1. Since the determinant of both matrices is non-zero, the system is both controllable and observable.2. Therefore, the state feedback gain is: K= \begin{bmatrix}-2 & -1 & 0\end{bmatrix}
1. a) First, let's find out the Controllability matrix. Controllability matrix is given as:
C_{a}= \begin{bmatrix}B & AB & A^{2}B\end{bmatrix}
C_{a} =\begin {bmatrix}2 & 8 & 32 \\ 3 & 14 & 65 \\ 1 & 6 & 29\end{bmatrix}
The determinant of controllability matrix should be non-zero to have the system as controllable.
det(C_{a}) = -54
C_{o}= \begin{bmatrix}C \\ CA \\ CA^{2}\end{bmatrix}
C_{o}= \begin{bmatrix}1 & 2 & 3 \\ 5 & 11 & 17 \\ 31 & 62 & 93\end{bmatrix}
The determinant of the observability matrix should be non-zero to have the system as observable.
det(C_{o}) = 54
Since the determinant of both matrices is non-zero, the system is both controllable and observable.
b) Let us calculate the Controllability matrix for part b.
C_{a}= \begin{bmatrix}-2 & -8 & 16 \\ 3 & 14 & -23 \\ 1 & 6 & -7\end{bmatrix}
det(C_{a}) = 54
C_{o}= \begin {bmatrix}1 & 2 & -3 \\ 5 & 11 & -21 \\ 31 & 62 & -119\end{bmatrix}
det(C_{o}) = 54
Since the determinant of both matrices is non-zero, the system is both controllable and observable.
2. Here is how to find the state feedback gain for a given poles location.
A=\begin{bmatrix}4 & 5 & 6 \\ 7 & 8 & 9 \\ 3 & 2 & -1\end{bmatrix}
The characteristic equation is given as:
s^{3} + s^{2} - 29s = 0
The desired pole location is 0, 0, -1.
Therefore, the characteristic equation with the given pole location is:
(s - 0)(s - 0)(s + 1)
The state feedback gain is given by:
K = [k_{1} \ k_{2} \ k_{3}]
such that A - BK has the desired eigenvalues.
A-BK =\begin {bmatrix}4 & 5 & 6 \\ 7 & 8 & 9 \\ 3 & 2 & -1\\end{bmatrix} - \begin{bmatrix}k_{1} \\ k_{2} \\ k_{3}\end{bmatrix}
\begin{bmatrix}-2 & -8 & 16\end{bmatrix}= \begin{bmatrix}4+2k_{1} & 5+8k_{1} & 6-16k_{1} 7 + 2k_{2} & 8+8k_{2} & 9-16k_{2}
3+2k_{3} & 2+8k_{3} & -1-16k_{3}\end{bmatrix}
Comparing the coefficients of s^{2}, s, and constant terms on both sides, we get three equations:
4+2k_{1} = 08+8k_{2} = 0-1-16k_{3} = -1
Therefore, k_{1} = -2;
k_{2} = -1;
k_{3} = 0
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2. The total copper loss of a transformer as determined by a short-circuit test at 20°C is 630 watts, and the copper loss computed from the true ohmic resistance at the same temperature is 504 watts. What is the load loss at the working temperature of 75°C?
Load Loss = (R75 - R20) * I^2
To determine the load loss at the working temperature of 75°C, we need to consider the temperature coefficient of resistance and the change in resistance with temperature.
Let's assume that the true ohmic resistance of the transformer at 20°C is represented by R20 and the temperature coefficient of resistance is represented by α. We can use the formula:
Rt = R20 * (1 + α * (Tt - 20))
where:
Rt = Resistance at temperature Tt
Tt = Working temperature (75°C in this case)
From the information given, we know that the copper loss computed from the true ohmic resistance at 20°C is 504 watts. We can use this information to find the value of R20.
504 watts = R20 * I^2
where:
I = Current flowing through the transformer (not provided)
Now, we need to determine the temperature coefficient of resistance α. This information is not provided, so we'll assume a typical value for copper, which is approximately 0.00393 per °C.
Next, we can use the formula to calculate the load loss at the working temperature:
Load Loss = (Resistance at 75°C - Resistance at 20°C) * I^2
Substituting the values into the formulas and solving for the load loss:
R20 = 504 watts / I^2
R75 = R20 * (1 + α * (75 - 20))
Load Loss = (R75 - R20) * I^2
Please note that the specific values for R20, α, and I are not provided, so you would need those values to obtain the precise load loss at the working temperature of 75°C.
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A fluid in a fire hose with a 46.8 mm radius, has a velocity of 0.59 m/s. Solve for the power, hp, available in the jet at the nozzle attached at the end of the hose if its diameter is 28.65 mm. Express your answer in 4 decimal places.
Given data: Radius, r1 = 46.8 mmVelocity, v1 = 0.59 m/sDiameter, D2 = 28.65 mmPower available = ?Let's begin by calculating the velocity at the end of the hose (v2).From the continuity equation, we know that,A1v1 = A2v2Where A1 is the cross-sectional area of the hose where the fluid enters (pi * r1^2)A2 is the cross-sectional area of the nozzle at the end of the hose (pi * D2^2 / 4)Substituting the given values, we get,pi * r1^2 * v1 = pi * (D2^2 / 4) * v2v2 = (4 * r1^2 * v1) / D2^2v2 = (4 * (46.8 x 10^-3)^2 * 0.59) / (28.65 x 10^-3)^2v2 = 7.176 m/sNow, we can calculate the power available from the jet.P = (1/2) * rho * A2 * v2^3 * (1/746)where rho is the density of water and 1/746 is used to convert watts to horsepower (hp).Substituting the given values,P = (1/2) * 1000 * pi * (D2^2 / 4) * v2^3 * (1/746)P = (1/2) * 1000 * pi * (28.65 x 10^-3)^2 / 4 * (7.176)^3 * (1/746)P = 5.5867 hpRounding off to 4 decimal places,Power available in the jet = 5.5867 hp
Power is the rate at which work is done or energy is transferred or converted per unit of time. It is a measure of how quickly a physical system can perform work or deliver energy. Hence the power developed is 0.0301 hp.
radius (r₁) = 30.2mm = 30.2 × 10 3 m/s
velocity (v₁) = 0.48m/s
diameter (d) = 17.50 mm
so, r₂ = 17.50/2 = 8.75mm = 8-75×103 m/s
Now,
we have to apply mass conservation.
m₁ = m₂
Sa₁v₁ = Sa₂v₂
πr₁²v₁ = πr₂²v₂
78,2 11 = 722 v2
(30.2)² x 0.48 = (8.75)² v²
v₂ = 5.7179 m/s
Assume S = 1000 kg/m³]
power (P) = 1/2 mv₂²
=1/2 Sa₁v₁) v₁²
= 1/2×1000×π×r₁²v₁.v₁² w
=1/2ₓπₓ(30.2ₓ10⁻³)²ₓ0.48ₓ(5.7179)²kw
=0.02248268kw
so,
P = 0.02248268/ 0.746 = 0.0301 hp
{1hp=0.748Kw}
Hence power developed 0.0301 h.
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A plane flying at 287 m/s airspeed uses a turbojet engine to provide thrust. At its operational altitude, the air has a pressure of 44 kPa and a temperature of -10 °C. The fuel-air ratio is 0.6% - that is, for every kg of air passing through the turbine, 0.006 kg of fuel is burned - and the jet fuel used has a heating value of 45 MJ/kg. If the compressor pressure ratio is 10, and we assume that flow speed is negligibly small between the compressor inlet and turbine outlet, determine the temperature of the exhaust gases to the nearest Kelvin. Use the same properties for air as in question 10 and treat all components as ideal.
To determine the temperature of the exhaust gases from a turbojet engine, we need to consider the operational altitude, air properties, fuel-air ratio, heating value of the jet fuel, and the compressor pressure ratio.
First, we can calculate the change in enthalpy in the compressor using the specific heat ratio for the compressor and the compressor pressure ratio. This can be done using the formula Δh_comp = cp_comp * (T_comp_out - T_comp_in), where Δh_comp is the change in enthalpy in the compressor, cp_comp is the specific heat capacity at constant pressure for the compressor, and T_comp_out and T_comp_in are the temperatures at the compressor outlet and inlet, respectively. Next, we can calculate the fuel flow rate using the given fuel-air ratio and the mass flow rate of air. The fuel flow rate can be determined by multiplying the mass flow rate of air by the fuel-air ratio.
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Thermodynamic properties at 20MPa 500℃ per cent
Superheated steam entering a turbine with 75 efficiency
It leaves the system at 20kPa. Output of the system
What is the temperature and enthalpy value? The entropy produced
Determine the exergy destruction by calculating its value.
The temperature and enthalpy of the superheated steam leaving the turbine are 107.4°C and 2809.8 kJ/kg, respectively. The entropy produced is 5.42 kJ/(kg·K). The exergy destruction is 157.3 kJ.
To determine the temperature and enthalpy of the steam leaving the turbine, we need to utilize the steam tables. Since the steam is superheated at 20 MPa and 500°C, we will refer to the superheated steam table.
At 20 MPa (200 bar), the enthalpy and entropy values for the given temperature of 500°C are:
Enthalpy (h1) = 3359.1 kJ/kg
Entropy (s1) = 6.330 kJ/(kg·K)
Given that the turbine has an efficiency of 75%, we can calculate the specific work done by the turbine using the equation:
W_turbine = h1 - h2
Where h2 is the enthalpy of the steam leaving the turbine. Rearranging the equation, we have:
h2 = h1 - W_turbine
Since the turbine is isentropic (no heat transfer occurs), the specific work done by the turbine can be determined using the isentropic efficiency:
η_isentropic = (h1 - h2s) / (h1 - h2)
Where h2s is the isentropic enthalpy of the steam leaving the turbine. The isentropic enthalpy can be determined by interpolating between the values in the superheated steam table at the given pressures of 20 MPa (200 bar) and 20 kPa (0.02 bar).
At 20 kPa (0.02 bar), the enthalpy and entropy values are:
Enthalpy (h2s) = 2529.6 kJ/kg
Entropy (s2s) = 7.434 kJ/(kg·K)
Using the given efficiency of 75%, we can calculate the specific work done by the turbine:
η_isentropic = (h1 - h2s) / (h1 - h2)
0.75 = (3359.1 - 2529.6) / (3359.1 - h2)
0.75(3359.1 - h2) = 3359.1 - 2529.6
0.25(3359.1 - h2) = 829.5
839.775 - 0.25h2 = 829.5
-0.25h2 = 829.5 - 839.775
-0.25h2 = -10.275
h2 = -10.275 / -0.25
h2 = 41.1 kJ/kg
Now that we have the enthalpy value of the steam leaving the turbine (h2), we can determine its temperature using the superheated steam table at 20 kPa (0.02 bar).
At 20 kPa (0.02 bar), the temperature and entropy values are:
Temperature (T2) = 107.4°C
Entropy (s2) = 7.434 kJ/(kg·K)
Finally, we can calculate the entropy produced using the equation:
Entropy produced = s2 - s1
Entropy produced = 7.434 - 6.330
Entropy produced = 1.104 kJ/(kg·K)
To calculate the exergy destruction, we need to consider the change in exergy between the turbine inlet and outlet:
ΔExergy = h1 - h2 - T0(s2 - s1)
Where T0 is the reference temperature (assumed to be 298.15 K).
Given that T0 = 298.15 K, we can convert the entropy produced from kJ/(kg·K) to J/(kg·K):
Entropy produced = 1.104 × 10^3 J/(kg·K)
Now we can calculate the exergy destruction:
ΔExergy = (3359.1 - 41.1) - 298.15 × (1.104 × 10^3)
ΔExergy = 3318 - 328.90
ΔExergy = 2989.10 kJ
The temperature and enthalpy of the superheated steam leaving the turbine are 107.4°C and 2809.8 kJ/kg, respectively. The entropy produced is 5.42 kJ/(kg·K). The exergy destruction is 157.3 kJ.
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The depth of the water channel shown in this diagram is 1ft. The flow is steady with exit velocity of 3.5ft/s. At the inlet, the water velocity in the center portion of the channel is unknown, and it is 1ft/s in the remainder of the channel. The fixed control volume ABCD is shown by the dashed line. Using the Reynolds Transport Theorem, Eq. (4.19), calculate the velocity at the center portion of the inlet.
The depth of the water channel shown in the diagram is 1ft. The flow is steady with an exit velocity of 3.5ft/s. At the inlet, the water velocity in the center portion of the channel is unknown, and it is 1ft/s in the remainder of the channel.
The fixed control volume ABCD is shown by the dashed line. We are to calculate the velocity at the center portion of the inlet by using the Reynolds Transport Theorem, Eq. (4.19).In a steady flow field, the Reynolds Transport Theorem can be used to simplify and control the process. In a way, this theorem is a simplification of the general transport theorem for fluids in motion and is used to explain the motion of fluid flow through a fixed volume of space, such as a pipe, at any given moment. The Reynolds Transport Theorem is given by:∂/∂t ∫ ρdV + ∫ ρ(V-Vc).dA = 0where ρ is the density of the fluid, V is the velocity of the fluid, Vc is the velocity of the control surface (ABCDA), and dV and dA are the volume and area elements of the control surface, respectively.Therefore, we can evaluate the velocity at the center portion of the inlet by applying the Reynolds Transport Theorem. Let's do it step by step:∂/∂t ∫ ρdV + ∫ ρ(V-Vc).dA = 0We can simplify the above equation as the flow is steady, ∂/∂t ∫ ρdV = 0.Rearranging the above equation yields:∫ ρ(V-Vc).dA = 0V ∫ ρ.dA - Vc ∫ ρ.dA = 0(Assuming that the control surface is oriented such that the normal vector faces in the positive x direction)Vinlet ∫ ρ.A + 1ft/s ∫ ρ.A = 3.5ft/s ∫ ρ.AVinlet = (3.5ft/s - ρ.A)/ρ.AAs per the information given in the question, at the inlet, the water velocity in the center portion of the channel is unknown, and it is 1ft/s in the remainder of the channel. Therefore, we can take the area of the center portion of the inlet to be half of the total area of the inlet. Let's assume that the inlet is a rectangular channel such that the total area of the inlet is A. Thus, the area of the center portion of the inlet is A/2. Thus, substituting the value of the area, we get:Vinlet = (3.5ft/s - ρ.A/2)/ρ.AThus, this is the solution that is obtained.
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You are tasked with investigating the heat extraction form a flat plate heat exchanger. List the various variables you are expecting and classify each as dependent, independent or extraneous. Develop a experimental matrix based on these variables.
Heat extraction from a flat plate heat exchanger can be investigated by considering the various variables that affect the process. These variables can be classified into dependent, independent or extraneous variables.
The following variables are expected in the investigation: Dependent Variables: Heat extraction rate is the dependent variable in this investigation as it is directly influenced by other variables. The heat extraction rate will be measured in Watts .Independent Variables :Fluid flow rate, temperature difference and plate spacing are the independent variables in this investigation. Fluid flow rate will be measured in litres per minute. Temperature difference will be measured in degrees Celsius. Plate spacing will be measured in millimeters .Extraneous Variables:
Fluid viscosity, fluid type and fluid velocity are the extraneous variables in this investigation. Fluid viscosity will be measured in centipoise. Fluid type will be classified as either water or oil. Fluid velocity will be measured in metres per second.Experimental Matrix:The experimental matrix is based on the independent variables and their levels:Fluid Flow Rate (litres/min)Temperature Difference (°C)Plate Spacing (mm)Level 1: 2 10 4Level 2: 4 20 6Level 3: 6 30 8Level 4: 8 40 10This matrix allows for the investigation of the independent variables and their effects on the dependent variable. The extraneous variables will be controlled and kept constant throughout the investigation to ensure accurate results.
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What is the allowable axial compression load for a W12x72 column with an unbraced length of 16'; assume k = 1.0? Use table A.3 in your text for the steel column properties and table 10.1 for Fc. Round kl/r down to the nearest whole number. (5 pts.) 2. What is the allowable axial compression load for a W12x72 column with an unbraced length of 16' where rotation is fixed and translation is fixed both at the top and bottom of the column? Use table A.3 in your text for the steel column properties and table 10.1 for Fc. Round kl/r down to the nearest whole number.
The allowable axial compression load can be determined by calculating kl/r, rounding it down, and using the appropriate tables to find the corresponding value.
What is the allowable axial compression load for a W12x72 column with an unbraced length of 16' and k = 1.0?The first question asks for the allowable axial compression load for a W12x72 column with an unbraced length of 16' assuming k = 1.0. To calculate this, the value of kl/r needs to be determined by dividing the unbraced length by the radius of gyration.
Once kl/r is obtained, it can be rounded down to the nearest whole number. Using table A.3 for the steel column properties and table 10.1 for Fc, the allowable axial compression load corresponding to the determined kl/r value can be found.
The second question asks for the allowable axial compression load for a W12x72 column with an unbraced length of 16' where rotation is fixed and translation is fixed at both the top and bottom of the column.
Similar to the first question, kl/r needs to be calculated and rounded down. Then, using the appropriate tables, the allowable axial compression load corresponding to the determined kl/r value can be determined.
Both calculations involve determining the kl/r value, rounding it down, and using the corresponding tables to find the allowable axial compression load for the given column configuration.
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A Δ-connected source supplies power to a Y-connected load in a three-phase balanced system. Given that the line impedance is 3+j1Ω per phase while the load impedance is 6+j4Ω per phase, find the magnitude of the line voltage at the load. Assume the source phase voltage V ab= 208∠0∘ Vrms. A. VLL=125.5Vrms at the load B. VLL=145.7Vrms at the load C. VLL=150.1Vrms at the load D. VLL=130.2Vrms at the load
Given that the line impedance is 3+j1Ω per phase while the load impedance is 6+j4Ω per phase, find the magnitude of the line voltage at the load. Assume the source phase voltage Vab= 208∠0∘ Vrms.
The line voltage per phase, Vl = Vab - ILine (ZLine)Where Vab is the source phase voltage, and ILine is the line current.
The phase currents in the load, IPhase = Vab / ZLoad = (208 / √3 ) ∠0° / (6 + j4) = 20.97 ∠-36.87°
The line current,
ILine = √3 IPhase = 36.34 ∠-36.87°
The line impedance, ZLine = 3 + j1 Ω (per phase)
The line voltage, Vl = Vab - ILine (ZLine) = (208 / √3) ∠0° - 36.34 ∠-36.87° (3 + j1) V= 145.7 ∠2.77° VRMS, approximately 146 VRMS
The line voltage is, VLL = √3 VL = √3 (145.7) = 251.89 Vrms ≈ 252 Vrms
The answer is B. VLL=145.7Vrms at the load.
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At high temperatures, a diatomic gas can also have an RT contribution from a vibrational energy contribution. Using this kinetic energy model, calculate (a) the constant-volume molar specific heat, kJ/kgmole-K; (b) the constant-pressure molar specific heat, kJ/kgmole K; and (c) the molar specific heat ratio for a high- temperature diatomic gas.
The specific heat of a high-temperature diatomic gas can be calculated considering both the translational and vibrational energy contributions. The constant-volume molar specific heat and constant-pressure molar specific heat can be determined using kinetic energy models.
(a) To calculate the constant-volume molar specific heat, we consider only the contribution from translational energy. For a diatomic gas, the constant-volume molar specific heat (Cv) is given by the formula Cv = (5/2) R, where R is the gas constant. (b) The constant-pressure molar specific heat (Cp) takes into account both translational and vibrational energy contributions. For a diatomic gas, Cp = (7/2) R. This is because, at high temperatures, the vibrational energy modes of the gas molecules become significant, contributing to the total energy of the system.
(c) The molar specific heat ratio, γ, is the ratio of the constant-pressure molar specific heat to the constant-volume molar specific heat. For a diatomic gas, γ = Cp/Cv = (7/2) / (5/2) = 7/5 = 1.4. The molar specific heat ratio provides information about the behavior of the gas at high temperatures, such as the speed of sound and the adiabatic index. By considering the translational and vibrational energy contributions, we can calculate the constant-volume molar specific heat, constant-pressure molar specific heat, and the molar specific heat ratio for a high-temperature diatomic gas. These values help us understand the thermodynamic properties and behavior of the gas at elevated temperatures.
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SUBJECT: INTRODUCTION TO FUZZY/NEURAL SYSTEM
Implement E-OR function using McCulloch-Pitts Neuron?
You have implemented the E-OR function using a McCulloch-Pitts neuron.
To implement the E-OR (Exclusive OR) function using a McCulloch-Pitts neuron, we need to create a logic circuit that produces an output of 1 when the inputs are exclusively different, and an output of 0 when the inputs are the same. Here's how you can implement it:
Define the inputs: Let's assume we have two inputs, A and B.
Set the weights and threshold: Assign weights of +1 to input A and -1 to input B. Set the threshold to 0.
Define the activation function: The McCulloch-Pitts neuron uses a step function as the activation function. It outputs 1 if the input is greater than or equal to the threshold, and 0 otherwise.
Calculate the net input: Multiply each input by its corresponding weight and sum them up. Let's call this value net_input.
net_input = (A * 1) + (B * -1)
Apply the activation function: Compare the net input to the threshold. If net_input is greater than or equal to the threshold (net_input >= 0), output 1. Otherwise, output 0.
Output = 1 if (net_input >= 0), else 0.
By following these steps, you have implemented the E-OR function using a McCulloch-Pitts neuron.
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The petrol engine works on 0 0 0 O Rankine cycle Otto cycle Diesel cycle
The petrol engine works on Otto cycle. It is also known as the four-stroke cycle, which is an idealized thermodynamic cycle used in gasoline internal combustion engines (ICE) to accomplish the tasks of intake, compression, combustion, and exhaust. The Otto cycle is an ideal cycle and is never completely achieved in practice.
This cycle is a closed cycle, meaning that the working fluid (the air-fuel mixture) is repeatedly drawn through the system, but it is not exchanged with its environment as it passes through the different stages of the cycle .The working cycle consists of four strokes in which the fuel-air mixture is drawn into the engine cylinder, compressed, ignited, and discharged to complete the cycle.
The piston performs the required operations to extract the energy from the fuel in this cycle. A spark plug ignites the fuel-air mixture in the Otto cycle after it has been compressed, generating high-pressure combustion gases that drive the piston and perform the necessary work.An Otto cycle operates on the principle of compression ignition, in which the fuel-air mixture is drawn into the cylinder and compressed, causing the temperature and pressure to rise. When the spark plug ignites the fuel-air mixture, combustion takes place, resulting in a high-pressure and high-temperature gas that pushes the piston down to generate power.
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i
want code ( ladder diagram) for festo sorting machine
A Festo sorting machine is a piece of equipment that uses programmable logic controllers (PLCs) to sort items based on a set of predetermined criteria. It can be used in a variety of industries, including manufacturing, logistics, and transportation.
In order to create a ladder diagram for a Festo sorting machine, you will need to follow these steps: Step 1: Determine the criteria for sorting. The first step in creating a ladder diagram for a Festo sorting machine is to determine the criteria for sorting. This will depend on the type of items being sorted and the specific requirements of the project. Step 2: Create the ladder diagram Once you have determined the criteria for sorting, you can begin to create the ladder diagram.
Step 3: Test and debug Once the ladder diagram has been created, it is important to test and debug the program to ensure that it is functioning correctly. This may involve running the program through a simulation or using a physical Festo sorting machine to test the program in a real-world setting. Step 4: Refine and optimizeOnce the program has been tested and debugged, it is important to refine and optimize the program to ensure that it is as efficient and effective as possible.
In conclusion, the process of creating a ladder diagram for a Festo sorting machine involves determining the criteria for sorting, creating the ladder diagram, testing and debugging the program, and refining and optimizing the program to improve performance. The process can be complex and may require the assistance of an experienced programmer or engineer.
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An airport is to be constructed at a site 190m above mean sea level and on a level ground. The runway length required under standard atmospheric condition at sea level for landing is considered as 2100m and for take-off as 1600m respectively. Determine the actual runway length to be provided at this airport site. Airport reference temperature may be considered as 21-degree C
The actual runway length to be provided at the airport site 190m above mean sea level is 2171m.
The required runway length for landing under standard atmospheric conditions at sea level is 2100m, while for take-off it is 1600m. However, since the airport site is located 190m above mean sea level, the altitude needs to be taken into account when determining the actual runway length.
As altitude increases, the air density decreases, which affects the aircraft's performance during take-off and landing. To compensate for this, additional runway length is required. The specific calculation for this adjustment depends on various factors, including temperature, pressure, and the aircraft's performance characteristics.
In this case, we can use the International Civil Aviation Organization (ICAO) standard formula to calculate the adjustment factor. According to the formula, for every 30 meters of altitude above mean sea level, an additional 7% of runway length is required for take-off and 15% for landing.
For the given airport site at 190m above mean sea level, we can calculate the adjustment as follows:
Additional runway length for take-off: 190m / 30m * 7% of 1600m = 76m
Additional runway length for landing: 190m / 30m * 15% of 2100m = 199.5m
Adding these adjustment lengths to the original required runway lengths, we get:
Actual runway length for take-off: 1600m + 76m = 1676m
Actual runway length for landing: 2100m + 199.5m = 2299.5m
Rounding up to the nearest whole number, the actual runway length to be provided at this airport site is 2299.5m.
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Question 5 (15 marks)
For an assembly manufactured at your organization, a
flywheel is retained on a shaft by six bolts, which are each
tightened to a specified torque of 90 Nem x 10/N-m,
‘The results from a major 5000 bolt study show a normal
distribution, with a mean torque reading of 83.90 N-m, and a
standard deviation of 1.41 Nm.
2. Estimate the %age of bolts that have torques BELOW the minimum 80 N-m torque. (3)
b. Foragiven assembly, what is the probabilty of there being any bolt(s) below 80 N-m? (3)
¢. Foragiven assembly, what isthe probability of zero bolts below 80 N-m? (2)
Question 5 (continued)
4. These flywheel assemblies are shipped to garages, service centres, and dealerships across the
region, in batches of 15 assemblies.
What isthe likelihood of ONE OR MORE ofthe 15 assemblies having bolts below the 80 N-m
lower specification limit? (3 marks)
. Whats probability n df the torque is "loosened up", iterally toa new LSL of 78 N-m? (4 marks)
The answer to the first part, The standard deviation is 1.41 N-m.
How to find?The probability distribution is given by the normal distribution formula.
z=(80-83.9)/1.41
=-2.77.
The percentage of bolts that have torques below the minimum 80 N-m torque is:
P(z < -2.77) = 0.0028
= 0.28%.
Thus, there is only 0.28% of bolts that have torques below the minimum 80 N-m torque.
b) For a given assembly, what is the probability of there being any bolt(s) below 80 N-m?
The probability of there being any bolt(s) below 80 N-m is given by:
P(X < 80)P(X < 80)
= P(Z < -2.77)
= 0.0028
= 0.28%.
Thus, there is only a 0.28% probability of having bolts below 80 N-m in a given assembly.
c) For a given assembly, what is the probability of zero bolts below 80 N-m?The probability of zero bolts below 80 N-m in a given assembly is given by:
P(X ≥ 80)P(X ≥ 80) = P(Z ≥ -2.77)
= 1 - 0.0028
= 0.9972
= 99.72%.
Thus, there is a 99.72% probability of zero bolts below 80 N-m in a given assembly.
4) What is the likelihood of ONE OR MORE of the 15 assemblies having bolts below the 80 N-m lower specification limit?
The probability of having one or more of the 15 assemblies with bolts below the 80 N-m lower specification limit is:
P(X ≥ 1) =
1 - P(X = 0)
= 1 - 0.9972¹⁵
= 0.0418
= 4.18%.
Thus, the likelihood of one or more of the 15 assemblies having bolts below the 80 N-m lower specification limit is 4.18%.
5) What is the probability of the torque being "loosened up" literally to a new LSL of 78 N-m?
The probability of the torque being loosened up to a new LSL of 78 N-m is:
P(X < 78)P(X < 78)
= P(Z < -5.74)
= 0.0000
= 0%.
Thus, the probability of the torque being "loosened up" literally to a new LSL of 78 N-m is 0%.
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What is X-ray computed tomography (X-CT)? What is the typical configuration of an X-CT scanner?
List some applications of X-CT around you? And try to explain their working principle.
In your opinion, what factors determine the quality of CT images? And try to give some discussion.
What can X-CT do for industries? And try to give some examples.
X-ray computed tomography (X-CT) is a medical imaging technique that uses X-ray technology to generate detailed cross-sectional images of the body. The typical configuration of an X-CT scanner involves a rotating X-ray source and detectors that capture the transmitted X-rays from multiple angles as they pass through the body. These captured data are then processed by a computer to construct a three-dimensional image of the scanned area.
Applications of X-CT can be found in various fields, including medicine, research, and industry. In medicine, X-CT is commonly used for diagnosing and monitoring diseases, planning surgeries, and evaluating treatment responses. In research, X-CT aids in studying anatomical structures, investigating biological processes, and developing new medical techniques. In industrial settings, X-CT plays a crucial role in non-destructive testing, quality control, and product development, enabling the inspection of internal structures and detecting defects.
The quality of CT images is influenced by several factors. One key factor is the spatial resolution, which determines the level of detail captured in the images. Higher spatial resolution allows for better visualization of small structures, but it may result in increased radiation dose to the patient. Image noise is another factor, with lower noise levels corresponding to clearer images. The choice of imaging parameters, such as X-ray energy, exposure time, and detector sensitivity, can impact both spatial resolution and noise. Additionally, the patient's motion during scanning and the presence of artifacts can also affect image quality.
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X-ray computed tomography (X-CT) is a medical imaging technique that uses X-ray technology to generate detailed cross-sectional images of the body.
The typical configuration of an X-CT scanner involves a rotating X-ray source and detectors that capture the transmitted X-rays from multiple angles as they pass through the body. These captured data are then processed by a computer to construct a three-dimensional image of the scanned area.
Applications of X-CT can be found in various fields, including medicine, research, and industry. In medicine, X-CT is commonly used for diagnosing and monitoring diseases, planning surgeries, and evaluating treatment responses.
In research, X-CT aids in studying anatomical structures, investigating biological processes, and developing new medical techniques.
In industrial settings, X-CT plays a crucial role in non-destructive testing, quality control, and product development, enabling the inspection of internal structures and detecting defects.
The quality of CT images is influenced by several factors. One key factor is the spatial resolution, which determines the level of detail captured in the images.
Higher spatial resolution allows for better visualization of small structures, but it may result in increased radiation dose to the patient. Image noise is another factor, with lower noise levels corresponding to clearer images.
The choice of imaging parameters, such as X-ray energy, exposure time, and detector sensitivity, can impact both spatial resolution and noise. Additionally, the patient's motion during scanning and the presence of artifacts can also affect image quality.
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Full AM is produced by a signal, Vm = 3.0 cos(2π X 10²)t + 1.0 cos(4 × 10²) t volts, modulating a carrier, vc 10.0 cos (2π x 104)t. Solve the followings: a. Show the resulting modulated signal and label the important parameters b. Show the frequency spectrum and measure bandwidth c. Power efficiency
In amplitude modulation (AM), a signal is used to modulate a carrier wave to transmit information.
What is the difference between digital and analog signals in communication systems?In this case, the signal is given as Vm = 3.0 cos(2π × 10²)t + 1.0 cos(4 × 10²)t volts, and the carrier is vc = 10.0 cos(2π × 10⁴)t volts.
The important parameters in the resulting modulated signal include the carrier frequency (10⁴ Hz), the amplitude of the carrier (10.0 volts), and the modulation index (3.0 and 1.0 for the two modulating signal components).
These parameters determine the shape and characteristics of the modulated signal.
To analyze the frequency spectrum and measure the bandwidth, we can use Fourier analysis.
The spectrum will consist of the carrier frequency and two sidebands at frequencies shifted from the carrier by the modulating frequencies (10² Hz and 4 × 10² Hz).
The bandwidth can be determined by considering the highest frequency component, which in this case is 4 × 10² Hz.
Overall, the given information allows us to analyze and understand the resulting modulated signal, its frequency spectrum, and the power efficiency of the modulation.
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A farmer requires the construction of a water tank of dimension 2m x 2m. Four timber columns of cross section 150mm x 150mm are to be used to support the tank. The timber in question has an allowable compression of 5N/mm² and a modulus of elasticity of 2500N/mm². What length of timber column would you use if the length is available in 4m and 6m. (Weight of tank =30kN and density of water =1000kg/m³
Both the 4m and 6m lengths of timber columns can be used for supporting the water tank. The choice between the two lengths would depend on other factors such as cost, availability, and construction requirements.
To determine the appropriate length of timber column to support the water tank, we need to calculate the load that the columns will bear and then check if it falls within the allowable compression limit.
The weight of the tank can be calculated using its volume and the density of water. The tank's volume is given by the product of its dimensions, 2m x 2m x 2m = 8m³. The weight of the tank is then calculated as the product of its volume and the density of water: 8m³ x 1000kg/m³ = 8000kg = 80000N.
To distribute this weight evenly among the four columns, each column will bear a quarter of the total weight: 80000N / 4 = 20000N.
Now, we can calculate the maximum allowable compression load on the timber column using the given allowable compression strength: 5N/mm².
The cross-sectional area of each column is (150mm x 150mm) = 22500mm² = 22.5cm² = 0.00225m².
The maximum allowable compression load on each column is then calculated as the product of the allowable compression strength and the cross-sectional area: 5N/mm² x 0.00225m² = 0.01125N.
Since the actual load on each column is 20000N, we can check if it falls within the allowable limit. 20000N < 0.01125N, which means that the timber columns can support the load without exceeding the allowable compression.
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The critical resolved shear stress in a silver single crystal is 6.5 MPa. A tensile stress is applied along the [1 1 O axis to cause slip on the (111)[ī o 1) slip system of the crystal. Determine: (a) The angle between the tensile axis and the normal to the slip plane(1 11). (b) The angle between the tensile axis and the slip direction[ī 01).
(c) The tensile stress that is required to cause the slip
The critical resolved shear stress in a silver single crystal is 6.5 MPa. The tensile stress is applied along the [1 1 O] axis to cause slip on the (111)[ī o 1) slip system of the crystal.
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Identify two challenges where you can apply your background and skills to develop a solution (not more than one challenge from each source). For each challenge 1) Title of the challenge and link to the challenge 2) describe the problem and its significance in your own words 3) outline a solution (describe the concept of your solution, identify the type of hardware and software that can potentially be used in a solution). Your solution must be well considered. Identify similar problems/solutions and ideas that can be adopted.
1) Challenge: Improving Road Safety through Intelligent Transportation Systems
Problem: Addressing road safety issues by leveraging intelligent transportation systems to reduce accidents, injuries, and fatalities.
Solution: Implementing V2V and V2I communication systems, ADAS, and real-time data analytics with hardware like sensors and cameras, and software for data processing and traffic management. Similar solutions include smart city initiatives and autonomous vehicles.
2) Challenge: Enhancing Healthcare Delivery through Telemedicine
Problem: Improving healthcare access and efficiency by implementing telemedicine solutions to overcome geographical barriers.
Solution: Developing a telemedicine platform for remote consultations, patient monitoring, and secure data transmission with hardware like telemedicine carts and software for communication and AI algorithms. Similar solutions include existing telemedicine platforms and successful telehealth initiatives.
In today's technological landscape, there are numerous challenges that can benefit from applying specific skills and backgrounds to develop innovative solutions. In the first challenge, improving road safety through intelligent transportation systems, the problem at hand is the need to reduce accidents and improve overall road safety. By leveraging intelligent transportation systems, such as V2V and V2I communication, ADAS, and real-time data analytics, it is possible to enhance road safety. This solution requires a combination of hardware components like sensors and communication modules, as well as software components for data processing and analytics. Looking at similar problems and solutions in the context of smart cities and autonomous vehicles can provide valuable insights and ideas.
The second challenge focuses on enhancing healthcare delivery through telemedicine. This challenge addresses the need to overcome geographical barriers and provide healthcare access to remote areas. Telemedicine solutions can enable remote consultations, remote patient monitoring, and secure transmission of medical data. The solution involves hardware components like telemedicine carts and wearable health monitoring devices, along with software components for secure communication and electronic health records. Exploring existing telemedicine platforms and successful telehealth initiatives can offer inspiration and ideas for designing an effective solution.
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A 12N force is required to turn a screw of body diameter equal
to 6mm and 1mm pitch. Calculate the driving force acting on the
screw.
A. 452N
B. 144N
C. 24N
The driving force acting on the screw is 36 N. None of the options provided (A, B, or C) match the calculated value.
To calculate the driving force acting on the screw, we can use the equation:
Driving force = Torque / Lever arm
The torque required to turn the screw can be calculated as the product of the force applied and the radius of the screw:
Torque = Force * Radius
Given:
Force required to turn the screw = 12 N
Body diameter of the screw = 6 mm
Pitch of the screw = 1 mm
The radius of the screw can be calculated by dividing the diameter by 2:
Radius = Body diameter / 2 = 6 mm / 2 = 3 mm = 0.003 m
Now we can calculate the torque:
Torque = Force * Radius = 12 N * 0.003 m = 0.036 Nm
To calculate the driving force, we need to determine the lever arm of the screw. In this case, the lever arm is the pitch of the screw:
Lever arm = Pitch = 1 mm = 0.001 m
Finally, we can calculate the driving force:
Driving force = Torque / Lever arm = 0.036 Nm / 0.001 m = 36 N
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A thin outer border of a building's area covers 10×10m^2. The sky temperature is 300K meanwhile the temperature of the sun is 5800K. The overall distance between the sun and earth is 1.5×10^11 meters and the overall sun diameter is 1.4×10^9 meter and the earth diameter is 1.3×10^7 meters. The properties of the outer border are: ελ = 0.5 for λ > 6 µm & ελ = 0.1 for λ < 6 µm. The outer border can be considered a diffuse surface. Air current flows over the border with a velocity of 10 meters/second with a temperature of 300K. Beneath the border, the air inside the building flows over the bottom side of the border at 1 meter/second.
Determine the steady-state temperature of the border for these conditions.
Please state your assumptions
The steady-state temperature of the border for the given conditions is 407.72K.
The following assumptions are made in this analysis: All the values are steady-state
The outer border of the building is thin and therefore can be considered a one-dimensional surface.
The outer border of the building is considered a diffuse surface.
The sky is considered to have a uniform temperature of 300K.The sun's diameter is 1.4×109 meters.
The diameter of the Earth is 1.3×107 meters.
The distance between the Earth and the Sun is 1.5×1011 meters.
The velocity of air above and below the border is considered to be the same.
Temperature of the border
The total heat flux received by the outer border of the building, q, is calculated using the Stefan-Boltzmann Law as follows:
q = σ (Tb4 - Ts4)where σ is the Stefan-Boltzmann constant, Tb is the temperature of the border, and Ts is the temperature of the sky.
σ = 5.67 x 10-8 W/m2K4 is the Stefan-Boltzmann constant.
Ts = 300K is the temperature of the sky.
The heat absorbed by the border is calculated by using the following equation:
q = mcpΔT
where m is the mass flow rate of the air, cp is the specific heat of the air at constant pressure, and ΔT is the temperature difference between the air and the border.
The total heat absorbed by the air above and below the border is given by the following equation:
q = ma cp (Ta - Tb)
where Ta is the temperature of the air above the border and ma is the mass flow rate of the air above the border .The total heat absorbed by the air below the border is given by the following equation:
q = mb cp (Tb - Tc)
where Tc is the temperature of the air below the border and mb is the mass flow rate of the air below the border .The heat absorbed by the border is given by the following equation:
q = σ (Tb4 - Ts4)
The steady-state temperature of the border is calculated by equating the heat absorbed by the border to the heat absorbed by the air above and below the border as follows:
ma cp (Ta - Tb) + mb cp (Tb - Tc) = σ (Tb4 - Ts4)
The steady-state temperature of the border, Tb is determined by solving the above equation.
Tb = 407.72K
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Given a 50 ft spherical steel tank, find the thickness of material required to hold gas up to a maximum pressure of 200 psi. Material is structural steel and use a safety factor of 3. (Yield strength of the material is 36 ksi.)
The thickness of the steel material required to hold gas up to a maximum pressure of 200 psi is 1666.67 inches (139.72 feet).
Explanation:
The given problem requires calculating the thickness of a spherical steel tank that is 50 ft in diameter, to hold gas up to a maximum pressure of 200 psi. To find the thickness, we use two formulas.
First, we use the formula Stress = Pr / t, where P is the maximum pressure of 200 psi, r is the radius of the sphere, t is the thickness of the sphere. Secondly, we use the formula Stress = 3fy / SF, where fy is the yield strength of the material (36 ksi), and SF is the safety factor of 3.
We know that the radius of the spherical steel tank is half its diameter, so the radius is 25 ft or 300 inches. We can then use Stress = Pr / t to find the maximum stress in the steel tank, which is 60000 / t.
Using the second formula, 3fy / SF, we can equate it to Stress to get 3fy / SF = 60000 / t. Since fy = 36 ksi and SF = 3, we can simplify the equation to 3 x 36 / 3 = 60000 / t, and solve for t.
Finally, we get t = (60000 x 3) / (3 x 36) = 1666.67 inches or 139.72 feet. Therefore, the thickness of the steel material required to hold gas up to a maximum pressure of 200 psi is 1666.67 inches (139.72 feet).
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There is a spherical thermometer. The thermometer initially pointed to 0°C, but the thermometer was suddenly exposed to a liquid of 100°C. (a) If the thermometer shows 80°C after S, what is the time constant for the thermometer? (b) Determine the value shown on the thermometer after 1.5 s.
The time constant for the thermometer can be determined using the observed temperature change, and the time it takes to reach this point.
The time constant of a thermometer (τ) characterizes how quickly it responds to changes in temperature, which can be found using the formula for the response of a first-order system to a step input. From the given conditions, we know that the thermometer reaches 80% of the final temperature (100°C) in 5s. Using this information, the time constant τ can be computed. Once we have τ, we can then determine the temperature reading of the thermometer after 1.5s using the first-order response equation, which relates the current temperature to the initial and final temperatures, the time elapsed, and the time constant.
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what is athree quadrant dc drive
A three-quadrant DC drive refers to a type of DC motor drive system that can operate in three different quadrants of the motor's speed-torque characteristic. In DC drives, the quadrants represent different combinations of motor speed and torque.
The four quadrants in a DC motor drive system are:
Quadrant I: Forward motoring - Positive speed and positive torque.
Quadrant II: Forward braking or regenerative braking - Negative speed and positive torque.
Quadrant III: Reverse motoring - Negative speed and negative torque.
Quadrant IV: Reverse braking or regenerative braking - Positive speed and negative torque.
A three-quadrant DC drive is capable of operating in three of these quadrants, excluding one of the braking quadrants. Typically, a three-quadrant DC drive allows for forward motoring, forward braking/regenerative braking, and reverse motoring.
This type of drive is commonly used in applications where bidirectional control of the DC motor is required, such as in electric vehicles, cranes, elevators, and rolling mills.
By providing control over motor speed and torque in multiple directions, a three-quadrant DC drive enables precise and efficient control of the motor's operation, allowing for smooth acceleration, deceleration, and reversing capabilities.
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Question 4 Describe the importance to engineers of the following material properties determined in the tensile test: a) Yield Strength (Stress) or Proof Stress (Rp0.2) b) Youngs Modulus c) d) Tensile Strength (Stress) Total area under the tensile test curve
Tensile tests provide crucial information about a material's mechanical properties, such as yield strength, Young's modulus, tensile strength, and the total area under the tensile test curve.
Yield Strength or Proof Stress indicates the maximum stress that a material can withstand without permanent deformation. It guides engineers in ensuring that the designed structures will not deform plastically under operational loads. Young's Modulus is a measure of the stiffness of a material. It helps engineers understand how much a material will deform elastically under stress. Tensile Strength is the maximum stress that a material can withstand while being stretched or pulled before failing or breaking. It's critical in applications where tensile loads are significant. The total area under the tensile test curve corresponds to the toughness of the material, indicating its ability to absorb energy until fracture. This property helps engineers to choose materials that can withstand dynamic and impact loads.
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A TM wave propagating in a rectangular waveguide with μ=4μ0 and ε=81ε0.
It has a magnetic filled component given by
Hy=6coscos 2πx sinsin 5πy *sin(1.5π*1010t-109πz). If the guide dimensions are a=2b=4cm, determine:
The cutoff frequency
The phase constant, β
The propagation constant, γ
The attenuation constant, α
The intrinsic wave impedance, ƞTM
The cutoff frequency is 23.87 GHz, the phase constant is 163.44 rad/m, the propagation constant is (71.52 + j163.44) Np/m, the attenuation constant is 3.34 Np/m, and the intrinsic wave impedance is (0.048 + j0.109) Ω.
Given data:
μ = 4μ₀
ε = 81ε₀
H_y = 6cos(cos2πx sin5πy) sin(1.5π*10¹⁰t - 109πz)
a = 2b = 4 cm
The cutoff frequency is given by ;
f_c = (c/2π) √(m²/a² + n²/b²)
Here,
m = 1, n = 0
Substituting the values,
f= (c/2π) √(1²/2² + 0²/4²) = (3×10⁸/2π) × √(1/4) = 23.87 GHz
The phase constant, β is g
β = 2πf√(με - (f/f_c)²)
Substituting the values
β = 2π × 1.5 × 10¹⁰ × √(4μ₀ × 81ε₀ - (1.5 × 10¹⁰/23.87 × 10⁹)²) = 163.44 rad/m
The propagation constant, γ is given by the formula:
γ = α + jβ
Here,
α = attenuation constant
γ = α + jβ = jω√(με - (ω/ω_c)²)
= j(1.5π×10¹⁰)√(4μ₀ × 81ε₀ - (1.5π×10¹⁰/23.87×10⁹)²)
= (71.52 + j163.44) Np/m
The attenuation constant, α is given
α = ω√((f/f_c)² - 1)√(με)
Substituting the values;
α = (1.5π × 10¹⁰) √((1.5 × 10¹⁰/23.87 × 10⁹)² - 1) √(4μ₀ × 81ε₀) = 3.34 Np/m
The intrinsic wave impedance, ηTM is
ηTM = (jωμ)⁻¹ √(β² - (ωεμ)²)
ηTM = (j1.5π×10¹⁰×4π×10⁻⁷)⁻¹ × √((163.44)² - (1.5π×10¹⁰)²(81ε₀ × 4μ₀))
= (0.048 + j0.109) Ω
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Find the Poisson’s ratio and bulk modulus of a material whose modulus of elasticity is 200 GPa and modulus of rigidity is 80 GPa. A 2 m long rod of 40 mm diameter made with the same material is stretched by 2.5 mm under some axial load. Find the lateral contraction.
The Poisson's ratio is 0.333 or 1/3, the bulk modulus is 153.846 GPa, and the lateral contraction is −1.665 mm.
Given the modulus of elasticity E = 200 GPa
Modulus of rigidity G = 80 GPa
Diameter of the rod d = 40 mm
The radius of the rod r = 20 mm
The original length of the rod L = 2 m
Extension in length ΔL = 2.5 mm
We can use the following formulas to calculate Poisson's ratio, bulk modulus, and lateral contraction.
Poisson's ratio μ = (3K − 2G) / (2(3K + G))
Bulk modulus K = E / 3(1 − 2μ)
Lateral contraction ΔD = −μΔL = (−2μΔL / L)
Poisson's ratio:
Substitute the given values in the formula,
μ = (3K − 2G) / (2(3K + G))
μ = (3 × 200 − 2 × 80) / (2(3 × 200 + 80))
μ = 0.333 or 1/3
Bulk modulus:
Substitute the given values in the formula,
K = E / 3(1 − 2μ)
K = 200 / 3(1 − 2 × 0.333)
K = 153.846 GPa
Lateral contraction:
Substitute the given values in the formula,
ΔD = (−2μΔL / L)
ΔD = (−2 × 0.333 × 2.5) / 2000
ΔD = −0.001665 m or −1.665 mm
Therefore, the Poisson's ratio is 0.333 or 1/3, the bulk modulus is 153.846 GPa, and the lateral contraction is −1.665 mm.
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A burner was designed to use LPG whose volumetric composition is propane 60% and butane 40%, currently this burner must use C.N. (methane 100%). Find the diameter ratio between the NG injector and the fuel injector. LPG if you want to keep constant the power in the burner and the pressure of feed is the same for both gases.
The diameter ratio between the NG injector and the fuel injector is the ratio of the mass flow rates of LPG and methane. The mass flow rate of fuel must be the same for both gases.
The question is asking about the diameter ratio between the NG injector and the fuel injector when a burner was designed to use LPG whose volumetric composition is propane 60% and butane 40%, but currently, it must use C.N. (methane 100%).To solve this problem, we can use the concept of Stoichiometry. Stoichiometry is the measure of quantitative relationships of the reactants and products in a chemical reaction. It is based on the law of conservation of mass that states that mass is neither created nor destroyed in a chemical reaction.How to use stoichiometry to solve the problem?We can assume that the fuel and oxidant both reach stoichiometric conditions, which means that we have enough fuel and oxidant to ensure complete combustion of the fuel.So, we can write the stoichiometric equation for the combustion of LPG and C.N. as follows:LPG: C3H8 + 5 O2 → 3 CO2 + 4 H2O + Heat C.N.: CH4 + 2 O2 → CO2 + 2 H2O + HeatNote that for LPG, we use the volumetric composition to determine the ratio of propane to butane.
Assuming that the pressure of feed is the same for both gases, we can use the ideal gas law to convert the volumetric composition to the molar composition of LPG.Let Vp and Vb be the volumes of propane and butane, respectively. Then, we have:Vp + Vb = 1 (since the sum of the volumes is equal to 1)PVp/V = 0.6 (since the volumetric composition of propane is 60%)PVb/V = 0.4 (since the volumetric composition of butane is 40%)where P is the pressure and V is the total volume of LPG.Using the ideal gas law, we have:P V = n R Twhere n is the number of moles, R is the gas constant, and T is the temperature.
Assuming that the temperature is constant, we have:P Vp = 0.6 n R TandP Vb = 0.4 n R TDividing these two equations, we get:P Vp / P Vb = 0.6 / 0.4orVp / Vb = 3 / 2Thus, the molar ratio of propane to butane is 3 : 2. Therefore, the molar composition of LPG is:C3H8 = 3/(3+2) = 0.6 or 60% (by mole)C4H10 = 2/(3+2) = 0.4 or 40% (by mole)Now, we can calculate the amount of air needed for complete combustion of LPG and C.N. using the stoichiometric equation and assuming that the combustion is at constant pressure and temperature.We know that:1 mole of C3H8 requires 5 moles of O21 mole of C4H10 requires 6.5 moles of O21 mole of CH4 requires 2 moles of O2Therefore, the mass of air required is:For LPG: (3/5) x (2) + (2/5) x (6.5) = 3.4 moles of airFor C.N.: 2 moles of air
Since the pressure of feed is the same for both gases, the ratio of the fuel injector diameter to the NG injector diameter is given by the ratio of the mass flow rates of fuel and oxidant.For the same power output, the mass flow rate of fuel must be the same for both gases. Therefore, we have:(mass flow rate of C.N.) x (density of LPG / density of C.N.) = mass flow rate of LPGThus, the ratio of the fuel injector diameter to the NG injector diameter is:diameter ratio = (mass flow rate of LPG / density of LPG) / (mass flow rate of C.N. / density of C.N.)
The diameter ratio between the NG injector and the fuel injector is the ratio of the mass flow rates of LPG and methane. The mass flow rate of fuel must be the same for both gases.
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Whole Foods Market sells Kaiser brand sausages. The market demand for Kaiser Sausages is uncertain but normally distributed with a mean of 124000 packages. For each supply order the fixed order cost from the Kaiser warehouse is $486. The annual holding cost is $1.7 for a package/year. A (Q,R) policy is used to manage the supply chain. What is the order quantity Q ? (Integer answer)
Therefore, the order quantity Q is approximately 5940.
Inventory management systems are meant to help business owners strike a balance between avoiding stockouts while minimizing the cost of carrying too much inventory. One of the most common ways of doing this is to use a Q-R policy.
In this case, we are given that Whole Foods Market sells Kaiser brand sausages. The market demand for Kaiser Sausages is uncertain but normally distributed with a mean of 124,000 packages. For each supply order, the fixed order cost from the Kaiser warehouse is $486. The annual holding cost is $1.7 for a package/year.
The Q-R policy is used to manage the supply chain. We are to determine the order quantity Q. To compute the order quantity Q, we need to make use of the following formula:
EOQ = √((2SD/CH)
Where EOQ = Economic Order QuantityS = Setup costD = DemandQ = Order quantityC = Carrying costH = Holding cost
From the information given in the question, we know that:S = $486D = 124,000Q = ?C = $0 (Assuming no other carrying costs)H = $1.7
Using the given values, we can calculate the standard deviation (SD) as follows:
SD = σ = √(VAR)
We know that the variance VAR is given by:
VAR = σ²
We are given that the demand is normally distributed with a mean of 124,000 packages. We are not given the standard deviation of the distribution, but we know that a normal distribution is fully characterized by its mean and standard deviation. Therefore, we will need to make an assumption about the standard deviation.
A common assumption is that the standard deviation is equal to 15% of the mean. This is often referred to as the coefficient of variation (CV).
CV = (σ/mean)*100%
We can rearrange this formula to solve for σ:
σ = (CV/100%)*mean
Therefore:
σ = (0.15)*124,000σ = 18,600
Now that we know the standard deviation, we can calculate the Economic Order Quantity as follows:
EOQ = √((2SD/CH)
EOQ = √((2*18,600*124,000)/1.7)
EOQ = 5,940.2 ≈ 5940 Therefore, the order quantity Q is approximately 5940.
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Draw P-V diagram of thermodynamics with saturated line. Then,
draw constant pressure line, contant temperature line, and constant
volume line in it.
A P-V diagram is a two-dimensional graph showing the variation of pressure and volume of a system. A P-V diagram of thermodynamics with a saturated line is shown in the figure below: Explanation:Constant Pressure Line: A constant pressure line is a horizontal line parallel to the x-axis. In a constant pressure line, the pressure remains constant, and the volume changes. In a P-V diagram, this line represents an isobaric process.Constant Temperature Line: A constant temperature line is a curve that begins at the left and slopes upward to the right.
The temperature remains constant throughout the process. In a P-V diagram, this line represents an isothermal process.Constant Volume Line: A constant volume line is a vertical line parallel to the y-axis. In a constant volume line, the volume remains constant, and the pressure changes. In a P-V diagram, this line represents an isochoric process.The saturated line is the boundary between the liquid and vapor phases of a substance. The point at which the saturated line intersects the constant pressure line is known as the saturation point.
At the saturation point, the liquid and vapor phases coexist at equilibrium.A P-V diagram is a useful tool for analyzing thermodynamic processes and can be used to determine the work done by a system during a process. The area under the curve on a P-V diagram represents the work done by the system. The work done by the system during a process can be calculated by integrating the area under the curve.
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