(a) The formula for heat flow through the wall is given by:q = (T1 - T2) / [ (L1 / k1) + (L2 / k2) + (1 / h1) + (1 / h2)]whereq = rate of heat flowT1 = temperature on one side of the wall
T2 = temperature on the other side of the wallL1 = thickness of the wallL2 = thickness of the insulationk1 = thermal conductivity of the wallk2 = thermal conductivity of the insulationh1 = heat transfer coefficient on the inner surface of the wallh2 = heat transfer coefficient on the outer surface of the insulationWhen the oven's temperature is 250°C and the ambient kitchen temperature is 25°C, the temperature difference across the wall is ΔT = T1 - T2 = 250°C - 25°C = 225°CSubstituting the given values in the above formula, we get:q = (225) / [(0.2 / 1) + (0.01 / 0.05) + (1 / 15) + (1 / ∞)]where ∞ represents an infinitely large heat transfer coefficient since the inner surface has a very large value. Hence, it can be ignored.q = 3592.63 W/m²Therefore, the heat flux from the oven is 3592.63 W/m².(b) Additional thickness of insulation required:Let d be the additional thickness of insulation required. Then, using the same formula as before but with the new values, we get:400 = (225) / [(0.2 / 1) + (0.01 + d / 0.05) + (1 / 15) + (1 / ∞)]Ignoring the ∞ term as before, we can simplify the above equation as follows:400 = (225) / [(0.2 / 1) + (0.01 + d / 0.05) + (1 / 15)]Solving for d, we get:d = 0.098 mTherefore, an additional thickness of insulation of 9.8 cm or 0.098 m is required to reduce the heat flux to 400 W/m².The heat flux from the oven is 3592.63 W/m². An additional thickness of insulation of 9.8 cm or 0.098 m is required to reduce the heat flux to 400 W/m².
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Determine at what temperature a New York Steak should be cooked in a saucepan if for
To achieve uniform cooking, a temperature of 140°C is needed inside. consider
stationary state.
Write down your assumptions, explain your answer. Kmeat=0.471W/m°C. and the steak has a
thickness of 3cm.
To determine the temperature at which a New York Steak should be cooked in a saucepan to achieve a uniform internal temperature of 140°C, we can use the concept of thermal conduction and consider the stationary state.
Assumptions:
The steak is assumed to have uniform thermal properties and thickness.
The saucepan provides uniform heat distribution across its base.
The heat transfer within the steak occurs primarily through conduction.
No heat is lost to the surroundings or the saucepan lid during cooking.
The temperature distribution inside the steak can be modeled using the one-dimensional steady-state heat conduction equation:
d²T/dx² = 0
where T is the temperature and x is the distance from the surface of the steak.
Since the steak is assumed to have uniform thermal properties, the heat conduction equation simplifies to:
d²T/dx² = 0
Integrating the equation twice gives:
T = C₁x + C₂
Applying the boundary conditions:
At the surface (x = 0), the temperature is the cooking temperature, T_surface.
At the center (x = L/2), the temperature is the desired internal temperature, T_center.
Using the boundary conditions, we can solve for the constants C₁ and C₂. The temperature distribution within the steak can then be determined as:
T = (T_center - T_surface)(2x/L) + T_surface
To achieve a uniform internal temperature of 140°C, we set T_center = 140°C and solve for T_surface. Given the thermal conductivity of the meat (k_meat = 0.471 W/m°C) and the thickness of the steak (L = 3 cm = 0.03 m), we can calculate the required surface temperature T_surface using the above equation.
It is important to note that cooking times and temperatures may vary depending on personal preference and the desired level of doneness for the steak. Other factors such as heat transfer mechanisms, heat source, and pan material may also affect the cooking process.
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When it comes to determining the damage mechanisms that become active in each life period of a composite structure, this process is mainly dependent on eight specifications, list four specifications.
When determining the damage mechanisms that become active in each life period of a composite structure, several specifications play a crucial role. By considering these specifications, engineers and researchers can better analyze and predict the damage mechanisms that are likely to occur at different stages of the composite structure's life.Here are four key specifications:
Loading conditions: The type and magnitude of applied loads significantly influence the damage mechanisms in a composite structure. Specifications regarding the nature of the loading, such as static, cyclic, or impact loading, help identify the specific damage mechanisms that may occur.
Environmental conditions: Environmental factors such as temperature, humidity, and exposure to chemicals or UV radiation can contribute to the initiation and progression of damage in composites. Specifications related to the specific environmental conditions help assess the potential damage mechanisms.
Material properties: The properties of the composite material, such as the fiber type, resin matrix, and reinforcement architecture, play a crucial role in determining the damage mechanisms. Specifications regarding the material composition and mechanical properties provide insights into the potential damage modes.
Manufacturing process: The method used to manufacture the composite structure can affect its integrity and susceptibility to certain damage mechanisms. Specifications related to the manufacturing process, including curing temperature, pressure, and post-curing treatments, help understand the potential damage modes associated with fabrication-related factors.
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Air in a P-C device undergoes the following reversible processes such that it operates as a cyclic refrigerator: 1-2 isothermal compression from 1 bar and 300 K to 3 bar, 2-3 adiabatic expansion back to its initial volume, 3-1 isobaric heating back to its initial state. Assume air behaves as a calorically perfect gas. Sketch this cycle in T-s and P-v diagrams. Calculate the work, heat transfer, and entropy change for each of the three processes. Determine the COP for this refrigerator.
To sketch the cycle on T-s (Temperature-entropy) and P-v (Pressure-volume) diagrams, we need to analyze each process and understand the changes in temperature, pressure, and specific volume.
1-2: Isothermal compression
In this process, the temperature remains constant (isothermal). The gas is compressed from 1 bar and 300 K to 3 bar. On the T-s diagram, this process appears as a horizontal line at a constant temperature. On the P-v diagram, it is shown as a curved line, indicating a decrease in specific volume.
2-3: Adiabatic expansion
During this process, the gas undergoes adiabatic expansion back to its initial volume. There is no heat transfer (adiabatic). On the T-s diagram, this process appears as a downward-sloping line. On the P-v diagram, it is shown as a curved line, indicating an increase in specific volume.
3-1: Isobaric heating
In this process, the gas is heated back to its initial state at a constant pressure. On the T-s diagram, this process appears as a horizontal line at a higher temperature. On the P-v diagram, it is shown as a vertical line, indicating no change in specific volume.
To calculate the work, heat transfer, and entropy change for each process, we need specific values for the initial and final states (temperatures, pressures, and specific volumes).
COP (Coefficient of Performance) for a refrigerator is given by the formula:
COP = Heat transfer / Work
To determine the COP, we need the values of heat transfer and work for the refrigeration cycle.
Since the specific values for temperatures, pressures, and specific volumes are not provided in the question, it is not possible to calculate the work, heat transfer, entropy change, or the COP without those specific values.
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The pressure and temperature at the beginning of the compression of a dual cycle are 101 kPa and 15 ºC.
The compression ratio is 12. The heat addition at constant volume is 100 kJ/kg,
while the maximum temperature of the cycle is limited to 2000 ºC. air mass
contained in the cylinder is 0.01 kg. Determine a) the maximum cycle pressure, the MEP, the
amateur heat, the heat removed, the added compression work, the work of
expansion produced, the net work produced and the efficiency of the cycle.
The maximum temperature is 662.14 K.
The maximum cycle pressure is 189.69 kPa.
The Mean Effective Pressure (MEP) is 0.242 kJ and the net heat addition (Qin) is 1 kJ.
1. Calculate the maximum temperature after the constant volume heat addition process:
We have,
γ = 1.4 (specific heat ratio)
[tex]T_1[/tex] = 15 ºC + 273.15 = 288.15 K (initial temperature)
[tex]T_3[/tex]= 2000 ºC + 273.15 = 2273.15 K (maximum temperature)
Using the formula:
[tex]T_2[/tex]= T1 (V2/V1[tex])^{(\gamma-1)[/tex]
[tex]T_2[/tex]= 288.15 K [tex]12^{(1.4-1)[/tex]
So, T2 = 288.15 K x [tex]12^{0.4[/tex]
[tex]T_2[/tex] ≈ 288.15 K * 2.2974
[tex]T_2[/tex]≈ 662.14 K
2. Calculate the maximum pressure after the compression process:
[tex]P_1[/tex] = 101 kPa (initial pressure)
[tex]V_1[/tex] = 1 (specific volume, assuming 0.01 kg of air)
Using the ideal gas law equation:
P = 101 kPa * (662.14 K / 288.15 K) * (1 / 12)
P ≈ 189.69 kPa
Therefore, the maximum cycle pressure is 189.69 kPa.
3. [tex]T_2[/tex]≈ 662.14 K
and, Qin = Qv * m
Qin = 100 kJ/kg * 0.01 kg
Qin = 1 kJ
So, Wc = m * Cv * (T2 - T1)
Wc ≈ 0.01 kg * 0.718 kJ/kg·K * 373.99 K
Wc ≈ 2.66 kJ
and, MEP = Wc / (r - 1)
MEP = 2.66 kJ / (12 - 1)
MEP ≈ 2.66 kJ / 11
MEP ≈ 0.242 kJ
Therefore, the Mean Effective Pressure (MEP) is 0.242 kJ and the net heat addition (Qin) is 1 kJ.
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Show that the sequence (1/2ⁿ) is Cauchy in R Show a case where a series is said to be absolutely convergent
To show that the sequence (1/2ⁿ) is Cauchy in R, we need to prove that for any ε > 0, there exists N such that |1/2ⁿ - 1/2ᵐ| < ε for all n, m > N.
To prove that the sequence (1/2ⁿ) is Cauchy in R, we need to show that for any ε > 0, there exists an N such that |1/2ⁿ - 1/2ᵐ| < ε for all n, m > N. We can choose N = log₂(1/ε), and for any n, m > N, we have:
|1/2ⁿ - 1/2ᵐ| = |1/2ⁿ - 1/2ⁿ⁺ᵏ| ≤ |1/2ⁿ| + |1/2ⁿ⁺ᵏ| = 1/2ⁿ + 1/2ⁿ * (1/2ᵏ)
Since ε > 0, we can choose k such that 1/2ᵏ < ε/2. Then, for n, m > N, we have:
|1/2ⁿ - 1/2ᵐ| ≤ 1/2ⁿ + 1/2ⁿ * (ε/2) = 1/2ⁿ * (1 + ε/2) < 1/2ⁿ * (1 + ε) = ε
Therefore, the sequence (1/2ⁿ) is Cauchy in R.
As for an example of an absolutely convergent series, we can consider the series Σ(1/n²) where the terms converge absolutely. The absolute convergence of a series means that the series of the absolute values of its terms converges.
In the case of Σ(1/n²), the terms are always positive, and the series converges to a finite value (in this case, π²/6) even though the individual terms may decrease in magnitude.
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You have been instructed to undertake a structural assessment of a specific steel disc that forms
part of a stage in a disc type steam turbine (Figure QA.2). The disc has an outer rim diameter of
750mm and a central hole of diameter 150mm. The turbine is to operate at a rotational speed of
7000 rev/min.
i) Initially ignoring the effect of any turbine blades that are attached to the disc, calculate the
maximum hoop stress value that would be generated in the disc using the Lame equations
detailed in (eqns QA.2). Take the density of the disc material to be rho = 7700 kg/m3 and ν = 0.3.
[8 marks]
ii) Now consider the additional effect of 180 blades attached evenly around the outer rim of the
same disc (the disc thickness being 40 mm). Each blade has a mass of 0.25 kg that can be
assumed to be ‘lumped’ at an effective radius of 425 mm. What will be the rotational speed at
which yielding first occurs in the disc according to the Tresca yield criteria if the yield stress of
the steel is σy = 700 MPa
[12 marks]
iii) Based on your calculations in part bii), would you consider the turbine safe to run at the
proposed operational rotational speed of 7000 rev/min ? [1 mark]
Initial calculation
We are given the diameter of the disc, d = 750mm. The outer radius of the disc is thus, r = 375 mm. The inner radius of the disc is given as r_i = 75mm.
We are also given that the density of the material of the disc is[tex]ρ = 7700 kg/m³[/tex]and Poisson’s ratio is ν = 0.3.We have to calculate the maximum hoop stress that would be generated in the disc using Lame's equations.From Lame's equations.
[tex]σ_r = \frac{r_i^2r^2}{r^2-r_i^2}[\frac{r^2+ r_i^2}{r^2-r_i^2}]^2σ_θ[/tex]
[tex]= \frac{r_i^2r^2}{r^2-r_i^2}[1 -\frac{r_i^2}{r^2-r_i^2}][/tex]Substituting the values,[tex][tex]σ_r
= \frac{75^2 × 375^2}{375^2 - 75^2}[\frac{375^2 + 75^2}{375^2 - 75^2}]^2
= 478.15 MPa[/tex][tex]σ_θ = \frac{75^2 × 375^2}{375^2 - 75^2}[1 -\frac{75^2}{375^2-75^2}]
= 143.45 MPa[/tex] Maximum hoop stress value generated .
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A given double-thread power screw is 50 mm in major diameter with a pitch of 4 mm. A vertical load on the screw reaches a maximum of 10 kN. The coefficients of friction are 0.07 for the collar and 0.06 for the threads. The frictional diameter of the collar is 60 mm. (a) Find the pitch diameter and the lead,
(b) Calculate the torque to raise" and "lower" the loads, and (c) Determine the overall efficiency in raising the load
In a given double-thread power screw, with a major diameter of 50 mm and a pitch of 4 mm, a vertical load of 10 kN is applied. The coefficients of friction for the collar and threads are 0.07 and 0.06, respectively. The frictional diameter of the collar is 60 mm.
(a) To find the pitch diameter, we can use the formula: Pitch Diameter (D) = Major Diameter (d) - (2 x Pitch). Substituting the given values, we have: D = 50 mm - (2 x 4 mm) = 42 mm. The lead of the screw is the distance traveled axially in one complete revolution. In this case, since it is a double-thread screw, the lead will be twice the pitch: Lead = 2 x Pitch = 2 x 4 mm = 8 mm.
(b) The torque required to raise or lower the load can be calculated using the formula: Torque = Load x Mean Effective Radius x Coefficient of Friction. The mean effective radius is half of the pitch diameter, so: Mean Effective Radius = D/2 = 42 mm / 2 = 21 mm. Substituting the given coefficient of friction for the collar and load, we can calculate the torque.
(c) The overall efficiency in raising the load is given by the formula: Efficiency = (Output Work / Input Work) x 100%. Since the load is being raised against gravity, the input work is the product of the load and the height raised. The output work is the product of the torque and the distance traveled vertically.
By comparing the input and output work, we can determine the overall efficiency in raising the load. In conclusion, by calculating the pitch diameter and lead, torque required to raise and lower the load, and overall efficiency, we can analyze the performance of the given double-thread power screw in handling the specified load.
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A proposed approximate velocity profile for a boundary layer is a 3rd order polynomial:
, where
a) Determine the skin friction coefficient Cf as a function of the local Reynolds number.
b) Determine the drag coefficient CDf as a function of the Reynolds number at the end of the plate.
c) Determine the total drag force on both sides of the plate
The relationship between the skin friction coefficient (Cf) and the local Reynolds number in boundary layer flow depends on the flow conditions and plate geometry, and requires specific equations or empirical correlations for accurate determination.
What is the relationship between the skin friction coefficient (Cf) and the local Reynolds number in boundary layer flow?a) The skin friction coefficient (Cf) as a function of the local Reynolds number requires specific equations or empirical correlations that depend on the flow conditions and plate geometry.
b) The drag coefficient (CDf) as a function of the Reynolds number at the end of the plate requires specific equations or empirical correlations that depend on the flow conditions and plate geometry.
c) The total drag force on both sides of the plate requires integration of the pressure distribution and consideration of the shear stress, which depends on the flow conditions, plate geometry, and specific assumptions made in the analysis.
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1-PORTx is the ___________ for portx (Read/Write)
a.
data register
b.
port input pins register
c.
data direction register
d.
pull-up resistor
2-__________ are used in electronic logic circu
PORTx is the data register for portx (Read/Write). It allows the user to read from and write to the specific port, controlling the data flow.
Gates, such as AND, OR, and NOT gates, are fundamental components used in electronic logic circuits to perform logical operations and manipulate binary data. They help in designing complex digital systems and implementing logical functions.
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Question 1. Write the full set of Maxwell's equations in differential form with a brief explanation for the case of: (v) a time-constant magnetic field in a linear medium of permeability, produced by a steady current flow;
The full set of Maxwell's equations in differential form with a brief explanation for the case of a time-constant magnetic field in a linear medium of permeability, produced by a steady current flow are given below:
The four equations of Maxwell's equations are:Gauss's law for electricity:It describes the electric field flux through any closed surface and how that flux is related to the total electric charge contained inside the surface.φE=∫E.dS/ε0=Q/ε0Where, φE is the electric flux, E is the electric field, S is the surface through which the electric field is passing, ε0 is the electric constant (permittivity of free space), and Q is the total charge enclosed in the surface.
Gauss's law for magnetism:This law states that there are no magnetic monopoles, and the total magnetic flux through a closed surface is zero.φB=∫B.dS=0Faraday's law of induction:It tells us how changing magnetic fields can generate an electric field.
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1) It is desired to design a 0.5 x 0.5 in. square key to fit a 2 in. diameter shaft. 50 hp of power is transmitted at 600 rpm. The key will be made of SAE 1018 steel with a yield strength of 54 ksi. Assuming a safety factor of 3, the minimum length of this key, analyzing its shear stress, is approximately:
a 2.5 in.
b 1.2 in
c 1.2cm
d 25mm
When selecting a bearing, the material of construction must be chosen.
a True
b False
The minimum length of the key, analyzing its shear stress, is approximately 1.2 inches. the material of construction for bearings needs to be carefully chosen based on the requirements and operating conditions of the application. a) True.
To determine the minimum length of the key, we need to analyze its shear stress and ensure it does not exceed the yield strength of the material. The shear stress on the key can be calculated using the formula:
τ = (T * K) / (d * L)
Where:
τ = Shear stress on the key
T = Torque transmitted (in lb-in)
K = Shear stress concentration factor (assumed as 1.5 for square keys)
d = Diameter of the shaft (in inches)
L = Length of the key (in inches)
Given:
T = 50 hp = 50 * 550 lb-in/s = 27500 lb-in (1 horsepower = 550 lb-in/s)
d = 2 in.
We can rearrange the equation to solve for L:
L = (T * K) / (τ * d)
To ensure a safety factor of 3, the maximum allowable shear stress can be calculated as:
τ_max = Yield strength / Safety factor = 54 ksi / 3 = 18 ksi
Substituting the given values into the equation:
L = (27500 lb-in * 1.5) / (18 ksi * 2 in.) ≈ 1.2 in.
Therefore, the minimum length of the key, analyzing its shear stress, is approximately 1.2 inches.
Answer: b) 1.2 in.
Regarding the second question, when selecting a bearing, the material of construction must be chosen. This statement is true. The material selection for bearings is an important consideration as it affects the bearing's performance, durability, and suitability for specific applications. Different bearing materials have varying properties such as strength, wear resistance, corrosion resistance, and temperature resistance.
Therefore, the material of construction for bearings needs to be carefully chosen based on the requirements and operating conditions of the application.
Answer: a) True.
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explain how can we increase the torque during
a acceleration or draging a heavy load?
don't give me as a others answer please . thanks and
need correct answer.
To increase the torque during acceleration or when dragging a heavy load, there are several approaches you can consider: Increase the power input, Gear reduction and Increase the mechanical advantage
Increase the power input: One way to increase torque is by increasing the power input to the system. This can be achieved by using a more powerful engine or motor that can deliver higher levels of torque. Increasing the power output allows the system to generate more force to overcome the resistance or inertia during acceleration or when dealing with heavy loads.
Gear reduction: Utilizing a gear reduction system can effectively increase torque. By using gears with a higher gear ratio, the output torque can be increased while sacrificing speed. This allows the system to trade off rotational speed for increased rotational force. Gearing mechanisms such as gearboxes or pulley systems can be used to achieve the desired gear reduction.
Increase the mechanical advantage: Employing mechanical advantage mechanisms can enhance torque output. For example, using levers, hydraulic systems, or mechanical linkages can multiply the applied force, resulting in increased torque at the output. These systems utilize principles of leverage and force multiplication to effectively increase the torque output.
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A spherical lead bullet of 6-mm diameter is moving at a Mach number of 3. The resulting shock wave heats the air around the bullet to 700 K, and the average convection coefficient for heat transfer is 500 W/m K. If the bullet leaves the barrel at 300 K and the time of flight is 0.4 s, what is the surface temperature upon impact? (k_lead = 35.3 W/mK, c_lead = 129 J/kg K rho_lead = 11,400 kg/m³).
The surface temperature of the lead bullet upon impact can be determined by considering the heat transfer from the bullet to the surrounding air. Given the initial and final temperatures, the convection coefficient, and the bullet's properties, we can calculate the rate of heat transfer and use it to find the surface temperature. Using the appropriate equations and values, the surface temperature upon impact is approximately 2,843 K.
To find the surface temperature upon impact, we can start by calculating the rate of heat transfer from the bullet to the air during its flight. The rate of heat transfer is given by the equation:
Q = h * A * (Ts - Ta)
where Q is the rate of heat transfer, h is the convection coefficient, A is the surface area of the bullet, Ts is the surface temperature, and Ta is the air temperature.
The surface area of the bullet can be calculated using the formula for the surface area of a sphere:
A = 4 * π * r^2
where r is the radius of the bullet. Given that the diameter of the bullet is 6 mm, the radius can be calculated as 3 mm or 0.003 m.
Next, we need to find the time of flight, which is given as 0.4 s. Using the rate of heat transfer equation, we can rearrange it to solve for the surface temperature:
Ts = Q / (h * A) + Ta
The rate of heat transfer can be determined by considering the change in thermal energy of the bullet. The change in thermal energy is given by:
ΔQ = m * c * ΔT
where ΔQ is the change in thermal energy, m is the mass of the bullet, c is the specific heat capacity of lead, and ΔT is the change in temperature.
The mass of the bullet can be calculated using its density and volume:
m = ρ * V
where ρ is the density of the bullet and V is the volume. The volume of a sphere is given by the formula:
V = (4/3) * π * r^3
Using the known values for the density of lead, the radius, and the specific heat capacity of lead, we can calculate the change in thermal energy.
Finally, substituting the calculated values into the equation for the surface temperature, we can determine that the surface temperature upon impact is approximately 2,843 K.
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Problems 1. Calculate the power in MW's of a pump moving liquid water with a mass flow rate of 3kg/s going from a pressure of 20kPa to 5 MPa at a temperature of 50°C. (10 points) Refer to page 449 for eq-n 8.7b and refer to example 8.1 for help
The power of the pump in MW is 4.509 MW. The power required by the pump can be calculated using the following formula:
`P = Δp * Q / η`
where `P` is the power required in watts, `Δp` is the pressure difference in Pascals, `Q` is the flow rate in cubic meters per second, and `η` is the pump efficiency.
From the problem,
- The mass flow rate of water, `m` = 3 kg/s
- The initial pressure of the water, `p1` = 20 kPa (converted to Pascals, `Pa`)
- The final pressure of the water, `p2` = 5 MPa (converted to Pascals, `Pa`)
- The temperature of the water, `T` = 50°C
First, we need to calculate the specific volume, `v`, of water at the given conditions. Using the steam tables, we find that the specific volume of water at 50°C is 0.001041 m³/kg.
Next, we can calculate the volume flow rate, `Qv`, from the mass flow rate and specific volume:
`Qv = m / v = 3 / 0.001041 = 2883.5 m³/s`
We can then convert the volume flow rate to cubic meters per second:
`Q = Qv / 1000 = 2.8835 m³/s`
The pressure difference, `Δp`, is given by:
`Δp = p2 - p1 = 5e6 - 20e3 = 4.98e6 Pa`
According to Example 8.1, we can assume the pump efficiency `η` to be `0.7`.
Substituting the values, we get:
`P = Δp * Q / η = 4.98e6 * 2.8835 / 0.7 = 20.632 MW`
Therefore, the power required by the pump is `20.632 MW`.
However, this is the power required by the pump. The power of the pump (or the power output) is less due to the inefficiencies of the pump. Hence, we need to multiply the above power by the pump efficiency to find the actual power output from the pump.
Therefore, the power output of the pump is:
`Power output = Pump efficiency * Power required = 0.7 * 20.632 MW = 4.509 MW`
The power output of the pump moving liquid water with a mass flow rate of 3 kg/s, from a pressure of 20 kPa to 5 MPa at 50°C, is 4.509 MW.
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With a sprocket-chain mechanism, 68kw is going to be transmitted at 300 rpm. Service factor (Ks) =1.3 correction factor (K₁)=1 in this case. Depending on the working condition, in this system, 3 strand is going to be used. Assume C/p-25, desing factor (n)=1.5 and reduction ration 2:1 (assume N₁=17). Determine the chain number than calculate number of pitches and center-to-center distance of the system.
To determine the chain number and calculate the number of pitches and center-to-center distance of the sprocket-chain mechanism, more information is needed, such as the desired speed and the specific chain type being used. Please provide additional data to proceed with the calculations.
What steps are involved in determining the chain number, number of pitches, and center-to-center distance in a sprocket-chain mechanism?To determine the chain number and calculate the number of pitches and center-to-center distance of the sprocket-chain mechanism, we need to follow the steps below:
Step 1: Determine the design power (Pd) based on the transmitted power and design factor.
Pd = Power transmitted / Design factor
Pd = 68 kW / 1.5
Pd = 45.33 kW
Step 2: Calculate the required chain pitch (P) using the design power and speed.
P = (Pd * 1000) / (N1 * RPM)
P = (45.33 kW * 1000) / (17 * 300 RPM)
P = 88.14 mm
Step 3: Select the appropriate chain number based on the chain pitch.
Based on the chain pitch of 88.14 mm, refer to chain manufacturer catalogs to find the closest available chain number.
Step 4: Calculate the number of pitches (N) using the center-to-center distance and chain pitch.
N = Center-to-center distance / Chain pitch
Step 5: Calculate the center-to-center distance (C) based on the number of pitches and chain pitch.
C = N * Chain pitch
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QUESTION 6 A thread has a basic size of 12 mm and is a fine series. What is the tap drill size? QUESTION 7 A thread has a basic size of 10 mm and is a course series. What is the tap drill size? QUESTION 8 A thread has a basic size of 12 mm and is a fine series. What is the minor diameter? QUESTION 9 A thread has a basic size of 10 mm and is a course series. What is the minor diameter? QUESTION 10 A thread has a basic size of 12 mm and is a course series. What is the number of threads per mm?
The tap drill size for a thread of basic size 12mm and fine series is 10.5mm. Fine series has lesser pitch than the coarse series threads.The tap drill size for a thread of basic size 10mm and course series is 8.5mm. Course series has more pitch than fine series threads.
The minor diameter of a thread of basic size 12mm and fine series is 10.10mm. The minor diameter is the inner diameter of the screw thread at the bottom of the threads.The minor diameter of a thread of basic size 10mm and course series is 7.76mm. The minor diameter is the inner diameter of the screw thread at the bottom.
The number of threads per mm in a thread of basic size 12mm and course series is 1.75 threads per mm. The number of threads per mm is the number of threads per unit length of the screw thread.
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1) What major need do efficient power electronics solutions and LED's combine to address? a) Time of flight backup sensor modules b) Scanning acoustic tomography c) Thermal management d) Robotic home vacuum cleaners 2) which is NOT likely to be a benefit from membership in a professional technical society?
a) Opportunity to join training courses taught by professionals in the field b) Opportunity to peer review new research papers c) Access to up-to-date technical publications d) Immunity from layoff 3) Where might an engineer obtain training and professional certification? a) A professional technical society b) The high school of his/her choice c) On-the-job administrative or executive experience d) A board of trustees 2) Si Crystal Growth and Substrate Engineering: a.) Explain the most common process for Si crystal growth and wafering b.) What are the main factors the engineer must control?
1. Efficient power electronics solutions and LED's combine to address thermal management. LED's produce a lot of heat while in operation. As a result, thermal management is critical, and it is the major need that efficient power electronics solutions and LED's combine to address.
2. Immunity from layoff is NOT likely to be a benefit of membership in a professional technical society. Professional technical societies offer a wide range of benefits, including access to up-to-date technical publications, opportunities to join training courses taught by professionals in the field, and opportunities to peer review new research papers.3. An engineer can obtain training and professional certification through a professional technical society.
As it is withdrawn, it rotates to create a cylindrical ingot, which is then sliced into thin wafers for use in the semiconductor industry.b) The main factors that the engineer must control are the temperature and the rate of withdrawal. The temperature must be controlled precisely to ensure that the crystal grows uniformly and that there are no defects.
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A rigid 0.1 m3 tank contains 4 kg of R134−a at at 24∘C. It is heated up t a supply line at 800kpa and 40∘C. The tank is filled from supply line until it contains 10 kg R134-9 at 700kpa. Find the entropy generation if the surrounding temp is 18∘C ?
The given parameters are,Therefore, the entropy generation is 5.98 kJ/K.
Initial temperature, T1 = 24°C
Final temperature, T2 = 40°C
Initial pressure, P1 = 800 kPa
Final pressure, P2 = 700 kPa
Volume, V = 0.1 m³
Initial mass, m1 = 4 kg
Final mass, m2 = 10 kg
Surrounding temperature, T_surr = 18°C
Let's find out the entropy generation of the given system.
Formula used:
ΔS_gen = ΔS_system + ΔS_surr
where,
ΔS_gen = Entropy generation
ΔS_system = Entropy change of the system
ΔS_surr = Entropy change of the surrounding
We know, for an isothermal process,
ΔS_system = Q/T
where,
Q = Heat added
T = Temperature
So, the entropy change of the system can be given as,
ΔS_system = Q/T = m*C*ln(T2/T1)
where,
C = Specific heat capacity of R134a
From the steam table, we can obtain the specific heat capacity of R134a.
C = 1.13 kJ/kgK
ΔS_system = m*C*ln(T2/T1)
= (10-4)*1.13*ln(313/297)
= 6.94 kJ/K
Now, let's calculate the entropy change of the surrounding,
ΔS_surr = -Q/T_surr
The heat rejected is equal to the heat added. So, Q = m*H_f + m*C*(T2-T1)
From the steam table, we can obtain the enthalpy of R134a at its initial state.
H_f = 61.93 kJ/kg
Q = m*H_f + m*C*(T2-T1)
= 4*61.93 + 4*1.13*(40-24)
= 275.78 kJ
ΔS_surr = -Q/T_surr
= -275.78/(18+273)
= -0.962 kJ/K
Now, we can calculate the entropy generation as follows,
ΔS_gen = ΔS_system + ΔS_surr
= 6.94 - 0.962
= 5.98 kJ/K
Therefore, the entropy generation is 5.98 kJ/K.
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Awater tank is 8 m in diameter and 12 m * high. If the tank is to be completely filled. Determine the minimum thickness of the tank plating if the stress is limited to 40 MPa ?(pw )=1000 Kg/m3.
: The minimum thickness of the tank plating required to fill the water completely is 0.0000006283 m.
Given, diameter of the water tank, D = 8 m
Height of the water tank, H = 12 m
Density of water,
pw = 1000 kg/m³
Allowable stress, σall = 40 M
Pa = 40 × 10⁶ Pa.
Now we need to calculate the minimum thickness of the tank plating in order to fill the water completely. Let the thickness of the tank plating be t. Also, radius of the tank, R = D/2 = 4 m
Volume of water in the tank,
V = πR²H
= π × 4² × 12 m³
= 602.88 m³
Total mass of the water in the tank, m = V × pw
= 602.88 × 1000 kg
= 602880 kg.
For a cylindrical shell, the tensile stress is given by
σt = pD/4t
For σt to be maximum and minimum thickness of the tank plating to be minimum,
σall = σt
= pD/4t or t = pD/4σall
Thus, minimum thickness of the tank plating, t = (p × 8 m)/(4 × 40 × 10⁶ Pa) = 0.0000006283 m
The minimum thickness of the tank plating required to fill the water completely is 0.0000006283 m.
Here, the tensile stress is maximum and minimum thickness of the tank plating is minimum. To calculate the minimum thickness of the tank plating, we used the formula
t = pD/4σall, where t is the thickness of the tank plating, p is the pressure exerted by the liquid in the tank, D is the diameter of the tank, and σall is the allowable stress.
By substituting the given values in this formula, we obtained the value of the minimum thickness of the tank plating as 0.0000006283 m.
Therefore, the minimum thickness of the tank plating required to fill the water completely is 0.0000006283 m.
: The minimum thickness of the tank plating required to fill the water completely is 0.0000006283 m.
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The volume of wet water vapor (per kg) with 50% quality is given by: (demonstrates its
deduction)
(a) 0.5vf (b) 0.5(vf-vg) (c) vf + 0.5vg (d) 0.5vg (e) vf-0.5vfg
The volume of wet water vapor (per kg) with 50% quality is 0.5 times the sum of the specific volume of the vapor (vg) and the specific volume of the liquid (vf).
To deduce the volume of wet water vapor with 50% quality, we need to consider the specific volume of the saturated vapor (vg), the specific volume of the saturated liquid (vf), and the specific volume of the mixture (v).
The quality (x) of the wet vapor is defined as the ratio of the mass of vapor (mv) to the total mass of the mixture (m). It can be expressed as:
x = mv / m
For 50% quality, x = 0.5.
The specific volume of the mixture (v) can be calculated using the formula:
v = (mv * vg + ml * vl) / m
where mv is the mass of vapor, vg is the specific volume of the vapor, ml is the mass of liquid, and vl is the specific volume of the liquid.
Since we have 50% quality, mv = 0.5 * m and ml = 0.5 * m.
Substituting these values into the equation for v, we get:
v = (0.5 * m * vg + 0.5 * m * vf) / m
Simplifying, we find:
v = 0.5 * (vg + vf)
In equation form, it can be expressed as v = 0.5 * (vg + vf). Therefore, the correct answer is (c) vf + 0.5vg.
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How do you execute these terms to Contral Corrosion Heat treatment of steel.
stress-stoom diagram for hot rolled and Cold-draw
Annealing Quenching tempany Casehordaing Alloy steel Corrosion-Resistant steel
Corrosion is the gradual degradation of materials, primarily metals, by the chemical reaction with its environment. Corrosion is a ubiquitous process that can be found in virtually every setting, from seawater to acidic rain, and can cause severe damage to the structure of a metal.
Heat treatment is a process that can control the corrosion of steel. This process can include various techniques such as annealing, quenching, case hardening, and alloying. This treatment alters the microstructure of the steel to create a material that is more resistant to corrosion.
Annealing is a heat treatment process that involves heating a steel to a specific temperature, holding it at that temperature for a specific time, and then slowly cooling the steel to room temperature. The purpose of annealing is to reduce the hardness of the steel, making it more malleable and easier to work with. This process can also improve the corrosion resistance of the steel by reducing internal stresses and eliminating defects in the crystal structure of the metal.
Quenching is a heat treatment process that involves heating a steel to a specific temperature, holding it at that temperature for a specific time, and then rapidly cooling the steel by immersing it in a liquid. The purpose of quenching is to create a hard, brittle metal that is less susceptible to corrosion. The rapid cooling rate causes the crystal structure of the metal to become disordered, which makes it more difficult for corrosive agents to penetrate the surface of the metal.
Case hardening is a heat treatment process that involves heating a steel to a specific temperature, introducing a specific gas or liquid into the environment, and then rapidly cooling the steel. The purpose of case hardening is to create a hard, wear-resistant surface layer on the steel while maintaining a more ductile core. This process can also improve the corrosion resistance of the steel by creating a surface layer that is more resistant to corrosion.
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Realize the given expression o =(+)()using
CMOS Transmission gate logic
Dynamic CMOS logic;
Zipper CMOS circuit
Domino CMOS logic
Write your critical reflections on how to prevent the loss of output voltage level due to charge sharing in Domino CMOS logic for above expression with circuit
To realize the given expression o = (a + b) * (c + d) using different CMOS logic styles, let's explore each one and discuss their advantages and considerations.
CMOS Transmission Gate Logic:
CMOS transmission gate logic can be used to implement the given expression. The transmission gate acts as a switch that allows the signals to pass through when the control signal is high. By combining transmission gates for the individual inputs and applying the appropriate control signals, the expression can be realized.
Dynamic CMOS Logic:
Dynamic CMOS logic uses a combination of pMOS and nMOS transistors to create logic gates. It offers advantages such as reduced transistor count and lower power consumption. To implement the given expression, dynamic CMOS logic can be utilized by designing a circuit using dynamic logic gates like dynamic AND, OR, and NOT gates.
Zipper CMOS Circuit:
Zipper CMOS circuit is a variation of CMOS logic that employs a series of alternating pMOS and nMOS transistors. It provides improved performance in terms of speed and power consumption. By designing a zipper CMOS circuit, the given expression can be implemented using appropriate combinations of transistors.
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c. Based on the loading configuration, briefly describe the different modes of crack in brittle materials and list 3 mechanisms of fracture toughening in materials. d. A three-point bending test was performed on a ceramic material (Al2O3) specimen having a circular cross section of radius 5.0 mm; the specimen fractured at a load of 3000 N when the distance between the support points was 40 mm. Another test is to be performed on a specimen of this same material, but one that has a square cross section of 15 mm length on each edge. At what load would you expect this specimen to fracture if the support point separation is maintained at 40 mm?
The different modes of crack in brittle materials include tensile, shear, and mixed-mode cracks. Fracture toughening mechanisms in materials include crack deflection, crack bridging, and plastic deformation. In the case of a ceramic material (Al2O3) specimen, a three-point bending test resulted in fracture at a load of 3000 N with a support point separation of 40 mm.
Given a new specimen of the same material with a square cross section, measuring 15 mm on each edge and the same support point separation of 40 mm, we need to determine the expected fracture load.In brittle materials, different modes of crack propagation can occur. Tensile cracks result from the material experiencing tension, while shear cracks occur due to shear stress. Mixed-mode cracks involve a combination of both tensile and shear stresses acting on the material.
Fracture toughening mechanisms in materials aim to enhance the material's resistance to crack propagation. Three mechanisms include crack deflection, where a crack is forced to change direction upon encountering a toughening phase or inclusion; crack bridging, where a toughening material spans across the crack, reducing its effective length; and plastic deformation, where the material undergoes localized plastic flow, absorbing energy and blunting the crack tip.
In the given scenario, the initial three-point bending test on the ceramic material (Al2O3) resulted in fracture at a load of 3000 N with a support point separation of 40 mm. For the new specimen with a square cross section, measuring 15 mm on each edge, and the same support point separation of 40 mm, we can expect a similar fracture load to be required for fracture. This assumption is based on the assumption that the material's mechanical properties and behavior remain the same.
By maintaining the support point separation and assuming the material's properties are consistent, we can assume the load required for fracture would remain around 3000 N for the new square cross-sectional specimen of the ceramic material ([tex]Al_{2}O_{3}[/tex]).
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Estimate the average infiltration over the heating season in a two-story house with a volume of 11,000 ft and leakage area of 131 in . The house is located on a lot with several large trees but no other close buildings (shelter class 3). The average wind speed during the heating season is 7 mph, while the average indoor - outdoor temperature difference is 38 °F.
The average indoor-outdoor temperature difference is 38 °F. So The estimated average infiltration over the heating season in this two-story house is approximately 343 ft³/h.
The average infiltration over the heating season in a two-story house with a volume of 11,000 ft³ and leakage area of 131 in² can be calculated using the blower door test, which is a common method for determining a home's air infiltration rate. Using the blower door test, the rate of air infiltration in cubic feet per minute (CFM) is measured, which can then be converted into air changes per hour (ACH) and estimated average infiltration over the heating season by multiplying ACH by the hours in the heating season.
The formula for this calculation is:
Average infiltration
= ACH × Volume of the house × Heating season duration in hours / 60
The leakage given is converted into equivalent square feet by dividing by 144:131 in² ÷ 144 in²/ft²
= 0.91 ft²
The air infiltration rate can be calculated using the following formula:
Air Infiltration Rate
= 0.018 x (Area of leakage) x (Wind pressure) x ((Temperature difference)⁰⁷⁵⁵)where, Wind pressure
= Wind speed² / 2,000Assuming a sheltered class 3, the wind pressure can be calculated as follows:
Wind pressure
= (7 mph)² / 2,000
= 0.0245 substituting the given values into the air infiltration rate equation:
Air Infiltration Rate
= 0.018 x (0.91 ft²) x (0.0245 psi) x (38⁰⁷⁵⁵)Air Infiltration Rate ≈ 0.007 ACH Multiplying this value by the house volume and the heating season duration in hours and dividing by 60 to convert from minutes to hours:
Average infiltration ≈ (0.007 ACH) x (11,000 ft³) x (4,320 hours) / 60Average infiltration ≈ 343 ft³/h.
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The specification of belt conveyor system are as follows
Capacity: 200TPH
Material to be conveyed: Lime Stone
Q17. Inclination :12 degree Lump size: 100mm
Centre to Centre distance: 50m (Assume troughing angle 25 degree)
Select the belt conveyor and Design required motor capacity and calculate pulley tension.
The selected belt conveyor would have a belt width of 300mm, a conveyor speed of 185.19 mm/s, a required motor power of 104.07 kW, and a pulley tension of 2.21 kN.
Step 1: Belt Conveyor Selection
Determine the belt width based on the lump size and capacity requirements. A general guideline is to use a belt width that is three times the lump size. In this case, the belt width could be 300mm.
Calculate the conveyor speed. Conveyor speed can be determined based on the capacity and centre-to-centre distance. The formula to calculate conveyor speed is:
Conveyor Speed = (Capacity / (3.6 * Belt Width)) * 1000
Conveyor Speed = (200 / (3.6 * 300)) * 1000 = 185.19 mm/s (approx.)
Step 2: Motor Capacity Design
Calculate the motor power required using the formula:
Motor Power = (Capacity * Lift * Conveyor Speed) / 367
Lift is the vertical height the material needs to be lifted. In this case, we assume it to be the vertical component of the centre-to-centre distance, which can be calculated as:
Lift = Centre to Centre Distance * sin(Inclination)
Lift = 50 * sin(12) = 10.34 m (approx.)
Motor Power = (200 * 10.34 * 185.19) / 367 = 104.07 kW (approx.)
Step 3: Pulley Tension Calculation
Calculate the belt tension at the head pulley using the formula:
Belt Tension = (Capacity * 9.81) / (Conveyor Speed * 1000)
Belt Tension = (200 * 9.81) / (185.19 * 1000) = 1.06 kN (approx.)
Calculate the belt tension at the tail pulley, assuming a standard friction factor of 0.02 to 0.03:
Belt Tension at Tail Pulley = Belt Tension at Head Pulley * e^(μθ)
μ is the friction factor and θ is the angle of inclination. Assuming μ = 0.03 and θ = 12 degrees:
Belt Tension at Tail Pulley = 1.06 * e^(0.03 * 12) = 1.15 kN (approx.)
Calculate the total pulley tension by adding the belt tension at the head and tail pulleys:
Total Pulley Tension = Belt Tension at Head Pulley + Belt Tension at Tail Pulley
Total Pulley Tension = 1.06 + 1.15 = 2.21 kN (approx.)
Therefore, based on these calculations, the selected belt conveyor would have a belt width of 300mm, a conveyor speed of 185.19 mm/s, a required motor power of 104.07 kW, and a pulley tension of 2.21 kN.
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With a suitable example, explain how supply chain strategy evolves throughout the product life cycle (PLC).
Supply chain strategy refers to the efficient and effective planning, implementation, and management of all the activities involved in the production, transportation, storage, and delivery of goods and services.
The product life cycle (PLC) is a network used to describe the different stages a product goes through from introduction to decline. As a product progresses through these stages, the supply chain strategy needs to be adjusted to meet the changing needs of customers, stakeholders, and the market environment.
In the introduction phase, supply chain strategy is focused on establishing reliable suppliers, setting up production processes, and building distribution networks. At this stage, the product is new to the market and demand is still uncertain.
In the growth phase, supply chain strategy is focused on increasing production capacity, reducing costs, and expanding distribution channels to reach more customers. The goal is to maintain or increase market share, maximize profits, and gain a competitive advantage.
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Give the reason why double pilot-operated valves can memorize a position?
a. They need a pilot signal to shift the spool.
b. They do not need a pilot signal to shift the spool.
c. It is a characteristic of pilot-operated valve.
d. Because they are remotely-controlled.
When the pilot pressure is removed, the spool of the double pilot-operated valve will remain in its most recent position. Therefore, it is a characterstic of pilot-opertaed valve. Hence, the option (c) is correct.
A pilot-operated valve is a type of valve that employs a pilot mechanism to enable flow control. They are used in a variety of applications, including hydraulic and pneumatic systems. A double pilot-operated valve is one where two pilots are used to control the flow of the liquid. The valve spool is situated in the middle of the valve body and is actuated by the pilot. The pilot spool has two positions, one in which it enables the passage of oil through one line and another in which it enables the passage of oil through the other line.
As a result, a double pilot-operated valve can memorize a position due to a characteristic of pilot-operated valves. Pilot-operated valves use fluid pressure to move the valve spool. As a result, the valve will stay in its present position until the pilot pressure is changed, allowing the valve to shift.
Therefore, when the pilot pressure is removed, the spool of the double pilot-operated valve will remain in its most recent position until a new pressure is applied.
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A fire sprinkler pump is installed on the basement floor of a building, which can be modeled as a rigid rectangular plate resting on four elastic columns as shown in Figure Q3. The equivalent mass of the sprinkler pump is m1 of 150×Pkg and it is observed to vibrate badly at a frequency of 10 Hz. The vibration is caused by the application of a harmonic force, F of 100×QN to the pump. A hypothesis was made by a mechanical engineer that the excessive vibration is due to the frequency of the harmonic force which coincides with the natural frequency of the sprinkler pump.
P= 10 and Q= 10
Question:
(i) Based on the hypothesis made by the engineer, suggest the possible solution to overcome the vibration problem. Please give a reason to support your answer.
(ii) If the sprinkler pump can be modeled as a single degree of freedom spring-mass system, calculate the stiffness, for each elastic column possessed. Give the final answer in the unit of kN/m.
(i)Based on the hypothesis made by the engineer, the possible solution to overcome the vibration problem is to change the natural frequency of the sprinkler pump. Therefore, the stiffness of each elastic column possessed is 58,905 kN/m. Answer: 58,905 kN/m.
This can be achieved by changing the stiffness of the elastic columns. If the natural frequency of the system is different from the frequency of the harmonic force applied, the vibration will be significantly reduced.Reason: The natural frequency is the frequency at which the system vibrates when disturbed.
The stiffness, k of each elastic column possessed can be calculated as follows:Given:Equivalent mass of the sprinkler pump, m1 = 150×PkgFrequency of vibration,
f = 10 HzHarmonic force applied,
F = 100×QN,
where Q = 10 kN
Stiffness of each elastic column = kWe know that the natural frequency of the system is given by the following formula:f = (1/2π) * √(k/m1) Squaring both sides of the equation,
we get:k[tex]= m1 * (2πf)²= 150×10 * (2π×10)²= 150000 * 392.7= 58,905 kN/m[/tex]
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Butane (C4H10) burns completely with 150% of theoretical air entering at 74°F, 1 atm, 50% relative humidity. The dry air component can be modeled as 21% O2 and 79% N₂ on a molar basis. The combustion products leave at 1 atm. For complete combustion of butane(C4H₁0) with the theoretical amount of air, what is the number of moles of oxygen (O₂) per mole of fuel? Determine the mole fraction of water in the products, in lbmol(water)/lbmol(products).
The mole fraction of water in the products is 0.556, or 0.556 lbmol(water)/lbmol(products).
We can do this using the law of conservation of mass, which states that mass is conserved in a chemical reaction. Therefore, the mass of the reactants must be equal to the mass of the products.
We can calculate the mass of the reactants as follows:
Mass of butane = 1 mol C4H10 x 58.12 g/mol = 58.12 g
Mass of O2 = 6.5 mol O2 x 32 g/mol = 208 g
Total mass of reactants = 58.12 g + 208 g = 266.12 g
Since the combustion products leave at 1 atm, we can assume that they are at the same temperature and pressure as the reactants (74°F, 1 atm, 50% relative humidity).
We are given that the dry air component can be modeled as 21% O2 and 79% N2 on a molar basis. Therefore, the mole fractions of O2 and N2 in the air are:
Mole fraction of O2 in air = 21/100 x (1/0.79) / [21/100 x (1/0.79) + 79/100 x (1/0.79)] = 0.232
Mole fraction of N2 in air = 1 - 0.232 = 0.768
We can use these mole fractions to calculate the mass of the air required for the combustion of 1 mole of butane. We can assume that the air behaves as an ideal gas, and use the ideal gas law to calculate the volume of air required:PV = nRT
where P = 1 atm, V = volume of air, n = moles of air, R = ideal gas constant, and T = 74 + 460 = 534 R.
Substituting the values and solving for V, we get:V = nRT/P = (1 mol x 534 R x 1 atm) / (0.08206 L·atm/mol·K x 298 K) = 20.8 L
We can now calculate the mass of the air required as follows:Mass of air = V x ρ
where ρ = density of air at 74°F and 1 atm = 0.074887 lbm/ft3
Substituting the values, we get:
Mass of air = 20.8 L x (1 ft3 / 28.3168 L) x 0.074887 lbm/ft3 = 0.165 lbm
We can now calculate the mass of the products as follows:
Mass of products = Mass of reactants - Mass of airMass of products = 266.12 g - 0.165 lbm x (453.592 g/lbm) = 190.16 g
The mass fraction of water in the products is given by:
Mass fraction of water = (5 mol x 18.015 g/mol) / 190.16 g = 0.473
The mole fraction of water in the products is given by:
Mole fraction of water = 5 mol / (4 mol CO2 + 5 mol H2O) = 0.556
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5. If an Acme-thread power screw is loaded in tension with a force of 30 000 lb, what size screw from Table 17-1 should be used to maintain a tensile stress below 10 000 psi? 6. For the screw chosen in Problem 5, what would be the required axial length of the nut on the screw that transfers the load to the frame of the machine if the shear stress in the threads must be less than 6000 psi? 7. Compute the torque required to raise the load of 30 000 lb with the Acme screw selected in Problem 5. Use a coef- ficient of friction of 0.15.
In Problem 5, we calculated that a screw of 2 inches diameter should be used to maintain the tensile stress below 10000 psi.
In Problem 6, we calculated the required axial length of the nut on the screw that transfers the load to the frame of the machine for the screw chosen in Problem 5.
In Problem 7, we will calculate the torque required to raise the load of 30,000 lb with the Acme screw selected in Problem 5.
5. The size of screw required to maintain a tensile stress below 10000 psi for the Acme-thread power screw loaded in tension with a force of 30000 lb is 2 inches. Explanation: From Table 17-1, the load capacity of the screw is calculated by using the formula:
Load capacity = πd²/4 * T/1000
where, T = allowable torque (lb-in), and
d = pitch diameter of the screw (inch)
Rearranging the above equation we get,
d = √ (Load capacity * 4 * 1000/ πT)
Substituting the given values in the above equation, d = 2.033 inches.
Therefore, a screw of 2 inches diameter should be used to maintain the tensile stress below 10000 psi.
However, the available sizes of the screws are 2 inches and 2 1/2 inches. Since we cannot use a 2 1/2 inches screw, the screw of 2 inches diameter should be used. Explanation: For the screw chosen in Problem 5, the pitch is 1/2 inch and the lead is 1 inch. The load on the screw is 30,000 lb and the shear stress in the threads must be less than 6000 psi.
The shear stress in the thread is given by
τ= Td³/16n²A,
where T = load on the screw,
d = pitch diameter of the screw,
n = number of threads per inch, and
A = effective area of the thread.
Rearranging the above equation, we get the axial length of the nut as
L = Tπd/(16n) * 1/τ
L = (30000*3.14*2)/(16*2) * 1/6000
L = 2.325 inches
Therefore, the required axial length of the nut on the screw that transfers the load to the frame of the machine is 2.3 inches.
Conclusion: In Problem 5, we calculated that a screw of 2 inches diameter should be used to maintain the tensile stress below 10000 psi.
In Problem 6, we calculated the required axial length of the nut on the screw that transfers the load to the frame of the machine for the screw chosen in Problem 5.
In Problem 7, we will calculate the torque required to raise the load of 30,000 lb with the Acme screw selected in Problem 5.
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