Answer:
The diffusion coefficient for magnesium in aluminum at the given conditions is 2.22x10⁻¹⁴m²/s.
Explanation:
The diffusion coefficient represents how easily a substance (solute, e.g.: magnesium) can move through another substance (solvent, e.g.: aluminum).
The formula to calculate the diffusion coefficient is:
D=D₀.exp(- EA/R.T)
Each term of the formula means:
D: diffusion coefficient
D₀: Pre-exponential factor (it depends on each particular system, in this case the magnesium-aluminium system)
EA: activation energy
R: gas constant
T: temperature
1st) It is necessary to make a unit conversion for the temperature from °C to K, because we need to solve the problem according to the units of the gas constant (R) to assure the units consistency, so:
Temperature conversion from °C to K: 500 + 273 = 773 K
2nd) Replace the terms in the formula and solve:
D=D₀.exp(- EA/R.T)
D=1.2x10⁻⁴m²/s . exp[- 144,000 J/mole / (8.314 J/mol K . 773K)]
D=1.2x10⁻⁴m²/s . exp(-22.41)
D=1.2x10⁻⁴m²/s . 1.85x10⁻¹⁰
D= 2.22x10⁻¹⁴m²/s
Finally, the result for the diffusion coefficient is 2.22x10⁻¹⁴m²/s.
3. Suppose that a class named Bicycle contains a private nonstatic integer named height, a public nonstatic String named model, and a public static integer named wheels. Which of the following are legal statements in a class named BicycleDemo that has instantiated an object as Bicycle myBike new Bicycle C);? f. Bicycle. model Hurricane a. myBike height 26; b. my Bike model Cyclone g. Bicycle. int 3 3; c. myBike Wheels 3 d. my Bike .model 108; i. Bicycle wheels 2 e. Bicycle height 24; j. Bicycle yourBike myBike
Answer:
The solution to the given problem is provided below.
Explanation:
a.) myBike.height = 26; Not Legal statement
b.) myBike.model = “Cyclone”: Legal statement
c.) myBike.wheels = 3; Legal statement
d.) myBike.model = 108; Not legal statement
e.) Bicycle.height = 24; Not Legal statement
f.) Bicycle.model = “Hurricane”; Not legal statement
g.) Bicycle.int = 3; Not Legal statement
h.) Bicycle.model = 108; Not Legal Statement
i.) Bicycle.wheels = 2; Legal Statement
j.) Bicycle yourBike = myBike; Legal Statement
The portable lighting equipment for a mine is located 100 meters from its dc supply source. The mine lights use a total of 5 kW and operate at 120 V dc. Determine the required cross-sectional area of the copper wires used to connect the source to the mine lights if we require that the power lost in the copper wires be less than or equal to 5 percent of the power required by the mine lights.
To calculate the required cross-sectional area of copper wires needed to connect the DC supply source to the mine lights with less than 5% power loss, calculate the permissible power loss, and then use the relationship between power loss, current, and wire resistance. Considering the resistivity of copper and the round trip length of the wire, the formula A = ρL/(δP/I²) determines the necessary wire thickness.
Explanation:To determine the required cross-sectional area of copper wires for the lighting equipment, we need to ensure the power loss (δP) is no more than 5% of the lights' power usage (P), which is 5 kW (5000 W). As the power loss in wires is given by δP = I²R, where I is the current and R is the resistance of the wire, we must first calculate the current using P = IV, giving I = P/V = 5000W/120V = 41.67 A. The power loss allowed is thus 5% of 5000 W, equating to 250 W. Given δP, we can find R using δP = I²R, which gives R = δP/I².
The resistance of a copper wire is also given by R = ρL/A, where ρ is the resistivity of copper (1.68 x 10^-8 Ωm), L is the length of the wire (200 meters round trip), and A is the cross-sectional area we need to find. Equating the two expressions for R and solving for A gives A = ρL/(δP/I²). Substituting the given and calculated values yields the required cross-sectional area. Finally, as resistance depends on the entire length of the circuit, remember to double the distance to account for both the outgoing and return paths.
The wet density of a sand was found to be 1.9 Mg/m3 and the field water content was 10%. In the laboratory, the density of solids was found to be 2.66 Mg/m3, and the maximum and minimum void ratios were 0.62 and 0.44, respectively.
a. What is the field relative density?
b. How much will a 3 m thick stratum of this sand settle if the sand is densified to a relative density of 65%?
Answer:
a) 44.4%
b) 72 mm
Explanation:
See attached pictures.
a. The field relative density is 44.44%.
b. A 3 m thick stratum of this sand will settle by 0.111 m when densified to a relative density of 65%.
Let's solve the problem step-by-step.
Given Data
- Wet density of sand [tex](\( \rho_{wet} \)) = 1.9 Mg/m\(^3\)[/tex]
- Field water content ( w ) = 10% = 0.10
- Density of solids [tex](\( \rho_s \))[/tex] = 2.66 [tex]Mg/m\(^3\)[/tex]
- Maximum void ratio [tex](\( e_{max} \))[/tex] = 0.62
- Minimum void ratio [tex](\( e_{min} \))[/tex] = 0.44
a. Calculation of Field Relative Density
First, we need to calculate the dry density of the sand:
[tex]\[ \rho_{dry} = \frac{\rho_{wet}}{1 + w} = \frac{1.9}{1 + 0.10} = \frac{1.9}{1.10} = 1.727 \text{ Mg/m}^3 \][/tex]
Now, we use the dry density to find the void ratio e :
[tex]\[ e = \frac{\rho_s}{\rho_{dry}} - 1 = \frac{2.66}{1.727} - 1 = 1.54 - 1 = 0.54 \][/tex]
Relative density [tex](\( D_r \))[/tex] is given by the formula:
[tex]\[ D_r = \frac{e_{max} - e}{e_{max} - e_{min}} \times 100\% \][/tex]
Substituting the values:
[tex]\[ D_r = \frac{0.62 - 0.54}{0.62 - 0.44} \times 100\% = \frac{0.08}{0.18} \times 100\% = 44.44\% \][/tex]
b. Settlement Calculation
To find the settlement of a 3 m thick stratum of sand when densified to a relative density of 65%, we need to determine the void ratio corresponding to 65% relative density.
[tex]\[ D_r = 65\% = 0.65 \][/tex]
Using the relative density formula again, solve for e :
[tex]\[ 0.65 = \frac{e_{max} - e_{new}}{e_{max} - e_{min}} \][/tex]
[tex]\[ 0.65 = \frac{0.62 - e_{new}}{0.62 - 0.44} \][/tex]
[tex]\[ 0.65 \times (0.62 - 0.44) = 0.62 - e_{new} \][/tex]
[tex]\[ 0.65 \times 0.18 = 0.62 - e_{new} \][/tex]
[tex]\[ 0.117 = 0.62 - e_{new} \][/tex]
[tex]\[ e_{new} = 0.62 - 0.117 = 0.503 \][/tex]
Now calculate the initial and final volumes of voids:
Initial void ratio [tex]\( e_{initial} = 0.54 \)[/tex]
Final void ratio [tex]\( e_{new} = 0.503 \)[/tex]
Initial volume of voids [tex]\( V_{v_initial} \):[/tex]
[tex]\[ V_{v_initial} = e_{initial} \times V_s \][/tex]
Final volume of voids [tex]\( V_{v_final} \):[/tex]
[tex]\[ V_{v_final} = e_{new} \times V_s \][/tex]
The change in void volume:
[tex]\[ \Delta V_v = V_{v_initial} - V_{v_final} = (e_{initial} - e_{new}) \times V_s \][/tex]
For the 3 m thick stratum:
[tex]\[ \Delta H = \Delta V_v \][/tex]
[tex]\[ \Delta H = (e_{initial} - e_{new}) \times H \][/tex]
[tex]\[ \Delta H = (0.54 - 0.503) \times 3 \text{ m} \][/tex]
[tex]\[ \Delta H = 0.037 \times 3 \text{ m} \][/tex]
[tex]\[ \Delta H = 0.111 \text{ m} \][/tex]
So, the sand stratum will settle by 0.111 m when densified to a relative density of 65%.
A man can swim at 4 ft/s in still water. He wishes to cross tje 40-ft wide river to point B, 30 ft downstream. If the river flows with a velocity of 2 ft/s, determine the speed of the man and the time needed to make the crossing. Note While in the water he must not direct himself toward point B to reach the point.
Vector addition is used to calculate the speeds of the swimmer and the water in the river, understanding relative velocity is key in solving the problem.
Explanation:To determine the speed of the water in the river, we first calculate the resultant velocity of the swimmer using vector addition. The swimmer's speed with respect to a friend at rest on the ground is found by considering the swimmer's velocity and the water current's velocity. By understanding the concepts of relative velocity and vector addition, we can accurately calculate the required speeds.
You are considering purchasing a compact washing machine, and you have the following information: The Energy Guide claims an estimated yearly electricity use of 350 kW-hrs, based on 8 loads of laundry being washed per week. The Energy Guide claims an estimated yearly operating cost of $38. This estimate is based on $0.1065 per kW-hr, and eight loads of laundry being washed per week. Local electricity costs $0.086 per kW-hr. You wash four loads of laundry per week. Based on this information, first calculate the energy that would be used by this compact washing machine in a year. Then calculate the yearly energy cost. a. $3.27 b. $19.00 c. $15.34 d. $178.40
Answer: $15.34
Explanation: see image below
To find the yearly energy cost of the washing machine, half the estimated energy usage is taken due to halved weekly loads, resulting in 175 kW-hrs per year. Multiplying this by the local electricity cost gives an annual operating cost close to $15.34.
Explanation:To calculate the annual energy usage of the compact washing machine, you should first adjust the estimated yearly electricity use based on the difference in the number of loads washed per week. Since you are washing half the number of loads (4 instead of 8), you should cut the energy usage in half:
Annual Energy Usage = 0.5 × 350 kW-hrs = 175 kW-hrs per year.
To calculate the annual energy cost of operating the machine, you multiply the adjusted energy usage by your local electricity cost:
Annual Energy Cost = 175 kW-hrs × $0.086 per kW-hr = $15.05
Thus, the answer closest to the calculated annual energy cost is (c) $15.34.
Bridge A is the longest suspension bridge in a Country. Bridge B is 5555 feet shortershorter than Bridge A. If the length of Bridge A is m feet, express the length of Bridge B as an algebraic expression in m. Write an expression representing the length of Bridge B in terms of m.
The length of Bridge B is expressed as m - 5555 feet, where m represents the length of Bridge A. For example, if Bridge A is 10,000 feet long, then Bridge B would be 4445 feet long.
Explanation:Bridge B is 5555 feet shorter than Bridge A, so we can represent the length of Bridge B as m - 5555 feet. This expression represents the length of Bridge B in terms of m, where m represents the length of Bridge A. For example, if Bridge A is 10,000 feet long, then Bridge B would be 10,000 - 5555 = 4445 feet long.
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What is the purpose of the following algorithm? input somenum Repeat the following steps for 14 times input variable1 if variable1 < somenum then somenum = variable1 print somenum
Answer:
The purpose of the algorithm is to print the least digit among a total of 15 digita
Explanation:
input somenum
Repeat the following steps for 14 times
input variable1
if variable1 < somenum then
somenum = variable1
print somenum
On line 1, the algorithm takes an input through variable1
An iteration is started on line 2 and ends on line 6
Line 3,4,5 re performed repeatedly;
On line 3, the algorithm accepts another input through somenum and it keep accepting it till the end of the iteration.
On line 4, the algorithm tests if variable1 is lesser than somenum.
If yes, line 5 is executed and the value of variable1 is assigned to somenum
Else, line 5 is skipped; the iteration moves to line 3 as long as the condition is still valid.
At the end of the iteration, the least value stored in somenum is printed through
Develop a simulation model for a square-wave inverter connected to a dc source of 96 V and an output frequency of 60 Hz. The load is a series RL load with R = 5 Ohm and L = 100 mH.
Answer:
The answer to this question is attached fully with the explanation.
A platinum resistance temperature sensor has a resistance of 120 Ω at 0℃ and forms one arm of a Wheatstone bridge. At this temperature the bridge is balanced with each of the other arms being 120 Ω. The temperature coefficient of resistance of the platinum is 0.0039/K. What will be the output voltage from the bridge for a change in temperature of 20℃? The loading across the output is effectively open circuit and the supply voltage to the bridge is from a source of 6.0 V with negligible internal resistance.
The output voltage from a Wheatstone bridge with a change in temperature of 20℃ in one of its platinum resistance temperature sensor arms is calculated to be approximately 0.233 V, taking into account the specific temperature coefficient of resistance for platinum.
Explanation:The student's question involves calculating the output voltage from a Wheatstone bridge when a platinum resistance temperature sensor, which forms one arm of the bridge, changes its resistance due to a temperature change. With a temperature coefficient of resistance for platinum of 0.0039/K and an initial balance condition at 0℃ with each arm having a resistance of 120 Ω, the temperature change of 20℃ will lead to a change in resistance in the platinum arm, affecting the bridge's balance and generating an output voltage.
To calculate the change in resistance (ΔR) for the platinum sensor due to the temperature change: ΔR = Ro·α·ΔT, where Ro is the initial resistance (120 Ω), α is the temperature coefficient of resistance (0.0039/K), and ΔT is the temperature change (20℃). Therefore, ΔR = 120·0.0039·20 = 9.36 Ω. The new resistance of the platinum sensor at 20℃ is 120 Ω + 9.36 Ω = 129.36 Ω.
Given the supply voltage (Vs) is 6.0 V, and considering the bridge was initially balanced, the output voltage (Vo) from the bridge can be calculated using the formula derived from the Wheatstone bridge principles: Vo = Vs · (ΔR / (2Ro + ΔR)). Substituting the values gives Vo = 6.0 · (9.36 / (240 + 9.36)) = 0.233 V. Thus, the output voltage from the bridge for a change in temperature of 20℃ is approximately 0.233 V.
3. In the text, we described a multithreaded file server, showing why it is better than a single-threaded server and a finite-state machine server. Are there any circumstances in which a single-threaded server might be better
Answer and Explanation:
• 1 thread awaits the incoming request
• 1 thread responds to the request
• 1 thread reads the hard disk
A multithreaded file server is better than a single-threaded server and a finite-state machine server because it provides better response compared to the rest and can make use of the shared Web data.
Yes, there are circumstances in which a single-threaded server might be better. If it is designed such that:
- the server is completely CPU bound, such that multiple threads isn't needed. But it would account for some complexity that aren't needed.
An example is, the assistance number of a telephone directory (e.g 7771414) for an community of say, one million people. Consider that each name and telephone number record is sixty-four characters, the whole database takes 64 MB, and can be easily stored in the server's memory in order to provide quick lookup.
NOTE:
Multiple threads lead to operation slow down and no support for Kernel threads.
"A horizontal curve is being designed for a new two-lane highway (12-ft lanes). The PI is at station 250 + 50, the design speed is 65 mi/h, and a maximum superelevation of 0.07 ft/ft is to be used. If the central angle of the curve is 38 degrees, design a curve for the highway by computing the radius and stationing of the PC and PT."
Answer:
Radius = 1565ft ; PC = 245 + 11.13 ; PT = 255 + 48.88
Explanation:
1. Accordingly to the law of mechanics;
Centrifugal factor =S+F = V²/15R
Where; S = Super-elevation slope = 0.07ft/ft
F= Slide friction factor
V= Design speed=65mi/h
R= Radius
From the graph (see attached), at design speed of 65mi/h, coefficient of slide friction factor, F =0.11
Applying the figures in the equation above;
0.07+0.11 = 65²/15R
R=281.67/0.18
R=1564.8
Approximately Radius = 1565ft
2. Stationing PC = Stationing PI - T
where T = Tangent distance
T= Rtan(Δ/2) where Δ = central angle = 38° & Stationing PI = 250 + 50
T=1565tan19°
T=538.87ft
Stationing PC = 250 + 50 - (5 + 38.87)
PC = 245 + 11.13
3. Stationing PT = Stationing PC + L
Where L = Length of the circular curve
L = π/180*(RΔ)
L=0.01745*1565*38
L=1037.75
Therefore;
Stationing PT= 245 + 11.13 + (10 +37.75)
PT = 255 + 48.88
A bridge hand consists of 13 cards. One way to evaluate a hand is to calculate the total high point count (HPC) where an ace is worth four points, a king is worth three points, a
Answer: Let us use the pickled file - DeckOfCardsList.dat.
Explanation: So that our possible outcome becomes
7♥, A♦, Q♠, 4♣, 8♠, 8♥, K♠, 2♦, 10♦, 9♦, K♥, Q♦, Q♣
HPC (High Point Count) = 16
Before entering an underground utility vault to do repairs, a work crew analyzed the gas in the vault and found that it contained 29 mg/m3of hydrogen sulfide. Because the allowable exposure level is 14 mg/m3, the work crew began ventilating the vault with a blower. If the volume of the vault is 160 m3and the flow rate of contaminant-free air is 10 m3/min, how long will it take to lower the hydrogen sulfide level to a level that will allow the work crew to enter? Assume the manhole behaves as a CMFR and that hydrogen sulfide is nonreactive in the time period considered.
Answer:
11.65 minutes.
Explanation:
See the attached picture for detailed explanation.
Answer:
11.65 min
Explanation:
Hydrogen sulfide is very poisonous and as a result, it is essential to reduce the concentration of the gas to the lowest possible value to minimize its effects. The time taken to reduce the amount of hydrogen sulfide in the system to the allowable limit can be estimated as shown below:
t = (V/Q)*ln(Ci/Co) = (160/10)*ln(14/29) = 16*0.728 = 11.65 min
At what forward voltage does a diode conduct a current equal to 10,000 Is ? In terms of Is , what current flows in the same diode when its forward voltage is 0.7 V?
Answer:
a) The forward voltage is 0.23 V
b) The current that flows [tex]I_{d} = (1.45*10^{12}I_{s})A[/tex]
Explanation:
The forward voltage is the minimum voltage that must be applied to a diode before it starts to conduct. The equation is given by:
a) At what forward voltage does a diode conduct a current equal to 10,000 Is ? In terms of Is
[tex]I_{d} = I_{s}(e^{\frac{v_{f} }{0.025} }-1)[/tex]
Where:
Id is the diode current = 10000Is,
Vd is the forward voltage at which the diode begins to conduct,
Is is the saturation current.
[tex]I_{d} = I_{s}(e^{\frac{v_{f} }{0.025} }-1)[/tex]
[tex]10000I_{s} = I_{s}(e^{\frac{v_{f} }{0.025} }-1)[/tex]
Dividing through by Is,
[tex]10000 = (e^{\frac{v_{f} }{0.025} }-1)[/tex]
[tex]10000 +1= e^{\frac{v_{f} }{0.025} }[/tex]
[tex]10001= e^{\frac{v_{f} }{0.025} }[/tex]
Taking the natural logarithm of both sides,
[tex]ln(10001)= {\frac{v_{f} }{0.025} }[/tex]
[tex]9.21= {\frac{v_{f} }{0.025} }[/tex]
multiplying through by 0.025
[tex]{v_{f} }= 0.23[/tex] = 0.23 V
The forward voltage does a diode conduct a current equal to 10,000 Is is 0.23 V
b) what current flows in the same diode when its forward voltage is 0.7 V?
[tex]I_{d} = I_{s}(e^{\frac{v_{f} }{0.025} }-1)[/tex]
[tex]I_{d} = I_{s}(e^{\frac{0.7}{0.025} }-1)[/tex]
[tex]I_{d} = I_{s}(1.45*10^{12} -1)[/tex]
[tex]I_{d} = (1.45*10^{12}I_{s})A[/tex]
A particular NMOS device has parameters VT N = 0.6 V, L = 0.8µm, tox = 200 Å, and µn = 600 cm2 /V–s. A drain current of ID = 1.2 mA is required when the device is biased in the saturation region at VGS = 3 V. Determine the required channel width of the device.
Answer:
[tex]W= 3.22 \mu m[/tex]
Explanation:
the transistor In saturation drain current region is given by:
[tex]i_D}=K_a(V_{GS}-V_{IN})^2[/tex]
Making [tex]K_a[/tex] the subject of the formula; we have:
[tex]K_a=\frac {i_D} {(V_{GS} - V_{IN})^2}[/tex]
where;
[tex]i_D = 1.2m[/tex]
[tex]V_{GS}= 3.0V[/tex]
[tex]V_{TN} = 0.6 V[/tex]
[tex]K_a=\frac {1.2m} {(3.0 - 0.6)^2}[/tex]
[tex]K_a = 208.3 \mu A/V^2[/tex]
Also;
[tex]k'_n}=\frac{\mu n (\frac{cm^2}{V-s} ) \epsilon _{ox}(\frac{F}{cm} ) }{t_{ox}(cm)}[/tex]
where:
[tex]\mu n (\frac{cm^2}{V-s} ) = 600[/tex]
[tex]\epsilon _{ox}=3.9*8.85*10^{-14}[/tex]
[tex]{t_{ox}(cm)=200*10^{-8}[/tex]
substituting our values; we have:
[tex]k'_n}=\frac{(600)(3.988.85*10^{-14})}{(200*10^{-8})}[/tex]
[tex]k'_n}=103.545 \mu A/V^2[/tex]
Finally, the width can be calculated by using the formula:
[tex]W= \frac{2LK_n}{k'n}[/tex]
where;
L = [tex]0.8 \mu m[/tex]
[tex]W= \frac{2*0.8 \mu m *208.3 \mu}{103.545 \mu}[/tex]
[tex]W= 3.22 \mu m[/tex]
Checkpoint 4.72 Write a statement that uses a conditional expression that determines if the credits variable is less than 0. If the condition is true, assign the value 0 to the credits variable, otherwise the value of the credits variable should remain unchanged.
Answer:
See step to step explanations for answer.
Explanation:
This is the expression to check if credits is less than 0 assuming variable name is credits:
if(credits<0)
{
credits = 0;
}
Q 4.69:
this is the expression checking the name is Swordfish or not
if(name=="Swordfish")
{
cout<<"We have a match";
}
Q 4.67
This is the expression to check the character assuming that character is ch
if(ch>='1' && ch<='9')
{
cout<<"Digit detected";
}
Q 4.59:
This is the statement to check if the number is between 0 and 500 inclusive . Assuming the variable is n
if(n>=0 && n<=500)
{
cout<<"The number is valid";
}
To address the programming question about conditional expressions, a ternary operator can be used to set the variable 'credits' to 0 if its value is less than 0, and otherwise keep the current value.
Explanation:The student's question pertains to the use of a conditional expression in a programming context. A conditional expression evaluates a condition and based on its truth value, executes one of two expressions. The statement required should check if the credits variable is less than 0 and if so, assign the value 0 to credits; otherwise, it should leave the value of credits as is.
An example in a generic programming language would be:
credits = 0 if credits < 0 else creditsThis line of code is known as a ternary operator or conditional assignment. It reads as 'Set credits to 0 if credits is less than 0; otherwise, keep the value of credits.'
Silicon carbide nanowires of diameter 15 nm can be grown onto a solid silicon carbide surface by carefully depositing droplets of catalyst liquid onto a flat silicon carbide substrate. Silicon carbide nanowires grow upward from the deposited drops, and if the drops are deposited in a pattern, an array of nanowire fins can be grown, forming a silicon carbide nano-heat sink. Consider finned and unfinned electronics packages in which an extremely small, 10 μm × 10 μm electronics device is sandwiched between two 100-nm-thick silicon carbide sheets. In both cases, the coolant is a dielectric liquid at 20°C. A heat transfer coefficient of 1.0 × 105 W/m2·K exists on the top and bottom of the unfinned package and on all surfaces of the exposed silicon carbide fins, which are each 300 nm long. Each nano-heat sink includes a 50 × 50 array of nanofins. Determine the maximum allowable heat rate that can be generated by the electronic device so that its temperature is maintained at 95°C for (a) the unfinned and (b) the finned packages
Answer:
Please find attached file for complete answer.
Explanation:
(CLO 3—Boolean/Comb. Logic) It is desired to multiplex four different input data lines, a-d, onto one output. Three address lines, ("x" [MSB] through "z" [LSB]) control input-to-output selection. The three-bit address can be stated as a decimal number ranging from 0 to 7. Input a is MUXed out on address 3, b on address 4, c on 6, d on 7. Draw the MUX circuit below.
Answer:
Please find attached file for complete answer solution and explanation of same question.
Explanation:
Calculate the RWL and the LI for the following task.As forgings exit a cooling bath,they are loaded into various tumblers for finishing.Each forging weighs 15 pounds and is lifted from a conveyor that is 36 inches high to a tumbler that is 48 inches high.The forgings are relatively small, so the hands are only 5 inches from the waist.The process completes a forging every 10 seconds.The coupling is considered fair, and the operator works a full 8-hour shift.
Answer:
The solution is given in the attachments
. A steam turbine operates between 500°C and 3.5 MPa to 200°C and 0.3 MPa. If the turbine generates 750 kW and the heat loss is 100 kW, what is the flow rate of steam through the turbine?
Answer:
1.757 kg/s
Explanation:
According to the First Law of Thermodynamics, the physical model for a turbine working at steady state is:
[tex]-\dot Q_{out} - \dot W_{out} + \dot m \cdot (h_{in}-h_{out})=0[/tex]
The flow rate of steam is:
[tex]\dot m = \frac{\dot Q_{out}+\dot W_{out}}{h_{in}-h_{out}}[/tex]
Water enters and exits as superheated steam. After looking for useful data in a property table for superheated steam, specific enthalpies at inlet and outlet are presented below:
[tex]h_{in} = 3451.7 \frac{kJ}{kg} \\h_{out} = 2967.9 \frac{kJ}{kg} \\[/tex]
Finally, the flow rate is calculated:
[tex]\dot m = \frac{100 kW + 750 kW}{3451.7 \frac{kJ}{kg} - 2967.9 \frac{kJ}{kg}}\\\dot m =1.757 \frac{kg}{s}[/tex]
An insulated piston-cylinder device contains 5 L of saturated liquid water at a constant pressure of 175 kPa. Water is stirred by a paddle wheel while a current of 8 A flows for 45 min through a resistor placed in the water. If one-half of the liquid is evaporated during this constant-pressure process and the paddle-wheel work amounts to 400 kJ, determine the voltage of the source. Also, show the process on a
Answer:
note:
solution is attached in word form due to error in mathematical equation. furthermore i also attach Screenshot of solution in word due to different version of MS Office please find the attachment
The voltage of the source can be determined by dividing the total energy transferred (sum of the paddle-wheel work and heat required to evaporate water) by the product of current and time. The process will be seen as a horizontal line on a piston-cylinder diagram
Explanation:The heat transferred to the water can be calculated from the energy supplied by the electrical source and the work done by the paddle wheel. Since power is the energy transferred per unit time, we can use the equation Power = Voltage x Current. We know that the current is 8 A and the energy transferred is the sum of the work done by the paddle wheel and the heat required to evaporate half of the water, which is 45 minutes (converted to seconds) times the power. Solving for voltage we get:
Voltage = (Energy transferred) / (Current x Time)
In terms of a piston-cylinder diagram, the process will appear as a horizontal line since the pressure is constant. The line will move upwards as heat is added and some of the water is turned into steam.
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c++ If your company needs 200 pencils per year, you cannot simply use this year’s price as the cost of pencils 2 years from now. Because of inflation the cost is likely to be higher than it is today.
Answer:
note:
please find the attached code
The water behind Hoover Dam is 206m higher than the Colorado river below it. At what rate must water pass through the hydraulic turbines of this dam to produce 100 MW of power if the turbines are 100 percent efficient?
Answer:
m' = 4948.38 kg/s
Explanation:
For a case of 100% efficiency, the power produced must be equal to the rate of potential energy conversion
GIVEN THAT
Power = 100 MW
rate of Potential energy = (m')*g*h
100*10^6 = (m')*9.81*206
m' = 4948.38 kg/s
Answer:
49.484 m³ / s
Explanation:
Volume flow rate = Power in W / (efficiency × density × height × acceleration due to gravity)
Volume flow rate = 100 × 10⁶ / ( 1 × 1000 kg/m³ × 206 m × 9.81 m/s²)
V = 49.484 m³ / s
Prob. 4.2.1. A well that pumps at a constant rate of 0.5 m3/s fully penetrates a confined aquifer of 34-m thickness. After a long period of pumping, steady-state drawdowns are measured at two observation wells 50 and 100 m from the pumping well as 0.9 m and 0.4 m, respectively. Determine: (a) the hydraulic conductivity and transmissivity of the aquifer; (b) the radius of influence of the pumping well; (c) the expected drawdown in the pumping well if the radius of the well is 0.4 m.
Answer:
Part (a)
K = 0.00406 m / s
T = 0.14 m2 / s
Part (b)
R = Radius of influence of Pumping well = 237.94 m
Part (c)
S = Drawdown at well = 3.68 m
Explanation:
General formula for wells at confined aquifer is
Q = [tex]{2*3.1416*K*B*(S1-S2)} / {2.303 log (R/r)}[/tex] ............ eq (A)Where ,
Q = Discharge
K = Hydraulic conductivity
B = Thickness of aquifer
S1 = Draw-down at point 1
S2 = Draw-down at point 2
R = Radius of influence of well
r = Radius of well
Part (a)
We will use
Q = [tex]{2*3.1416*K*B*(S1-S2)} / {2.303 log (r2/r1)}[/tex] ......... eq (1)Where,
r 1 = Distance of first observation well from main well
r2 = Distance of 2nd observation well from main well
Given data: Q = 0.5 m3/s B = 34 m r 1 = 50 m
r2 = 100 m S1 = 0.9 m S2 = 0.4 m
Put all these values in equation 1
0.5 = 2*3.1416*K*34*(0.9 - 0.5) / {2.303 log(100 / 50)}
Write Equation in terms of K = hydraulic conductivity
K = {0.5*2.303 log (100 / 50)} / {2*3.1416*34*(0.9 - 0.5)}
K = 0.00406 m / s
Now Transmissivity
T = K*B
T = 0.14 m2 / s
Part (b)
To calculate radius of influence, use equation (A)
Q = [tex]{2*3.1416*K*B*(S1-S2)} / {2.303 log (R/r)}[/tex]
At distance R from main well drawdown (S2) = 0
use r = r1 = 50 m and S1 = 0.9
use ln ( R / r) = 2.303 log (R / r)
0.5 = 2* 3.1416 * 0.00406*34* (0.9 - 0) / ln(R / 50)
Write equation in terms of R
ln( R / 50) = 2* 3.1416 * 0.00406*34* (0.9 - 0) / 0.5
ln( R / 50) = 1.56
Take anti log (e) of above equation
R / 50 = 4.76
R = Radius of influence of Pumping well = 237.94 m
Part (c)
Use equation A
Q = [tex]{2*3.1416*K*B*(S1-S2)} / {2.303 log (R/r)}[/tex]
S1 = ?
Put S2 = 0 R = 237.94 r = 0.4
0.5 = 2* 3.1416* 0.00406*34*(S1 - 0) / 2.303 log(237.94 / 0.4)
Write equation in terms of S1
S1 = 0.5* 2.303 log(237.94 / 0.4) / 2*3.1416*0.00406*34
S1 = Drawdown at well = 3.68 m
The hydraulic conductivity and transmissivity of the aquifer are respectively; 0.0032 m/s and 0.11 m³/s
What is the hydraulic conductivity?
A) We are given;
Pump rate; Q = 0.5 m³/s
thickness of quifer; b = 34 m
depth 1; r₁ = 50 m
depth 2; r₂ = 100 m
distance 1; S₁ = 0.9 m
distance 2; S₂ = 0.4 m
Formula for the pump rate is;
Q = 2π × b × k × (S₁ - S₂)/(In r₂/r₁)
making k the subject gives;
k = Q(In r₂/r₁)/(2π × b × (S₁ - S₂))
k = 0.5(In 100/50)/(2π × 34 × (0.9 - 0.4))
Solving for K gives;
Hydraulic conductivity is; k = 0.0032 m/s
Transmissivity is;
T = K * b
T = 0.0032 * 34
T = 0.11 m³/s
B) Formula for radius of incfluence is;
S_w = S₁ - [(Q/2π × b × k) In (r_w/r₁)]
Plugging in the relevant values gives;
S_w = 4.338 m
C) Formula for expected drawdown is;
R = r₁ e^(2πbk(S_w - S₁)/Q)
R = 100 * e^(2π*34*0.0032(-78.9)/0.5)
R = 147.7 m
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For each of the characteristic equations of feedback control systems given, determine the range of K so that the system is asymptotically stable. Determine the value of Kso that the system is marginally stable and the frequency of sustained oscillation if applicable. s4 + Ks3 + 2s2 + (K + 1)s + 10 = 0
Answer:
Explanation:
The method or principle applied is the Routh- hurtwitz criterion for solving characteristics equation.
The steps by step analysis and appropriate substitution is carefully shown in the attached file.
A 9-m length of 6-mm-diameter steel wire is to be used in a hanger. The wire stretches 18mm when a tensile force P is applied. If E = 200 GPa, determine the magnitude of the force P, and the normal stress in the wire.
Force P is 11304 N and normal stress is 400 N/mm²
Explanation:
Given-
Length, l = 9 m = 9000 mm
Diameter, d = 6 mm
Radius, r = 3 mm
Stretched length, Δl= 18 mm
Modulus of elasticity, E = 200 GPa = 200 X 10³MPa
Force, P = ?
According to Hooke's law,
Stress is directly proportional to strain.
So,
σ ∝ ε
σ = E ε
Where, E is the modulus of elasticity
We know,
ε = Δl / l
So,
σ = E X Δl/l
σ =
[tex]200 X 10^3 * \frac{18}{9000} \\\\ = 400N/mm^2[/tex]
We know,
σ = P/A
And A = π (r)²
σ = P / π (r)²
[tex]400 N/mm^2 = \frac{P}{3.14 X (3)^2} \\\\400 = \frac{P}{28.26} \\\\P = 11304N[/tex]
Therefore, Force P is 11304 N and normal stress is 400 N/mm²
The magnitude of the force is 11.3KN and the normal stress is 400 MPa
Given that length (L) = 9 m, diameter (d) = 6 mm = 6 * 10⁻³ m, extension (δ) = 18 mm = 18 * 10⁻³ m, E = 200 GPa = 200 * 10⁹ Pa
The area of the wire (A) is:
[tex]A=\pi*\frac{diameter^2}{4}=\pi*\frac{(6*10^{-4})^2}{4} =28*10^{-6}\ m^2[/tex]
[tex]\delta=\frac{PL}{AE} \\\\P=\frac{AE\delta}{L}=\frac{28*10^{-6}*200*10^9*18*10^{-3}}{9}=11300N\\\\\\Normal\ stress(\sigma)=\frac{P}{A} =\frac{11300}{28*10^{-6}} =400*10^6\ Pa[/tex]
The magnitude of the force is 11.3KN and the normal stress is 400 MPa
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15 points) A horizontal curve is being designed for a new two-lane highway (12-ft lanes). The PI is at station 250 00, design speed is 65 mph, and a maximum superelevation of 0.08 ft/ft is to be used. If the central angle of the curve is 35 degrees, design a curve for the highway by computing the radius and stationing of the PC and PT.
Answer:
59.78 m
Explanation:
Data:
PI station = 250 will allow a speed of 65 mph
The maximum superelevation will be = 0.08 ft/ft
Central angle of the curve = 35 degrees
A figure will be used to present the information. This gives the height of 59.78 m as the maximum elevation for the safe speed of the vehicle.
Refrigerant 134a enters a horizontal pipe operating at steady state at 40°C, 300 kPa, and a velocity of 25 m/s. At the exit, the temperature is 90°C and the pressure is 240 kPa. The pipe diameter is 0.1 m. Determine: (a) the mass flow rate of the refrigerant, in kg/s, (b) the velocity at the exit, in m/s, and (c) the rate of heat transfer between the pipe and its surroundings, in kW.
Answer:
a) 2.42 [tex]kg/s[/tex]
b) 37.20 m/s
c) 120.56 kW
Explanation:
Given that:
The fluid in the Refrigerant = R-134a
Diameter (d) = 0.1 m
In the Inlet:
Temperature [tex]T_1 = 40^0C[/tex]
Pressure [tex]P_1= 300kPa[/tex]
Velocity [tex]V_1[/tex] = 25 m/s
At the exit:
Temperature [tex]T_2 = 90^0C[/tex]
Pressure [tex]P_2 = 240 kPa[/tex]
From the Table A-12 for Refrigerant R-134a at [tex]T_1 = 40^0C[/tex] and [tex]P_1= 300kPa[/tex]
Specific Volume [tex]v_1 = 0.0809 m^3/kg[/tex]
From the Table A-12 for Refrigerant R-134a at [tex]T_2 = 90^0C[/tex] and [tex]P_2 = 240 kPa[/tex]
Specific Volume [tex]v_2 = 0.12038 kJ/kg[/tex]
Their corresponding Enthalpy [tex]h_1[/tex] and [tex]h_2[/tex] are as follows:
Enthalpy [tex]h_1[/tex] =284.05 kJ/kg
Enthalpy [tex]h_2[/tex] = 333 kJ/kg
a) The mass flow rate of the refrigerant can be calculated as :
[tex]m_1 = \frac{AV_1}{v_1}[/tex]
[tex]m_1 = \frac{\frac{\pi (0.1)^2}{4}*25}{0.08089}[/tex]
[tex]m_1 = 2.42 kg/s[/tex]
b) The velocity at the exit point:
we knew that:
[tex]m=m_1 =m_2[/tex]
∴
[tex]\frac{AV_1}{v_1} =\frac{AV_2}{v_2}[/tex]
[tex]V_2 = \frac{v_2}{v_1} V_1[/tex]
[tex]V_2 = \frac{0.12038}{0.08089} *25[/tex]
[tex]V_2 = 37.20 m/s[/tex]
c) Expression for calculating heat transfer (as long as there is no work that is said to be done and the pipe is horizontal) can be represented as:
[tex]Q_{cv}= m[(h_2-h_1)+\frac{1}{2}(V_2^2-V_1^2)][/tex]
[tex]Q_{cv}= 2.42*[(333.49-284.05)+\frac{1}{2}(37.20^2-25^2)][/tex]
[tex]Q_{cv}= 2.42*[49.44+379.42][/tex]
[tex]Q_{cv}= 119.6448kW+918.19W(\frac{1kW}{1000W} )[/tex]
[tex]Q_{cv}= 119.6448kW+0.92 kW[/tex]
[tex]Q_{cv} = 120.56 kW[/tex]
Following are the solution to the given points:
Obtain the following property at pressure [tex]300\ kPa[/tex] and [tex]40^{\circ} \ C[/tex] from the property of superheated [tex]134a[/tex]
Using the interpolation method,
Specific volume, [tex]v_1 = 0.0866 -(0.0866 -0.07518) (\frac{0.3-0.28}{0.32-0.28})= 0.08089 \frac{kg}{m^3}[/tex]
Enthalpy, [tex]h_1 = 284.42 - (284.42 - 283.67) (\frac{0.3-0.28}{0.32-0.28}) = 284.05\ \frac{kJ}{kg}\\\\[/tex]
Obtain the following property at pressure [tex]240 \ kPa \ and \ 90^{\circ} \ C[/tex] from the property of superheated [tex]134a[/tex].
Specific volume,[tex]v_2 = 0.12 \ \frac{kg}{m^3}[/tex]
Enthalpy of superheated [tex]134a, \ \ h_2 = 333 \ \frac{kJ}{kg}[/tex]
For point a:
Calculating the refrigerant weight rate flow:
[tex]m_1 =\frac{AV_1}{v_1} =\frac{ \frac{ \pi (0.1)^2}{4} \times 25}{0.08089} = \frac{0.196}{0.08089} \\\\ m_1 = 2.42 \frac{kg}{s}[/tex]
Thus, refrigerant weight rate flow is [tex]2.42\ \frac{m^3}{kg}\\\\[/tex]
For point b:
Calculate the exit velocity:
[tex]m_1 = m_2\\\\ \frac{A V_1}{v_1}=\frac{AV_2}{v_2}\\\\ V_2=\frac{V_2}{v_1} V_1\\\\v_2= \frac{0.12038}{ 0.08089} \times 25\\\\ V_2 = 37.20 \frac{m}{s}\\\\[/tex]
Thus, the exit velocity is [tex]37.20\ \frac{m}{s}\\\\[/tex]
For point c:
From the energy rate balance Since, there is no work being done and the pipe is horizontal. So, the above equation can be written as
[tex]\to Q_{cv} = m [(h_2 - h_1)+ \frac{1}{2}(v_{2}^{2}- v_{1}^{2})] \\\\[/tex]
[tex]= 2.42 \times [(333.49 - 284.05) +\frac{1}{2}(37.20^2-25^2)]\\\\ = 2.42 \times [49.44 +379.42] \\\\= 119.64\ kW +918.19 \ W |\frac{1 \ KW}{1000\ W}| \\\\= 119.64 \ kW +0.92\ kW\\\\ =120.56\ kW[/tex]
Thus, the heat transfer rate among pipe and its surrounding [tex]120.56\ kW[/tex]
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In a production facility, 1.6-in-thick 2-ft × 2-ft square brass plates (rho = 532.5 lbm/ft3 and cp = 0.091 Btu/lbm·°F) that are initially at a uniform temperature of 75°F are heated by passing them through an oven at 1500°F at a rate of 340 per minute. If the plates remain in the oven until their average temperature rises to 900°F, determine the rate of heat transfer to the plates in the furnace.
Answer:
106600 btu/s
note:
solution is attached due to error in mathematical equation. please find the attachment
How many trips would one rubber-tired Herrywampus have to make to backfill a space with a geometrical volume of 5400 cubic yard? The maximum capacity of the machine is 30 cubic yard (heaped), or 40 tons. The material is to be compacted with a shrinkage of 25% (relative to bank measure) and has a swell factor of 20% (relative to bank measure). The material weighs 3,000 lb/cu yd (bank). Assume that the machine carries its maximum load on each trip. Check by both weight and volume limitations
The rubber-tired Herrywampus machine would need to make 288 trips to backfill the space with the given geometrical volume, considering both volume and weight limitations.
The Breakdown
we need to consider the volume and weight limitations of the rubber-tired Herrywampus machine.
Geometrical volume of the space to be backfilled: 5400 cubic yards
Maximum capacity of the machine: 30 cubic yards (heaped) or 40 tons
Compaction shrinkage: 25% (relative to bank measure)
Swell factor: 20% (relative to bank measure)
- Material weight: 3,000 lb/cu yd (bank)
Calculate the actual volume of material required to backfill the space.
Actual volume = Geometrical volume / (1 - Compaction shrinkage)
Actual volume = 5400 cubic yards / (1 - 0.25)
Actual volume = 7200 cubic yards
Calculate the volume of material to be loaded into the machine, considering the swell factor.
Swelled volume = Actual volume × (1 + Swell factor)
Swelled volume = 7200 cubic yards × (1 + 0.20)
Swelled volume = 8640 cubic yards
Calculate the number of trips required based on the machine's volume capacity.
Number of trips = Swelled volume / Machine capacity
Number of trips = 8640 cubic yards / 30 cubic yards
Number of trips = 288 trips
Check the weight limitation.
Weight of material per trip = Machine capacity × Material weight
Weight of material per trip = 30 cubic yards × 3,000 lb/cu yd
Weight of material per trip = 90,000 lb
Total weight of material = Swelled volume × Material weight
Total weight of material = 8640 cubic yards × 3,000 lb/cu yd
Total weight of material = 25,920,000 lb
Number of trips based on weight limitation = Total weight of material / Weight of material per trip
Number of trips based on weight limitation = 25,920,000 lb / 90,000 lb
Number of trips based on weight limitation = 288 trips
Therefore, the rubber-tired Herrywampus machine would need to make 288 trips to backfill the space with the given geometrical volume, considering both volume and weight limitations.