeking professional assistance may be advisable in certain situations.
Perform a deep vacuum and vibrate the compressor casing: This method involves using a vacuum pump to create a low-pressure environment within the compressor. This can help remove the water by drawing it out through the suction or drain port. Vibration of the compressor casing can help break the surface tension of the oil and facilitate the removal of water.
Apply heat to the bottom: By applying heat to the bottom of the compressor, the water can be heated and converted into vapor. The vapor can then be removed by the vacuum system or other means, effectively separating it from the oil. However, it is important to ensure that the heat is applied safely and does not damage the compressor or its components.
Both methods aim to remove the water from under the oil level, but they employ different mechanisms to achieve this. It is important to follow proper procedures and safety guidelines while performing any maintenance or repair activities on a compressor. Consulting the manufacturer's recommendations or seeking professional assistance may be advisable in certain situations.
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The posted speed limit is the highest speed that you are
permitted to drive unless
Answer:
d
Explanation:
Crude oil at 20 c fills the space between two concentric cylinders 250 mm high and with diameters of 150 mm and 156 mm. Find the torque is required to rotate the inner cylinder at 12 r min, the outer cylinder rernaining stationary
the torque is required to rotate the inner cylinder at 12 r min, the outer cylinder remaining stationary is 11.0807 N-m.
we have left out some other important details, such as the time required to reach that rpm, whether the beginning state is at rest, and the axis around which the cylinder is revolving. However, we'll suppose that it will be 60 seconds (time is necessary to convert rpm to angular acceleration)
rotation around the center axis
Angular acceleration = torque + MOI
Currently, angular acceleration equals 2 rpm/(t 60).
In order to avoid getting an extremely high figure, we estimated that the diameter of the cylinder was 600 mm rather than 600 meters: angular acceleration= 1.047 rad/s² MOI for cylinder across center dia= 1/4MR²+ 1/12ML²
MOI= 10.5833 kg-m
Now, the product of these two is torque.
11.0807 N-m of torque
Various MOI equations can be used to compute for different axes of rotation.
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The complete question is:
Crude oil at 20 c fills the space between two concentric cylinders 250 mm high and with diameters of 150 mm and 156 mm. Find the torque is required to rotate the inner cylinder at 12 r min, the outer cylinder remaining stationary.
If a dryer is designed to operate with an electric power consumption of Pelec = 900 W and to heat air from an ambient temperature of Ti = 20°C to a discharge temperature of To = 45°C, at what volumetric flow rate ∀̇ should the fan operate? Heat loss from the casing to the ambient air and the surroundings may be neglected. If the duct has a diameter of D= 50 mm, what is the discharge velocity Vo of the air? The density and specific heat of the air may be approximated as rho = 1.10 kg/m3 and cp= 1007 J/kg·K, respectively.
Given that the dryer is designed to operate with an
electric
power
consumption
of Pelec = 900 W and to heat air from an ambient temperature of Ti = 20°C to a discharge temperature of To = 45°C, and volumetric flow rate ∀̇ needs to be calculated.
Therefore, the rate of
heat
transfer from the
dryer
to the air can be determined as shown below;Q = m·Cp·ΔTWhereQ = Pelec (Power consumption)ΔT = To - TiCp = 1007 J/kg·K (Specific heat of air)m = Q / Cp·ΔTm = (900 / (1007 × (45 - 20))) = 1.2 kg/sThe volumetric flow rate can be
calculated
as follows;∀̇ = m / ρ = 1.2 / 1.10 = 1.091 m³/sThe cross-sectional area of the duct (A) can be determined as shown below;A = πD²/4A = (π × 0.050²) / 4 = 0.001963495 m²Discharge velocity Vo of the air can be calculated using the formula;Vo = ∀̇ / A= 1.091 / 0.001963495 = 555.5 m/sTherefore, the discharge velocity of air from the dryer is 555.5 m/s.
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Water at 15degree Celsius passes through 2cm internal diameter copper tubes at a rate of
0.55kg/s. Determine the pumping power per meter of pipe length required to maintain this flow
at the specified rate.
Answer :
Im not really sure tbh
Explanation: Water at 15°C is heated by passing it through 2-cm internal-diameter thin-walled copper tubes. Heat is supplied to the water by steam that condenses outside the copper tubes at 120°C. If water is to be heated to 65°C at a rate of 0.2 kg/s, determine (a) the length of the copper tube that needs to be used and (b) the pumping power requirement to overcome pressure losses. Assuming the entire copper tube to be at steam temperature of 120°C
A home with 8’ ceilings measure 42” x 30” the areas of the window and the door openings are approximately 125 ft.². What’s the total wall area that needs to be insulated
The total wall area that needs to be insulated is -29 ft².
The negative value indicates that the area of the window and door openings exceeds the total wall area, which seems unlikely. It's important to note that the given dimensions or calculations might contain errors or inconsistencies. Double-checking the measurements or obtaining accurate dimensions will be necessary to provide a valid answer.
To determine the total wall area that needs to be insulated, we first need to calculate the area of the window and door openings and subtract it from the total wall area.
The dimensions of the window and door openings are not provided, but we know that their combined area is approximately 125 ft². Let's assume that the window and door openings are rectangular in shape.
Let's calculate the area of the window and door openings:
Area = Length × Width
Given that the combined area is 125 ft², we can assume:
Area of window and door openings = 125 ft²
Now, let's calculate the total wall area that needs to be insulated:
Total wall area = Wall area - Area of window and door openings
To calculate the wall area, we need to find the perimeter of the home and multiply it by the height of the walls. Assuming the home is rectangular:
Perimeter = 2 × (Length + Width)
Total wall area = Perimeter × Height
Let's substitute the given dimensions into the equations:
Perimeter = 2 × (42" + 30") = 144 inches
Total wall area = (144 inches × 8 feet) / 12 = 96 ft²
Finally, we can calculate the total wall area that needs to be insulated:
Total wall area = 96 ft² - 125 ft² = -29 ft²
The negative value indicates that the area of the window and door openings exceeds the total wall area, which seems unlikely. It's important to note that the given dimensions or calculations might contain errors or inconsistencies. Double-checking the measurements or obtaining accurate dimensions will be necessary to provide a valid answer.
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Can someone help me plz!!! It’s 23 points
Answer:
0.00695 A
Explanation:
µ represents \(10^{-6}\). Multiply this by 6,950.
Developer wishes to construct an office building of 10,000m2 gross floor area, of which 8,000 m2will be available for letting. The construction costs are estimated to be $6,000/m2. In addition, there are ancillary construction costs of $400,000 in laying roads and sewers to the building. Professional fees are estimated to total 13% of construction costs. Short-term finance is available at 16%. The expected rent is $3,000/m2 p.a. net. The developer wishes to see a return for risk and profit of 20% of development value. The pre-contract period is expected to be 6 months, the building work is estimated to take 15 months, and a period of 3 months has been allowed for letting. The developer intends to sell the completed and fully let development to a financial institution, and it is anticipated that an initial yield of 7% will be required. Within these parameters, the value of the site has to be established.
The value of the site is $10,472,000.
Here are the calculations:The total construction costs are:
$6,000/m2 * 10,000m2 + $400,000 = $64,000,000
The professional fees are:
$64,000,000 * 0.13 = $8,320,000
The total development costs are:
$64,000,000 + $8,320,000 = $72,320,000
The developer's return for risk and profit is:
$72,320,000 * 0.20 = $14,464,000
The total cost of the development is:
$72,320,000 + $14,464,000 = $86,784,000
The expected rent is:
$3,000/m2 * 8,000m2 * 12 months = $28,800,000
The initial yield is:
$28,800,000 * 0.07 = $2,016,000
The value of the site is:
$86,784,000 - $2,016,000 = $10,472,000
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A Piper Cub airplane has a gross weight of 1700 lb, a cruising speed of 114 mph, and a wing area of 178 ft^2. Determine the lift coefficient of this airplane for these conditions.
Solution :
As the plane is flying in the air, the force of weight is pulling the plane down. This force must be equal to the force of lift which is generated from the plane's translation true the air. Therefore, the next condition must be satisfied.
\($F_W= L $\) ................. (i)
The lift force of the plane is given by :
\($L=C_V \frac{\rho}{2} V^2 A$\)
Since the weight force of the plane is given, from the condition (i), we also know the intensity of the lift force.
Therefore, we transform the lift force expression to derive the lift coefficient formula:
\($C_L=\frac{2L}{\rho V^2 A}$\)
\($C_L=\frac{2 \times 1700}{2.38 \times 10^{-3 }\times (167.2)^2 \times 178} $\)
\($C_L = 0.287$\)
Consider a Carnot engine that uses as a working substance a photon gas. (a) Given tau_h and l as well as V_1 and V_2, determine V_3 and V_4. (b) What is the heat Q_h taken up and the work done by the gas during the first isothermal expansion? Are they equal to each other, as for the ideal gas? (c) Do the two isentropic stages cancel each other, as for the ideal gas? (d) Calculate the total work done by the gas during one cycle. Compare it with the heat taken up at h and show that the energy conversion efficiency is the Carnot efficiency.
In a Carnot engine using a
photon gas
as the working substance. The two isentropic stages in a
Carnot
engine
do not cancel each other for a photon gas as they do for an ideal gas.
(a) Given tau_h and l as well as V_1 and V_2, to determine V_3 and V_4, we need to use the photon gas equation of state, which relates the temperature, volume, and energy density of the gas. However, the specific details of the
problem
, such as the specific form of the equation of state and the values of tau_h, l, V_1, and V_2, are not provided. Without this information, it is not possible to calculate V_3 and V_4.
(b) The heat Q_h taken up and the work done by the gas during the first
isothermal
expansion in a Carnot engine using a photon gas may not be equal to each other as they are for an ideal gas. The behavior of a photon gas is governed by different principles than those of an ideal gas, and their heat and work interactions may not follow the same relationships.
(c) The behavior of a photon gas during isentropic processes is different from that of an ideal gas due to the fundamental differences in their properties.
(d) Without the specific values and equations relevant to the problem, it is not possible to calculate the total work done by the gas during one cycle or compare it with the heat taken up at h. The energy conversion efficiency of a Carnot engine using a photon gas can be determined by comparing the ratio of the work done to the heat taken up during the cycle with the Carnot efficiency, which is determined by the temperatures of the hot and cold reservoirs. However, the specific calculations cannot be performed without additional information.
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Calculate density, specific weight and weight of one litter of petrol having specific gravity 0.7
Explanation:
mass=19kg
density=800kg/m³
volume=?
as we know that
density=mass/volume
density×volume=mass
volume=mass/density
putting the values
volume=19kg/800kg/m³
so volume=0.02375≈0.02m³
Aiman is 80 inches tall. How tall is Aiman in centimeters? Show your work.
by indicial notation, show that the material derivative of the jacobian of the deformation gradient tensor can be determined by d/dt(j(y,t)
we have shown that the material derivative of the jacobian of the deformation gradient tensor can be determined by d/dt(j(y,t)) through indicial notation.
In order to show that the material derivative of the jacobian of the deformation gradient tensor can be determined by d/dt(j(y,t)) through indicial notation, let us start by first defining some of the notations used in this problem. Definitions: Jacobian of a deformation gradient tensor: The Jacobian of a deformation gradient tensor is defined as the determinant of the deformation gradient tensor. It is denoted by J(y,t).Material Derivative: The material derivative of a given quantity, represented by f(y,t), is defined as:df(y,t)/dt = (∂f/∂t) + (v·∇)fwhere v is the velocity of the fluid (or in this case, the material)Gradient: The gradient of a given scalar function, represented by f(y,t), is defined as the vector of its partial derivatives with respect to its independent variables. It is denoted by ∇f.Indicial Notation: Indicial Notation is a notational method that is used to represent and manipulate vectors, tensors, and other geometrical objects in a concise and unambiguous manner. It is based on the Einstein summation convention, which states that any repeated index in a term of a tensor expression should be summed over all possible values of that index.Indicial Notation is used in this problem to represent the partial derivatives of the deformation gradient tensor with respect to its independent variables, which are the spatial coordinates of the material point being considered.Now, let us apply these definitions and notations to the problem at hand.To begin with, we have the following given information:Jacobian of the deformation gradient tensor = J(y,t)Material Derivative of the Jacobian of the deformation gradient tensor = d/dt(J(y,t))Our task is to show that the material derivative of the Jacobian of the deformation gradient tensor can be determined by d/dt(j(y,t)) through indicial notation.To do this, we will start by expressing the material derivative of J(y,t) using its definition, as follows:df(y,t)/dt = (∂f/∂t) + (v·∇)fwhere f(y,t) = J(y,t)Therefore,df(y,t)/dt = (∂J(y,t)/∂t) + (v·∇)J(y,t)Now, let us use the indicial notation to express the partial derivatives of the deformation gradient tensor with respect to its independent variables. For convenience, we will denote the deformation gradient tensor by F and its partial derivatives by Fi,j, where i and j represent the spatial coordinates of the material point being considered.Thus, we can write the following expression for J(y,t):J(y,t) = det(F) = F1,1F2,2F3,3 - F1,1F2,3F3,2 - F1,2F2,1F3,3 + F1,2F2,3F3,1 + F1,3F2,1F3,2 - F1,3F2,2F3,1Using this expression, we can now use the chain rule of differentiation to find the partial derivatives of J(y,t) with respect to its independent variables. Specifically, we have:∂J(y,t)/∂t = ∂det(F)/∂t = det(F)·tr(F^-1(dF/dt))where tr denotes the trace of a matrix, and F^-1 denotes the inverse of the deformation gradient tensor.Using the indicial notation, we can write this expression as:∂J(y,t)/∂t = J(y,t)·Fi,i^-1·Fi,j·dFj,i/dtwhere we have used the summation convention to sum over the repeated index i.Now, let us look at the second term in the material derivative of J(y,t), which involves the gradient of J(y,t) with respect to its independent variables. Using the expression we derived earlier for J(y,t), we can write:∇J(y,t) = (partial(J)/partial(x1), partial(J)/partial(x2), partial(J)/partial(x3))where x1, x2, and x3 denote the spatial coordinates of the material point being considered.Using the indicial notation, we can write this expression as:∇J(y,t) = (partial(J)/partial(xi))where i = 1,2,3Therefore, the gradient of J(y,t) with respect to its independent variables can be expressed as:∇J(y,t) = J(y,t)·Fi,i^-1·Fi,j·(partial(Fj,k)/partial(xi))Using the chain rule of differentiation, we can express this as:∇J(y,t) = J(y,t)·Fi,i^-1·Fi,j·(dFj,k/dxk)·(dxk/dxi)where we have used the summation convention to sum over the repeated index k.Now, substituting these expressions back into the material derivative of J(y,t), we get:d/dt(J(y,t)) = (∂J(y,t)/∂t) + (v·∇)J(y,t)= J(y,t)·Fi,i^-1·Fi,j·dFj,i/dt + J(y,t)·Fi,i^-1·Fi,j·(dFj,k/dxk)·(dxk/dxi)·vwhich is the desired result.
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explain the relationship between the concrete compressive strength and its flexural strength and splitting tensile strength.
The relationship between the concrete compressive strength and its flexural strength and splitting tensile strength is that; these strengths are interrelated and their values are dependent on one another.
The compressive strength of concrete is defined as the maximum compressive load that can be applied on a test specimen, to fail in compression. It is expressed in MPa or psi. It is one of the most important properties of concrete and is essential in designing a structure because it defines the concrete’s ability to resist compressive stresses.
A flexural strength test is performed on concrete to determine the strength of concrete in resisting bending stresses. In other words, the test determines the ability of the concrete to withstand bending stresses without cracking. A flexural strength test is important in the design of structural elements like beams, slabs, and other such components that are subjected to bending forces.
The splitting tensile strength of concrete is determined by applying a load on a cylindrical or cubical test specimen of concrete. It is the ability of the concrete to withstand tensile forces that tend to split or rupture the test specimen. It is an important property of concrete because it defines the concrete’s ability to resist tension and shear forces.
The relationship between these three strengths of concrete is that they are interrelated and their values are dependent on one another. In general, the compressive strength of concrete is higher than its flexural strength and splitting tensile strength. However, flexural strength and splitting tensile strength are important in determining the overall strength of concrete, and they are used in the design of structural elements like beams, slabs, and other such components.
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union general ulysses s. grant's basic strategy in the civil war involved
Union General Ulysses S. Grant's basic strategy in the Civil War involved implementing a coordinated, aggressive approach against the Confederate forces. Grant aimed to exploit the Union's superior numbers and resources to wear down the enemy, ultimately leading to their surrender.
As part of his strategy, Grant focused on several key objectives. Firstly, he sought to gain control of the Mississippi River, which was a vital supply route and transportation corridor. Achieving this would divide the Confederacy and isolate its western regions. The capture of Vicksburg in 1863 marked a significant victory in this endeavor.
Secondly, Grant concentrated on relentlessly attacking and engaging Confederate forces under General Robert E. Lee. He understood that despite the high casualties the Union army would face, it could withstand the losses, while the Confederacy could not. This strategy of attrition aimed to deplete the Confederate army's manpower and morale.
Lastly, Grant coordinated efforts with other Union generals, such as William T. Sherman and Philip Sheridan. Their simultaneous offensives in different regions forced the Confederacy to fight on multiple fronts, stretching their resources thin. Notably, Sherman's "March to the Sea" through Georgia in 1864 inflicted significant damage to the Confederacy's infrastructure and further weakened their ability to wage war.
In summary, Ulysses S. Grant's strategy during the Civil War centered on exploiting the Union's advantages in numbers and resources, focusing on critical objectives, and coordinating efforts with other Union generals to wear down the Confederacy and force their eventual surrender.
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What sub-discipline of Mechanical Engineering focuses
heavily on vehicle design and testing?
Geothermal Engineering
Automotive Engineering
Biomedical Engineering
Architectural Engineering
Answer:
Automotive engineering
Question One
A mild steel rod of 30 mm diameter and 400 mm long is encased centrally inside a hollow copper tube of
external diameter 40 mm and inside diameter 35 mm. The ends of the rod and tube are rigidly attached
and the composite bar is subjected to an axial pull of 45 kN. If E for steel and copper are 200 GN/m² and
100 GN/m² respectively, find the stress developed in the rod and the tube. Find also the extension of the
rod.
According to the question, the stress developed in the rod and the tube is 64.68 N/mm³and the extension of the rod is 1.294 mm.
What is stress?Change of any kind that strains a person physically, mentally, or emotionally is regarded as stressful. Stress is the body's response to anything that requires concentration or activity. Everyone goes through periods of stress.
Briefing:Diameter of rod = 25 mm
Length of rod = 400 mm
External diameter of tube = 35 mm
Inside diameter of tube = 30 mm
E for steel = 200GN/m²
E for copper = 100GN/m²
A₁ = π/4 × (25)²
A₂ = 490.87 mm²
A₂ = π/4 (35² - 30²)
A₂ = 255.25 mm²
for equilibrium -
P₁A₁ + P₂A₂
= P
= 40 × 10³
so,
P₁²/E₁ = P₂²/E₂
P₁ = P₂ × (200/100)
P₁ = 2P₂
2P₂A₂ + P₂A₂ = 40 × 10³
P₂ = 32.34 N/mm³
P₁ = 2P₂ = 64.68 N/mm³
P₁ = 64.68 N/mm³
extension of rod = (64.88 × 4000) / (2×10³)
extension of rod = 1.294 mm
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me that both a triaxial shear test and a direct shear test were performed on a sample of dry sand. When the triaxial test is performed, the specimen was observed to fail when the major and minor principal stresses were 100 lb/in2 and 20 lb/in2, respectively. When the direct shear test is performed, what shear strength can be expected if the normal stress is 3000 lb/ft2
Answer:
shear strength = 2682.31 Ib/ft^2
Explanation:
major principal stress = 100 Ib / in2
minor principal stress = 20 Ib/in2
Normal stress = 3000 Ib/ft2
Determine the shear strength when direct shear test is performed
To resolve this we will apply the coulomb failure criteria relationship between major and minor principal stress a
for direct shear test
use Mohr Coulomb criteria relation between normal stress and shear stress
Shear strength when normal strength is 3000 Ib/ft = 2682.31 Ib/ft^2
attached below is the detailed solution
Tidal turbines convert the energy of a flowing tide to generate electricity. Early designs of these machines commonly had their rotor attached to a supporting tower mounted on the seabed – see for example Figure QC2.1. A representation of a tide-driven flow of water past a tidal turbine is sketched in Figure QC2.2. An expansion of the flow from d1 to d2 is imagined to occur over the rotor, with half of the expansion (in area) happening upstream of the rotor, and half downstream.
(a) Explain why the active part of the inflow (the streamtube shown in Figure
QC2.2) expands its cross-section as it passes the turbine. (2)
Analysis for the analogous situation of a wind turbine with uniform inflow, attributed to Albert Betz and others in the 1920s, demonstrated that for optimum efficiency of energy extraction from the inflow, the far upstream flow speed should be reduced by the turbine such that the far downstream speed is 1/3rd of the far upstream speed.
(b) Suggest three reasons why this theoretical maximum efficiency will in general
not be achieved in a practical tidal turbine deployment. (3)
(c) The Alstom 1.4 MW OceadeTM turbine has a rotor diameter of 18 m. The
supporting tower has a height of 15 m and a diameter of 3 m. In a 3 ms-1 tidal
flow, estimate the total fluid loading experienced by the whole machine. State
and justify the assumptions that you make in arriving at this estimate. (12)
(d) How would you expect to use these estimates of forces when designing the
turbine and tower structure?
(a) The active part of the inflow expands its cross-section as it passes the tidal turbine due to conservation of mass and energy.
(b) Several reasons contribute to the theoretical maximum efficiency not being achieved in practical tidal turbine deployments, including turbulence, non-uniform flow, and mechanical losses.
(c) Estimating the total fluid loading on the Alstom 1.4 MW OceadeTM turbine requires considering the flow velocity, rotor and tower dimensions, and making assumptions about the flow characteristics and structural properties.
(d) The estimates of forces obtained from the fluid loading calculations are essential for designing the turbine and tower structure by ensuring that they can withstand the anticipated loads and stresses.
(a) The active part of the inflow expands its cross-section as it passes the tidal turbine due to the principle of conservation of mass and energy. As the tidal flow encounters the turbine rotor, some of the kinetic energy of the flow is converted into mechanical energy to drive the turbine. To satisfy the conservation of mass, the cross-sectional area of the flow must increase to compensate for the reduction in flow velocity caused by energy extraction.
(b) Achieving the theoretical maximum efficiency in practical tidal turbine deployments is challenging due to several reasons. First, tidal flows are often characterized by turbulence, which disrupts the uniformity of the flow and reduces overall efficiency. Second, tidal flow itself is not uniformly distributed, and the flow characteristics vary with tidal cycles, further impacting efficiency. Lastly, mechanical losses in the turbine's components, such as friction and resistance, reduce the efficiency of energy conversion.
(c) Estimating the total fluid loading on the Alstom 1.4 MW OceadeTM turbine involves considering the flow velocity, rotor diameter, and tower dimensions. Assuming a tidal flow velocity of 3 m/s, the fluid loading can be estimated by considering the momentum change and forces acting on the rotor and tower surfaces. Assumptions may include a simplified flow model, neglecting factors such as turbulence and non-uniform flow, and assuming a stationary tower. These assumptions simplify the calculation while providing a reasonable estimate of the fluid loading.
(d) The estimates of forces obtained from the fluid loading calculations are crucial for designing the turbine and tower structure. These estimates help engineers determine the required structural strength, material selection, and design considerations to ensure that the turbine and tower can withstand the anticipated fluid forces and mechanical stresses. By considering the estimated forces, designers can optimize the structural integrity, stability, and reliability of the turbine and tower, ensuring safe and efficient operation in tidal environments.
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There is a proposal to replace the entire system with a single generator that has a reliability as good or better than the current one-year reliability. 6. What would be the required MTBF (in hours) for the new generator (assume exponential and 8760 hours/year)? 7. How many total test hours should be allocated for the new generator (assuming 1 failure is allowed) at 50% confidence? 8. Suppose the budget only supported 30,000 total test hours for the new generator. What is the demonstrated MTBF (ΘL) at 50% confidence if no failures were observed? Was the requirement demonstrated? Consider the original system diagram with Generator B as continuously operating (not in standby mode) with no load sharing. 9. What is the static relaibility of the system for this situation? 10. Convert the block diagram to a Fault Tree. Calculate the probability of the top-level event (system failure)?
The required MTBF (in hours) for the new generator (assuming exponential and 8760 hours/year) will be 8760 hours.
7. Total test hours should be allocated for the new generator (assuming 1 failure is allowed) at 50% confidence should be 688 hours.
8. The demonstrated MTBF (ΘL) at 50% confidence if no failures were observed will be 43,800 hours. Yes, the requirement was demonstrated.
9. The static reliability of the system for this situation can be determined by calculating the probability of no failure. The probability of no failure will be 0.85 * 0.95 * 0.98 * 0.99 = 0.764. Therefore, the static reliability of the system for this situation will be 0.764.10.
Probability of the top-level event (system failure) can be calculated by adding the probabilities of all the paths leading to the top-level event. The probability of the top-level event (system failure) will be:
P(system failure) = P(Gen A failure) + P(Gen B failure) + P(Gen C failure) + P(Tie Bus failure) * P(No load shedding) + P(Tie Bus failure) * P(Load shedding)
P(Gen A failure) = 1 - e^(-8760/30000) = 0.215
P(Gen B failure) = 0.85 * (1 - e^(-8760/18000)) = 0.37
P(Gen C failure) = 0.95 * (1 - e^(-8760/30000)) = 0.276
P(Tie Bus failure) = 0.98
P(No load shedding) = 0.99
P(Load shedding) = 0.01
P(system failure) = 0.215 + 0.37 + 0.276 + 0.98 * 0.99 + 0.98 * 0.01 * (1 - P(Gen A failure)) * (1 - P(Gen B failure)) * (1 - P(Gen C failure)) * P(Tie Bus failure)P(system failure) = 0.215 + 0.37 + 0.276 + 0.98 * 0.99 + 0.98 * 0.01 * (1 - 0.215) * (1 - 0.37) * (1 - 0.276) * 0.98P(system failure) = 0.9644
Therefore, the probability of the top-level event (system failure) will be 0.9644.
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9. Calculate the total resistance and current in a parallel cir-
cuit with three resistors of 4, 8, and 16 ohms, using any
one of the five methods (calculator suggested). What is
the total resistance and current?
a. 27 ohms (0.4 ampere)
b. 14 ohms (0.8 ampere)
c. 4 ohms (3.0 amperes)
d. 2.3 ohms (5.3 amperes)
Answer:
d. 2.3 ohms (5.3 amperes)
Explanation:
The calculator's 1/x key makes it convenient to calculate parallel resistance.
Req = 1/(1/4 +1/8 +1/16) = 1/(7/16) = 16/7 ≈ 2.3 ohms
This corresponds to answer choice D.
__
Additional comment
This problem statement does not tell the applied voltage. The answer choices suggest that it is 12 V. If so, the current is 12/(16/7) = 21/4 = 5.25 amperes.
In a cantilever beam, slop and deflection at free end is:
options:
Same
Minimum
Maximum
Zero
The slope and deflection at the free end of a cantilever beam are both maximum.
What is the relationship between the slope and deflection at the free end of a cantilever beam?In a cantilever beam, the free end is unsupported and experiences the maximum bending moment.
As a result, the slope (rate of change of deflection) and the deflection itself are maximum at the free end.
The slope represents the angle of rotation of the beam, while the deflection indicates the vertical displacement of the free end.
Therefore, the correct answer is "Maximum."
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Consider a hypothetical material that has a grain diameter of 6.3 × 10−2 mm. After a heat treatment at 500 °C for 4 h, the grain diameter has increased to 1.10 × 10−1 mm. Compute the grain diameter when a specimen of this same original material (i.e., d0 = 6.3 × 10−2 mm) is heated for 5.5 h at 500°C. Assume the n grain diameter exponent has a value of 2.0
The time to achieve a grain diameter of 5.5 × 10⁻² mm is 477 minutes
What is the diameter?A straight line passes through the middle of a rounded object or shape and emerges at the opposing edge.
We have to calculate the K
Given that the grain diameter exponent (n) = 2.2
Grain diameter (d) = 5.6 × 10⁻² mm = 5.6 × 10⁻⁵ m
d₀ = 2.4 × 10⁻² mm = 5.6 × 10⁻⁵ m
t = 500 min
\(K = \dfrac{d^n - d^n\circ}{t} \\\\K = \dfrac{(5.6 \times 10^-^5)^{2.2} - (2.4 \times 10^-^5)^2}{500} \\\\K = 7.48\times 10^{-13} m/min\)
From K we can determine the time required based on the desired diameter grain diameter (d) = 5.5 × 10⁻² mm = 5.5 × 10⁻⁵ m
\(K = \dfrac{(5.6 \times 10^-^5)^{2.2} - (2.4 \times 10^-^5)^2}{7.8 \times 10^{-13}} \\\\K = 477 min.\)
Therefore, the time is 477 minutes.
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PROJECT MANAGEMENT
Activity – RENOVATING A HOME
Questions:
As a project manager, you realize there may be substantial resistance to changes brought about by this project, describe any strategy or strategies you would employ to resolve this issue. (Make mention of any group from which this resistance may originate.)
After analyzing this project what TWO (2) risks have you identified and how would you respond to these risks as the project manager?
As a project manager, I would employ the following strategy to address resistance to changes in the home renovation project:
Strategy: Effective Communication and Stakeholder Engagement
To address resistance to changes, it is crucial to establish open and transparent communication channels with all stakeholders involved in the project. This includes homeowners, contractors, architects, and any other relevant parties. By actively engaging with stakeholders and listening to their concerns, I can gain their trust and create a collaborative environment.
Firstly, I would conduct regular meetings to explain the purpose and benefits of the renovation project. This would help stakeholders understand the need for change and alleviate any uncertainties or misconceptions. Clear and concise communication is key to ensuring everyone is on the same page.
Secondly, I would encourage active participation from stakeholders, seeking their input and involvement in decision-making processes. By involving them in the planning and design stages, they will feel a sense of ownership and be more willing to embrace the changes. This approach also allows for potential conflicts or objections to be addressed early on, reducing resistance later in the project.
Additionally, I would establish a feedback mechanism to address any concerns or issues promptly. This could involve setting up a dedicated communication channel or having a designated project team member responsible for handling stakeholder queries. Regular updates on project progress and milestones would also help manage expectations and build trust.
By employing effective communication and stakeholder engagement strategies, I can minimize resistance to changes and foster a collaborative environment throughout the home renovation project.
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14. are especially useful when you are trying to determine what values in related tables cause referential integrity problems. 1. Inner joins 2. Outer joins 3. Equijoins 4. Theta joins 15. A contains at least all of the attribute names and characteristics for each table in the system. 1. data dictionary 2. relational schema 3. logical schema 4. database
Outer joins are especially useful when you are trying to determine what values in related tables cause referential integrity problems.
A data dictionary contains at least all of the attribute names and characteristics for each table in the system.
Any real or virtual component of restricted availability within a computer system is referred to as a system resource, often known as a resource in computing.
All linked equipment as well as internal system parts are considered resources. Virtual system resources include things like memory spaces, files, and network connections.
In computer programming, the organisation or structure of a database is referred to as a schema.
A schema is produced as a result of the data modelling process. The phrase can be used to describe both a graphic depiction of a building and a formal, text-based description.
In this situation, the schema can be used to understand more about the database, the entity attributes these tables hold, and how these tables are related.
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The mutual inductance between two coils is 170170mH. Find the magnitude of the e. M. F induced in one coil when the current in other is increasing at a rate of 40A/s
The magnitude of the e.m.f induced in one coil when the current in the other is increasing at a rate of 40 A/s is 6.8 V.
Mutual inductance is a property of two coils that are in close proximity to each other. It measures the amount of magnetic flux that is linked between the two coils. The mutual inductance between two coils is denoted by the symbol M and is measured in henries (H).
According to Faraday's law of electromagnetic induction, an e.m.f is induced in a coil whenever there is a change in the magnetic flux that links the coil. The magnitude of the induced e.m.f is given by the formula:
e = -M(dI/dt)
where e is the induced e.m.f, M is the mutual inductance, and dI/dt is the rate of change of current in the other coil.
Substituting the given values, we get:
e = -170 x 10^-3 H x (40 A/s) = -6.8 V
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