Routh's criterion can be used by substituting a small positive integer for zero and completing the array.
Routh's criterion is a mathematical method used to determine the stability of a system based on the coefficients of its characteristic equation. The Routh's array is constructed using these coefficients, and it provides a systematic way to check the number of unstable roots of the equation.
When a term in the first column of Routh's array becomes zero, it creates a problem because it results in division by zero, which is undefined. In such a case, the Routh criterion cannot be directly applied to determine the stability of the system.
However, to overcome this issue, we can substitute a small positive integer for zero in the zero element of the first column. By doing this, we are effectively making the zero element nonzero and avoiding division by zero. The rest of the array can then be completed using the regular rules of constructing the Routh's array.
This substitution allows us to continue the application of Routh's criterion and determine the stability of the system. The small positive integer serves as an approximation to avoid the undefined division and provides a practical workaround in situations where a zero element appears in the first column.
It's important to note that the chosen small positive integer should be sufficiently small to maintain the accuracy of the results. As the value gets smaller, the approximation becomes more accurate.
In summary, if any term in the first column of Routh's array becomes zero, we can still use Routh's criterion by substituting a small positive integer for zero and completing the array. This approach allows us to bypass the issue of division by zero and continue the stability analysis.
Learn more about array
brainly.com/question/31605219
#SPJ11
2. Consider a silicon JFET having an n-channel region of donor concentration 1x10¹⁶ cm. (a) Determine the width of the n-channel region for a pinch-off voltage of 12 V. (b) What would the necessary drain voltage (VD) be if the gate voltage is -9 V? (c) Assume the width of the n-channel region to be 40 μm. If no gate voltage is applied, what is the minimum necessary drain voltage for pinch-off to occur? (d) Assume a rectangular n-channel of length 1 mm. What would be the magnitude of the electric field in the channel for case (c) above?
The electric field in the channel is 12,000 V/m.
a) Pinch off occurs when the VGS = Vp. for silicon JFETs, Vp = |2 |V for n-channel JFETs. The channel width can be determined with the equation W = Φ/Vp, where Φ is the donor concentration in the channel. W = 1x10¹⁶ cm³/V·s/12 V = 8.3×10¹⁴ cm.
b) To maintain pinch-off with VGS = -9 V, the drain voltage (VD) must be greater than or equal to -12 V.
c) For a given channel width, the minimum VD necessary for pinch-off to occur, is Vp or 12 V.
d) The electric field in the channel can be calculated with the equation E = VD/L, where L is the length of the channel. E = 12V/1mm = 12,000 V/m.
Therefore, the electric field in the channel is 12,000 V/m.
Learn more about the electric field here:
https://brainly.com/question/11482745.
#SPJ4
59. A stepped torsion shall has diameters of 16 mm and 12 mm and a fillet radius of 2 mm. The shaft is subjected to a torque of 12 5 N-m. Find the maximum induced stres caused by the fillet Consider a stress concentration factor of 1.25. A 13 45 MPaa C46 OS MPa B32 78 MPa D 41 08 MPa ROFE 60. AV round steel shaft transm ha
The maximum induced stress caused by fillet is 41.08 MPa. The correct option is D.
Given data:Diameters of shaft,
D1 = 16 mm and D2 = 12 mm
Fillet radius, r = 2 mm
Torque, T = 125 N-m
Stress concentration factor, K = 1.25
To find: Maximum induced stress caused by fillet
Formula used:
Maximum induced stress caused by fillet
σ = K.T/(π.r²)
Where,
σ = Maximum induced stress caused by fillet
K = Stress concentration factor
T = Torqueπ = 3.14
r = Fillet radius
Calculation: Diameter of the bigger shaft, D1 = 16 mm
Diameter of the smaller shaft, D2 = 12 mm
Radius of bigger shaft,
r1 = D1/2
= 16/2
= 8 mm
Radius of smaller shaft,
r2 = D2/2
= 12/2
= 6 mm
We know that, Torque, T = 125 N-m
Fillet radius, r = 2 mm
Stress concentration factor, K = 1.25
Now, Maximum induced stress caused by fillet
σ = K.T/(π.r²)
= 1.25 × 125 / (3.14 × 2²)
= 41.08 MPa
Therefore, the maximum induced stress caused by fillet is 41.08 MPa. The correct option is D.
To know more about stress visit:
https://brainly.com/question/30263693
#SPJ11
In the instant lottery with 30°, winning tickets, if x is equal to the number of winning tickets among n = 8 that are purchased, then the probability of purchasing two winning tickets is a 0.2965 b 0.2936 c 0.1488 d None of the other options
The correct option is None of the other options. Instant lottery with 30°, winning tickets is considered to calculate the probability of purchasing two winning tickets. Here, the total winning tickets are given by 30° and x represents the number of winning tickets that are purchased from n = 8.
Now, we have to calculate the probability of purchasing two winning tickets. Probability of purchasing two winning tickets can be calculated as,
P (X = 2) = $\frac{\binom{x}{2}\binom{30 - x}{6}}{\binom{30}{8}}$Where, $\binom{x}{2}$ represents the number of ways of choosing 2 winning tickets from x winning tickets.$\binom{30 - x}{6}$
[tex]P (X = 2) = $\frac{\binom{x}{2}\binom{30 - x}{6}}{\binom{30}{8}}$$\implies P(X=2)=\frac{\binom{x}{2}\binom{30-x}{6}}{\binom{30}{8}}$$[/tex]
[tex]\implies P(X=2)=\frac{x(x-1)\binom{30-x}{6}}{\frac{30 \cdot 29 \cdot 28 \cdot 27 \cdot 26 \cdot 25 \cdot 24 \cdot 23}{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}}$$[/tex]
[tex]\implies P(X=2)=\frac{x(x-1)\cdot (30-x)(29-x)(28-x)(27-x)(26-x)(25-x)}{30 \cdot 29 \cdot 28 \cdot 27 \cdot 26 \cdot 25 \cdot 24 \cdot 23}$$\[/tex]
[tex]implies P(X=2)=\frac{x(x-1)(30-x)(29-x)(28-x)(27-x)(26-x)(25-x)}{(30 \cdot 29 \cdot 28 \cdot 27 \cdot 26 \cdot 25)^2}$$[/tex]
[tex]\implies P(X=2)=\frac{6! \cdot x(x-1)(30-x)(29-x)(28-x)(27-x)(26-x)(25-x)}{(30 \cdot 29 \cdot 28 \cdot 27 \cdot 26 \cdot 25)^2}$$[/tex]
[tex]\implies P(X=2)=\frac{6! \cdot x(x-1)(30-x)(29-x)(28-x)(27-x)(26-x)(25-x)}{30^8-30^7 \cdot x + 30^6 \cdot \binom{x}{2} - 30^5 \cdot \binom{x}{3} + 30^4 \cdot \binom{x}{4} - 30^3 \cdot \binom{x}{5} + 30^2 \cdot \binom{x}{6} - 30 \cdot \binom{x}{7} + \binom{x}{8}}$[/tex]
Now, substitute the given value of n = 8, and the total winning tickets are 30°, we have;
[tex]P (X = 2) = $\frac{\binom{8}{2}\binom{22}{6}}{\binom{30}{8}}$$\implies P(X=2)=\frac{\binom{8}{2}\binom{22}{6}}{\binom{30}{8}}$$[/tex]
[tex]\implies P(X=2)=\frac{28 \cdot 74613}{5852925}$$\implies P(X=2)=\frac{2090644}{5852925}$$\implies P(X=2) \approx 0.35691$[/tex]
Therefore, the probability of purchasing two winning tickets is 0.35691, which is not available in the given options.
To know more about probability visit:-
https://brainly.com/question/31828911
#SPJ11
Air with mass of 12 kg expands polytropically (n=1.50) in a closed system from 720 °C to 20 °C. Calculate in MJ both the work and the heat exchanged with the surroundings
By applying these calculations with the given values, we can determine both the work and the heat exchanged in megajoules during the polytropic expansion of air.
To calculate the work and heat exchanged during the polytropic expansion of air, we can use the first law of thermodynamics. The first law states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system:
ΔU = Q - W
In this case, we need to calculate the work done and the heat exchanged. The work done during the polytropic expansion can be expressed as:
W = ∫ P1V1 to P2V2 P dV / (1 - n)
Where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, n is the polytropic index (given as 1.50), and P is the pressure at any given point during the expansion.
To calculate the heat exchanged, we can use the relationship:
Q = ΔU + W
Given the initial and final temperatures, we can calculate the change in internal energy using the specific heat capacity of air at constant volume (Cv). The change in internal energy can be calculated as:
ΔU = m * Cv * (T2 - T1)
Where m is the mass of air.
Once we have ΔU, we can calculate the heat exchanged (Q) using the equation Q = ΔU + W.
Finally, we convert the work and heat from Joules to megajoules by dividing the results by 1,000,000.
To know more about polytropic visit
https://brainly.com/question/33284577
#SPJ11
A 12 1/8 inch hole is drilled 2,652 feet into the earth. Casing that has a 9 3/4 inch outside diameter is run to the bottom of the hole. 62 barrels of a spacer fluid is pumped down the casing and up the space between the casing and the hole. If each joint of casing is 30 feet long. How far out of the drilled hole will the casing be when it is resting on the bottom of the hole? a 89 b 2634 c 30 d 18
To determine the distance out of the drilled hole the casing will be when it is resting on the bottom of the hole.
Let's begin by identifying the given values before making use of the casing movement calculation. Provided values are:Hole diameter: 12 1/8 inchDistance drilled: 2,652 feetCasing diameter: 9 3/4 inchNumber of barrels of a spacer fluid pumped down the casing: 62Length of each joint of casing: 30 feet Calculation of the casing movementThe first thing to do is to determine the total length of the casing to be run from the surface to the bottom of the drilled hole. The casing will be run in sections of 30 feet length, so the total length of the casing to be run is the quotient of the distance drilled and the length of each joint of casing.
So:Total length of casing = Distance drilled / Length of each joint of casing = 2,652 feet / 30 feet = 88.4 ≈ 89 joints of casingNext, to calculate the length of the space between the casing and the hole, we subtract the diameter of the casing from the diameter of the hole and divide by 2. Then multiply by the number of joints of casing run to the bottom of the hole, and multiply again by 12 to convert feet to inches.So: Length of space between casing and hole = [(12 1/8 inch - 9 3/4 inch) / 2] × 89 × 12= (2 3/8 inch / 2) × 89 × 12= 2.375 × 89 × 12= 2,652 ≈ 2634 inch
Finally, to calculate the distance out of the drilled hole the casing will be when it is resting on the bottom of the hole, we subtract the length of the space between the casing and the hole from the distance drilled. So: Distance out of the drilled hole = Distance drilled - Length of space between casing and hole= 2,652 feet - (2634 inch / 12)= 2,652 feet - 219.5 feet= 2,432.5 feetTherefore, the distance out of the drilled hole the casing will be when it is resting on the bottom of the hole is approximately 2,432.5 feet, which is option C.
To know more about drilled hole visit:
brainly.com/question/31140236
#SPJ11
For a turning process, calculate the tangential (cutting) force, given the fact that the maximum diameter for the workpiece is 100 cm, the maximum tool length/diameter is 10 cm and the feed (equivalent the uncut chip thickness hm) is 0.520 mm/rev. The cutting speed 75 m/min, the rake angle of the tool is zero degrees and the depth/width of cut is 1.442 mm (note: this is not uncut chip thickness!). Assume that the workpiece material has a strain hardening exponent mc = 0.44 and a specific cutting force of Kc1 = 1500 N/mm². Give your answer in Newtons.
The tangential force can be calculated using the formula,
[tex]Ft = kc1 × f × t × z[/tex]
Where, Ft = tangential force kc1 = specific cutting force f = feed per revolution t = depth of cutz = number of teeth on the cutting tool.
Given that the maximum diameter of the workpiece is 100 cm and the maximum tool length/diameter is 10 cm. The diameter of the workpiece is[tex]100/2 = 50 cm = 500 mm[/tex]. And the length of the tool is 10 cm = 100 mm. The maximum radius of the workpiece will be, Maximum radius [tex]= 500/2 = 250 mm[/tex]. The width of cut will be 1.442 mm.
The feed per revolution (f) is 0.520 mm/rev. So, feed per minute (F) will be,
[tex]F = f × N, where N = speed in RPMN = (speed × 1000)/[3.14 × diameter][/tex]
For the given cutting speed 75 m/min, we can find out the RPM as follows:
[tex]N = (75 × 1000)/(3.14 × 500) = 478.36 rev/minF = 0.520 × 478.36 = 248.96 mm/min[/tex]
Now, the number of teeth on the cutting tool (z) is not given.
To know more about tangential visit:
https://brainly.com/question/12706657
#SPJ11
Exercises on fluid mechanics. Please, What assumptions/assumptions were used in the solution.
Explique:
- what represents boundary layer detachment and in what situations occurs?
- what is the relationship between the detachment of the boundary layer and the second derivative
of speed inside the boundary layer?
- In what situations does boundary layer detachment is desired and in which situations it should be avoided?
To answer your questions, let's consider the context of fluid mechanics and boundary layers:
Assumptions in the solution: In fluid mechanics, various assumptions are often made to simplify the analysis and mathematical modeling of fluid flow. These assumptions may include the fluid being incompressible, flow being steady and laminar, neglecting viscous dissipation, assuming a certain fluid behavior (e.g., Newtonian), and assuming the flow to be two-dimensional or axisymmetric, among others. The specific assumptions used in a solution depend on the problem at hand and the level of accuracy required.
Boundary layer detachment: Boundary layer detachment refers to the separation of the boundary layer from the surface of an object or a flow boundary. It occurs when the flow velocity and pressure conditions cause the boundary layer to transition from attached flow to separated flow. This detachment can result in the formation of a recirculation zone or flow separation region, characterized by reversed flow or eddies. Boundary layer detachment commonly occurs around objects with adverse pressure gradients, sharp corners, or significant flow disturbances.
Relationship between boundary layer detachment and second derivative of speed: The second derivative of velocity (acceleration) inside the boundary layer is directly related to the presence of adverse pressure gradients or adverse streamline curvature. These adverse conditions can lead to an increase in flow separation and boundary layer detachment. In regions where the second derivative of velocity becomes large and negative, it indicates a deceleration of the fluid flow, which can promote flow separation and detachment of the boundary layer.
Know more about fluid mechanics here:
https://brainly.com/question/12977983
#SPJ11
Consider a 210-MW steam power plant that operates on a simple ideal Rankine cycle. Steam enters the turbine at 10MPa and 5008C and is cooled in the condenser at a pressure of 10kPa. Sketch the cycle on a T-s diagram with respect to saturation lines, and determine: (a) the quality of the steam at the turbine exit, (b) the thermal efficiency of the cycle, (c) the mass flow rate of the steam. (d) Repeat Prob. (a)-(c) assuming an isentropic efficiency of 85 percent for both the turbine and the pump.
Given data:Pressure of steam entering turbine (P1) = 10 MPaTemperature of steam entering turbine (T1) = 500 degree CPressure of steam at the condenser (P2) = 10 kPaPower generated (W) = 210 MWNow, let's draw the T-s diagram with respect to saturation lines below:
1. The quality of steam at the turbine exit:From the T-s diagram, we can see that at the turbine exit, the state point lies somewhere between the two saturation lines.Using the steam tables, we can find the saturation temperature and pressure at the exit state:Pressure at the exit (P3) = 10 kPaSaturated temperature corresponding to P3 = 46.9 degree CEnthalpy of saturated liquid corresponding to P3 (h_f) = 191.81 kJ/kgEnthalpy of saturated vapor corresponding to P3 (h_g) = 2676.5 kJ/kgThe quality of steam (x) at the exit state is given by:x = (h - h_f)/(h_g - h_f)Where, h is the specific enthalpy at the exit state.
h = 191.81 + x(2676.5 - 191.81)h = 191.81 + 2421.69x= (h - h_f)/(h_g - h_f)x = (191.81 + 2421.69 - 191.81)/(2676.5 - 191.81)x = 0.91The quality of steam at the turbine exit is 0.91.2. Thermal efficiency of the cycle:For an ideal Rankine cycle, thermal efficiency is given by:eta_th = 1 - (T2/T1)Where, T2 and T1 are the temperatures of the steam at the condenser and the turbine inlet respectively.
To know more about Pressure visit:
https://brainly.com/question/24719118
#SPJ11
Square loop with sides a and wire radius b: LA = 2μo a/π=[In (a/b) - 0.774]
A square loop with sides a and wire radius b: LA = 2μo a/π=[In (a/b) - 0.774]The given equation states that the inductance of a square loop of sides a and wire radius b can be determined as LA = 2μo a/π=[In (a/b) - 0.774].
Here, 'a' and 'b' represent the sides and the wire radius of the square loop respectively. LA represents the inductance of the square loop.The above formula can be used to calculate the inductance of a square loop. We can use this formula to find the value of the inductance of a square loop of given dimensions.Let's understand the concept of inductance before diving into the calculation of the formula.What is Inductance?Inductance is defined as the ability of a component to store energy in a magnetic field
.Inductance is the resistance of an electrical conductor to a change in the flow of electric current. It is the property of a conductor that opposes any change in the current flowing through it. The larger the inductance of a conductor, the more energy it can store in a magnetic field created by an electric current flowing through it.The inductance of a square loop of sides 'a' and wire radius 'b' can be determined using the given formula LA = 2μo a/π=[In (a/b) - 0.774].
To know more about radius visit:
https://brainly.com/question/13449316
#SPJ11
Course: Power Generation and Control
Please ASAP I will like and rate your work.
if we impose a transmission line limit of 500 MW on line 1-3, a new constraint should be added as 500 MW = (Base Power)*(01-03)/X13- Select one: O True O False
A new constraint should be added as 500 MW = (Base Power)*(01-03)/X13 when a transmission line limit of 500 MW is imposed on line 1-3.
A transmission line limit is the maximum amount of power that can be transmitted through a transmission line. The transmission line's capacity is determined by the line's physical attributes, such as length, voltage, and current carrying capacity.
Transmission lines are the backbone of the electrical grid, allowing electricity to be transported over long distances from power plants to where it is required. The transmission line limits must be properly managed to prevent overloading and blackouts.
To know more about constraint visit:
https://brainly.com/question/17156848
#SPJ11
4. The following is the pattern of x-rays emitted according to the x-ray tube voltage when the Mo target is used.
1. Why do continuous x-rays occur?
2.Why does the swl move to the left as the tube voltage increases?
3. Why the x-ray intensity increases as the tube voltage increases
4.Why is the x-ray emitted not symmetric?
1. Continuous x-rays occur when a high energy electron strikes a metal atom in the target, causing the innermost electrons of the atom to be removed from their orbits. This process leaves an electronic vacancy in the inner shell, which can be filled by an electron from an outer shell. When an outer shell electron fills the inner shell vacancy, it releases energy in the form of an x-ray. However, because each electron shell has a different binding energy, the energy of the released x-ray varies.
2. The swl (short wavelength limit) moves to the left as the tube voltage increases because the x-ray energy and wavelength are inversely proportional. When the tube voltage increases, the energy of the emitted x-rays also increases, and the wavelength decreases. the swl shifts to the left on the graph as the tube voltage increases.
3. The x-ray intensity increases as the tube voltage increases because higher tube voltage results in more electron acceleration, which generates more x-rays. When the tube voltage is increased, more electrons are accelerated across the anode, resulting in more x-rays produced and higher x-ray intensity.
4. The x-ray emitted is not symmetric because of the characteristic x-rays and bremsstrahlung x-rays. Characteristic x-rays occur when an electron drops down to fill an inner shell vacancy, releasing energy in the form of an x-ray. The energy of characteristic x-rays is fixed because the energy difference between the two shells is fixed. Bremsstrahlung x-rays, on the other hand, are emitted when an electron is deflected by the positive charge of the nucleus.
The energy of bremsstrahlung x-rays can vary depending on the extent of electron deflection, resulting in a continuous spectrum of x-ray energies. This combination of characteristic and bremsstrahlung x-rays results in a non-symmetric distribution of x-ray energy.
To know about electron visit:
https://brainly.com/question/12001116
#SPJ11
When torsion subjected to long shaft, we can noticeable elastic twist. Equilibrium of a body requires both a balance of forces and balance of moments. Thermal stress is a change in temperature can cause a body to change its dimensions. Beams are classified to four types. If the beam is supported at only one end and in such a manner that the axis of the beam cannot rotate at that point. 1-:-A
Thermal stress is the stress that develops in a body due to a change in temperature, causing it to change its dimensions.
Given:When torsion subjected to long shaft, we can noticeable elastic twist. Equilibrium of a body requires both a balance of forces and balance of moments. Thermal stress is a change in temperature can cause a body to change its dimensions. Beams are classified to four types. If the beam is supported at only one end and in such a manner that the axis of the beam cannot rotate at that point.To classify the beams to four types, there are different criteria such as;1. based on supports or boundary conditions.
2. based on geometry and shape3. based on loading1. Based on supports or boundary conditions:a) Simply supported beamb) Cantilever beanc) Overhanging beamd) Fixed beam2. Based on geometry and shape:a) Rectangular beamb) T-section beamc) I-section beamd) Circular section beam3. Based on loading:a) Concentrated or point loadb) Uniformly distributed loadc) Uniformly varying loadd) Combination of the above loads.
4. Based on material properties:a) Homogeneous beamb) Composite beamc) Reinforced concrete beamd) Steel beamIf the beam is supported at only one end and in such a manner that the axis of the beam cannot rotate at that point, it is known as a cantilever beam.Torsion subjected to long shaftIf a long shaft is subjected to torsion, the torque causes a twisting effect to be induced along the axis of the shaft. The angle of twist is proportional to the torque and length of the shaft and is inversely proportional to the fourth power of the shaft radius. For torsion to be elastic, it is required that the value of the applied torque should be less than the torsional yield strength of the material.
Equilibrium of a body Equilibrium of a body is a state of balance in which no net force or net torque is acting. It requires both a balance of forces and balance of moments
Thermal stress is the stress that develops in a body due to a change in temperature, causing it to change its dimensions. It occurs when a temperature gradient exists within a body and is a result of the differential expansion or contraction of the material.
To know more about stress visit
https://brainly.com/question/33140251
#SPJ11
A fuel consist of 87% carbon, 9% hydrogen, 1% sulphur, 1.5% oxygen and the remainder incombustibles. the actual air/fuel ratio is 18,5: 1.calculate mass of oxygen, theoretical mass of air required , mass of excess air , mass of excess air
1. Theoretical mass of air required is 9.484375 units
2. Actual air/fuel ratio is 0.0948
3. Mass of excess air is 18.4052
How to calculate the value1. Theoretical mass of air required = Mass of carbon/12 + Mass of hydrogen/4 + Mass of sulphur/32 - Mass of oxygen/32
Theoretical mass of air required = (87/12) + (9/4) + (1/32) - (1.5/32)
Theoretical mass of air required = 7.25 + 2.25 + 0.03125 - 0.046875
Theoretical mass of air required = 9.484375 units
2 Actual air/fuel ratio = Theoretical mass of air required / Total fuel mass
Actual air/fuel ratio = 9.484375 / 100
Actual air/fuel ratio ≈ 0.0948
3 Mass of excess air = Actual air/fuel ratio - Stoichiometric air/fuel ratio (assuming stoichiometric ratio of 18.5)
Mass of excess air = 18.5 - 0.0948
Mass of excess air ≈ 18.4052
Learn more about mass on
https://brainly.com/question/86444
#SPJ4
16.58-cm spring is displaced by 18.94 cm when 25.93 N is
applied. What would be the resulting final length of the spring
(inches) when a tensile force of 50.08 N is applied?
Given a spring with a displacement of 18.94 cm when a force of 25.93 N is applied, the final length of the spring when a tensile force of 50.08 N is applied.
To find the final length of the spring, we can use Hooke's Law, which states that the force exerted on a spring is directly proportional to the displacement. Mathematically, we can express this as F = kx, where F is the force, k is the spring constant, and x is the displacement. First, we need to calculate the spring constant (k) using the given information. We have a displacement of 18.94 cm (0.1894 m) and a force of 25.93 N. Rearranging the equation, we get k = F/x. Once we have the spring constant, we can use it to calculate the final displacement of the spring when a force of 50.08 N is applied. Rearranging the equation, we get x = F/k.
Learn more about Hooke's Lawt here:
https://brainly.com/question/30379950
#SPJ11
What is the function of endplate, winglet, flaps, and slots of the airplane? Explain their streamline mechanism when the part was added in the airfoil. 2. What is the effect of the wingspan, planform area, and chord length of the wing for a bird on its flying performance? 3. The aspect ratio of the wing is AR=b²/ A where b is the wingspan and A is the planform area of the wing. What happen if the AR of the bird is low, and vise versa. Give example for each type of bird.
1. Functions of endplate, winglet, flaps, and slots of the airplane An endplate is a plate placed at the tip of an airplane's wing to create an up-wash of air to minimize air leakage from the high-pressure bottom of the wing to the low-pressure top of the wing.
This decreases the wingtip drag and raises the lift-to-drag ratio. Winglets, on the other hand, are vertical extensions at the end of the wing that act as a passive flow control system to minimize the drag caused by vortices by increasing the effective wing span and lowering the lift-induced drag.
Flaps are surfaces on the trailing edge of the wing that can be extended or retracted to modify the lift and drag characteristics of an aircraft. Flaps produce additional lift at takeoff and landing, enabling the plane to fly slower at a steeper angle of attack without stalling.
To know more about Functions visit:
https://brainly.com/question/31062578
#SPJ11
An ideal Otto engine with an air compression ratio of 9 starts
with an air pressure of 90kpa and a temperature of 25 C. what is
the temperature after compression?
the temperature after compression is 2682 K. In an ideal Otto engine with an air compression ratio of 9 starts with an air pressure of 90kpa and a temperature of 25 C,
the temperature after compression can be determined using the ideal gas law. The ideal gas law is given as;PV=nRTWhere P is the pressure, V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the temperature.In the problem above, we are interested in finding the final temperature (T2) after compression given initial conditions of pressure (P1)
temperature (T1) which are; P1 = 90 kPa and T1 = 25 °C = 298 K respectively. The air compression ratio is given as; r = 9. Therefore, the volume at the end of compression (V2) will be 1/9th of the initial volume (V1) that is;V2 = V1 / 9.From the ideal gas law, we have;P1V1 / T1 = P2V2 / T2Where;P2 = P1rV2 = V1/9Substituting the values gives;P1V1 / T1 = P1rV1 / 9T2 = T1r9T2 = 298 K x 9T2 = 2682 KT
To know more about temperature visit :-
https://brainly.com/question/14532989
#SPJ11
Briefly describe the difference between a constant strain and linear strain triangular finite element. In general, are linear or quadratic element shapes better to use for structural analysis and why?
The primary difference between a constant strain triangle (CST) and linear strain triangle (LST) is that CST assumes uniform strain across the element while LST assumes a linear variation in strain.
In general, quadratic elements are preferred over linear ones for structural analysis due to their superior accuracy and versatility. Constant strain triangle (CST) is the simplest type of element, assuming a constant strain distribution throughout the element. This leads to less accurate results in complex problems. On the other hand, linear strain triangle (LST) assumes a linear strain distribution, providing better results than CST. Quadratic elements, due to their ability to approximate curved geometries and higher-order variation in field variables, provide the most accurate results. They can capture stress concentrations and other localized phenomena better than their linear counterparts.
Learn more about finite element analysis here:
https://brainly.com/question/13088387
#SPJ11
Question 1: Answer all questions Write any two important difference between friction wheel and gear. [1 mark] Question 2: Write a short note on gear drives giving their merits and demerits. 11.5 marks
Wheel and Gear Friction Wheel and Gear both are used to transmit power. Friction wheel is a simple device that is commonly used in low power applications. It is also known as a belt drive and can be found in home appliances such as washing machines, mixers, etc.
Friction wheels work by using the friction between the wheel and the belt to transmit power. On the other hand, gear drives are more commonly used in high power applications. Gears can be found in cars, trains, wind turbines, and many other machines. They transmit power by meshing together and transferring torque. Two important differences between Friction Wheel and Gear are: Friction wheels are easy to maintain while gears require more maintenance. Friction wheels are less expensive than gears.
Merits of Gear Drives:High efficiency: Gear drives have high efficiency as compared to other drives like belt drives.No slippage: Gear drives have no slippage, making them suitable for high power transmission and critical applications.Long life: Gear drives have a longer life than belt drives as they are made of metal. Hence they are more reliable and can be used for a longer duration of time. Smooth operation: Gear drives provide smooth operation as they don't slip and produce less noise.
To know more about transmit visit:
https://brainly.com/question/32340264
#SPJ11
A tank with an inlet and an outlet initially contains 200 gal of water in which 40 lb of salt are dissolved. Then five gal of brine, each containing 10 lb of dissolved salt, run into the tank per minute through the inlet, and the mixture, kept uniform by stirring, runs out of the tank through the outlet at the same rate. (a) Find the amount of salt y(t) in the tank at any time t. (b) Find the limit of the salt in the tank.
The amount of salt in the tank at any time t is y(t) = 2000 - 50 e^(-t/40), the limit of the salt in the tank is 2000 pounds.
(a) The amount of salt y(t) in the tank at any time t:Initially, the tank contains 200 gallons of water with 40 pounds of salt. As brine is entering at a rate of 5 gallons per minute, then the amount of salt in this brine is 10 pounds per gallon. Let x(t) denote the number of gallons of brine that has entered the tank. Then, at any time t, the amount of salt in the tank is y(t).Thus, the differential equation of the amount of salt in the tank over time can be derived as:dy/dt = (10 lb/gal)(5 gal/min) - y/200 (5 gal/min)dy/dt = 50 - y/40
Rearranging the differential equation: dy/dt + y/40 = 50. The integrating factor is: e^(∫1/40dt) = e^(t/40)Multiplying both sides by the integrating factor: e^(t/40) dy/dt + (1/40) e^(t/40) y = (50/1) e^(t/40)Simplifying the left-hand side: (e^(t/40) y)' = (50/1) e^(t/40)Integrating both sides: e^(t/40) y = (50/1) ∫e^(t/40)dt + C, where C is the constant of integration.Rewriting the equation: y = 2000 - 50 e^(-t/40)
(b) The limit of the salt in the tank:The limit of y(t) as t approaches infinity can be found by taking the limit as t approaches infinity of the expression 2000 - 50 e^(-t/40).As e^(-t/40) approaches 0 as t approaches infinity, the limit of y(t) is 2000.
To know more about stirring visit :
https://brainly.com/question/31406450
#SPJ11
The percentage composition of a sample of coal was found to be as follows: C = 85% ; H2 = 3% ; O2 = 2% ; Ash = 10% Determine the minimum weight of air required for the complete combustion of one kg of coal.
Ans. 10.80 kg.
For the complete combustion of one kg of coal, the minimum weight of air required will be 10.80 kg. The balanced equation for combustion of coal can be written as
[tex]C + O2 → CO2 + Heat and H2 + 0.5O2 → H2O[/tex]
Here, the weight percentage of carbon (C) in coal is 85%. The weight of carbon present in 1 kg of coal can be calculated as: Weight of Carbon = 85% of 1 kg = 0.85 kg Similarly, the weight percentage of hydrogen (H2) is 3%. The weight of hydrogen present in 1 kg of coal can be calculated as:
Weight of Hydrogen = 3% of 1 kg = 0.03 kg
Now, let's calculate the weight of oxygen required to completely burn the given amount of carbon and hydrogen. n Weight of Oxygen Required for Carbon:
In the combustion reaction, one mole of carbon reacts with one mole of oxygen to produce one mole of carbon dioxide. The balanced equation is:[tex]C + O2 → CO2[/tex]. The molar mass of carbon is 12 g/mol and that of oxygen is 32 g/mol.
To know more about minimum visit:
https://brainly.com/question/21426575
#SPJ11
Find the root of the equation e⁻ˣ²−x³=0 using Newton-Raphson algorithm. Perform three iterations from the starting point x₀=1. (3 grading points). Estimate the error. (1 grading point). Solution of all problems MUST contain general formula and all intermediate results. Perform numerical computations using 4 digits after decimal point.
We also have to estimate the error and perform three iterations from the starting point x₀ = 1 using 4 digits after decimal point.1.
The general formula for Newton-Raphson Algorithm is given by:x1= x0-f(x0)/f'(x0)2. The equation is e⁻ˣ²−x³ = 0. Let us find the derivative of the equation, f(x) = e⁻ˣ²−x³ with respect to x. Using the chain rule, we get :f'(x) = (-2xe⁻ˣ²) - 3x²The equation becomes: f(x) = e⁻ˣ²−x³f'(x) = (-2xe⁻ˣ²) - 3x²3.
From the given starting point x₀ = 1, let us find x1 using the above formula.x1= x0-f(x0)/f'(x0)= 1 - (e⁻¹²-1)/(2e⁻¹²-3)= 0.9615Let us estimate the error. Error, E = |x₁ - x₀| = |0.9615 - 1| = 0.03854. Now, we can find x2 using the formula: x2 = x1 - f(x1)/f'(x1)= 0.9615 - (e⁻⁰.⁹²⁶⁷⁹⁷⁸⁴⁵⁶⁴⁸⁰⁸ - 0.9615)/(-0.0693)= 0.9425 Estimating the error, E = |x₂ - x₁| = |0.9425 - 0.9615| = 0.01905.
To know more about estimate visit:-
https://brainly.com/question/32645675
#SPJ11
Question [3] (a) Explain why rubber is effective in providing good mountings for delicate instruments etc. (6) (b) A delicate instrument with a mass of 1.2kg is mounted onto a vibrating plate using rubber mounts with a total stiffness of 3kN/m and a damping coefficient of 200Ns/m. (1) If the plate begins vibrating and the frequency is increased from zero to 650Hz. Sketch a graph of the amplitude of vibrations of the instrument versus the plate frequency highlighting any significant features. (5) (ii) Indicate on the graph what the effect of changing the rubber mounts with equivalent steel springs of similar stiffness would have on the response. (2) (c) Determine the maximum amplitude of vibrations of the instrument when the plate is vibrated with an amplitude of 10mm. (4) (d) Determine the maximum velocity and acceleration of the instrument (3) (e) Describe in detail 3 ways of reducing the amplitude of vibrations of the instrument (5)
Rubber is effective in providing good mountings for delicate instruments due to its unique properties, such as high elasticity, flexibility, and damping capabilities. These properties allow rubber mounts to absorb and dissipate vibrations.
(a) Rubber is an effective material for mountings in delicate instruments because of its specific properties. Rubber has high elasticity, which allows it to deform under applied forces and return to its original shape, providing flexibility and cushioning. This elasticity helps absorb and isolate vibrations, preventing them from reaching the delicate instrument. Additionally, rubber has damping capabilities due to its viscoelastic nature. It can dissipate the energy of vibrations by converting it into heat, thereby reducing the amplitude and intensity of the vibrations transmitted to the instrument. (b) When the plate begins vibrating and the frequency increases.
Learn more about dissipate vibrations here:
https://brainly.com/question/29148671
#SPJ11
A velocity compounded impulse turbine has two rows of moving blades with a row of fixed blades between them. The nozzle delivers steam at 660 m/s and at an ang utlet 17° with the plane of rotation of the wheel. The first row of moving blades has an outlet angle of 18° and the second row has an outlet angle of 36°. The row of fixed blades has an outlet angle of 22°. The mean radius of the blade wheel is 155 mm and it rotates at 4 000 r/min. The steam flow rate is 80 kg/min and its velocity is reduced by 10% over all the blades.
Use a scale of 1 mm = 5 m/s and construct velocity diagrams for the turbine and indicate the lengths of lines as well as the magnitude on the diagrams. Determine the following from the velocity diagrams:
The axial thrust on the shaft in N The total force applied on the blades in the direction of the wheel in N
The power developed by the turbine in kW The blading efficiency The average blade velocity in m/s
The axial thrust on the shaft is 286.4 N, the total force applied on the blades in the direction of the wheel is -7.874 N, the power developed by the turbine is 541.23 kW, the blading efficiency is 84.5%, and the average blade velocity is 673.08 m/s.
Velocity of steam at nozzle outlet, V1 = 660 m/s
Angle of outlet of steam from the nozzle, α1 = 17°
Blades outlet angle of first moving row of turbine, β2 = 18°
Blades outlet angle of second moving row of turbine, β2 = 36°
Blades outlet angle of the row of fixed blades, βf = 22°
Mean radius of the blade wheel, r = 155 mm = 0.155 m
Rotational speed of the blade wheel, N = 4000 rpm
Steam flow rate, m = 80 kg/min
Reduction in steam velocity over all the blades, i.e., (V1 − V2)/V1 = 10% = 0.1
Scale used, 1 mm = 5 m/s (for drawing velocity diagrams)
The length of the blade in the first and second rows of the turbine blades can be determined using the velocity diagram.
Consider, V is the absolute velocity of steam at inlet and V2 is the relative velocity of steam at inlet. Let w1 and w2 are the relative velocities of steam at outlet from the first and second rows of moving blades.
Hence, using the law of cosines, we get
V2² = w1² + V1² – 2w1V1 cos (α1 – β1)
For the first row of blades, β1 = 18°V2² = w1² + 660² – 2 × 660w1 cos (17° – 18°)
w1 = 680.62 m/s
The length of the velocity diagram is proportional to w1, i.e., 680.62/5 = 136.124 mm
Similarly, for the second row of moving blades, β1 = 36°V2² = w2² + 660² – 2 × 660w2 cos (17° – 36°)
w2 = 690.99 m/s
The length of the velocity diagram is proportional to w2, i.e., 690.99/5 = 138.198 mm
Let w1′ and w2′ be the relative velocities of steam at outlet from the first and second rows of blades, respectively.Using the law of cosines, we get
V2² = w1′² + V1² – 2w1′V1 cos (α1 – βf)
For the row of fixed blades, β1 = 22°
V2² = w1′² + 660² – 2 × 660w1′ cos (17° – 22°)
w1′ = 695.32 m/s
The length of the velocity diagram is proportional to w1′, i.e., 695.32/5 = 139.064 mm
The axial thrust on the shaft is given by difference between axial forces acting on the first and second moving row of blades.
Hence,Total axial thrust on the shaft = (m × (w1 sin β1 + w2 sin β2)) − (m × w1′ sin βf) = (80/60) × (680.62 sin 18° + 690.99 sin 36°) – (80/60) × 695.32 sin 22° = 286.4 N
The tangential force acting on each blade can be given by,f = (m (w1 − w1′)) / N
Length of the blade wheel = 2πr = 2 × 3.14 × 0.155 = 0.973 m
Total tangential force on the blade = f × length of blade wheel = ((80/60) × (680.62 − 695.32)) / 4000 × 0.973 = −7.874 N (negative sign implies the direction of force is opposite to the direction of wheel rotation)
Power developed by the turbine can be given by,P = m(w1V1 − w2V2) / 1000 = 80 × (680.62 × 660 − 690.99 × 656.05) / 1000 = 541.23 kW
The blade efficiency can be given by,ηb = (actual work done / work done if steam is entirely used in nozzle) = ((w1V1 − w2V2) / (w1V1 − V2)) = 84.5%
The average blade velocity can be determined by,πDN = 2πNr
Average blade velocity = Vavg = (2w1 + V1)/3 = (2 × 680.62 + 660)/3 = 673.08 m/s
Learn more about velocity at
https://brainly.com/question/33293748
#SPJ11
QUESTION 1 (10 MARKS) As a Graduate Metallurgist you are working in a plant to produce a product as fast as possible. The process uses a liquid with specific heat capacity of 75.44 J.K-1mol-1 . In the first furnace you start with a temperature of 45°C and your aim temperature is 155°C. You use 2 kg of fuel with a mole mass of 22 gmol-1 . In your second furnace you start at a temperature of 82°C and also aim for 155°C. You have here 150 kg of fuel, the same type as in furnace 1. In furnace 1 you use an element of 1200W and for furnace 2 you use 3650W. Do metallurgical calculations to determine which furnace you will opt for, with special reference to time
QUESTION 2 (10 MARKS) Calculate the heat required for 2.4 kg of steel to be heated from 130°C to 920°C if the specific heat capacity is 54.6 + 2.1 x 10-3T – 6.5 x 105T -2 . Mole mass of steel is 56 gmol-1 . If the heat price is R36.50 per 2000J and your budget account is R2420.00 will you be able to buy the energy? Prove by thermodynamic calculations. QUESTION 3 (5 MARKS) A company producing aluminium is using coke as a fuel. The furnace work temperature is 1100°C. Is it possible to produce aluminium in this furnace, comment on your answer? Do metallurgical calculations to prove your answer. You are told that when the enthalpy is zero chemical equilibrium is reached. Given: 2Al + 3 2 O2 = Al2O3 ∆H = −216510 + 169.4T Joules C + 1 2 O2 = CO ∆H = −165550 + 170.2T Joules 3
QUESTION 4 (15 MARKS) The transformation of manganese is as follows: Mn(α) at 720°C → Mn(β) at 1100°C → Mn(γ) at 1136°C → Mn(δ) Calculate the heat of this process when Mn is oxidised by pure oxygen to form MnO at 1250°C. Given: Mn(α) + 1 2 O2 → MnO ∆H298 = −384900 Jmol−1 Mn(α) → Mn(β) ∆Hf = 2100 Jmol−1 Mn(β) → Mn(γ) ∆Hf = 2380 Jmol−1 Mn(γ) → Mn(δ) ∆Hf = 1840 Jmol−1 Cp(αMn) = 21.55 + 15.56 × 10−3T JK −1mol−1 Cp(βMn) = 34.85 + 2.76 × 10−3T JK −1mol−1 Cp(γMn) = 45.55 JK −1mol−1 Cp(δMn) = 47.28 JK −1mol−1 Cp(MnO) = 46.44 + 8.12 × 10−3T − 3.68 × 105T −2 JK −1mol−1 Cp(Oxygen) = 29.96 + 4.184 × 10−3T − 1.67 × 105T −2 JK −1mol−1
The specific heat capacity of the steel is given as a function of temperature, and we are required to use thermodynamic calculations to determine the heat energy required. Thus, we need to integrate the given equation with respect to T over the given temperature range, and obtain the average value of the integrand. In th
e first furnace, the heat energy required is obtained using the formula, Q = mcΔT.
1. Hence, Q = 2 x 75.44 x (155 - 45) = 22632.32 J. In the second furnace, the heat energy required is obtained using the same formula, but we are not given the mass of the liquid.
Thus,t = Q/P
For furnace 2, the time required is given by,t = (150 x 1000) / 3650 = 41.1 sThus, furnace 2 will produce the product faster.
2. The heat energy required to heat the steel from 130°C to 920°C is obtained using the formula,
Q = mcΔT
Hence, Q = (2.4 x 10^3) x (1/790) x (54.6(790-130) + 2.1 x 10^-3 (790^2 - 130^2)/2 - 6.5 x 10^-5 (790^-1 - 130^-1)) = 5.63 x 10^5 J
The cost of the heat energy is given by,
C = (Q/2000) x R36.50 = (5.63 x 10^5 / 2000) x R36.50 = R101.31
Since R101.31 is less than R2420.00, the budget is sufficient to buy the energy.
To know more about temperature visit:
https://brainly.com/question/7510619
#SPJ11
For a passive LP RC filter (Note: v, is taken across the capacitor) where R = 1k0 and C = 100 nF: a. Calculate H(jω) at ω, 0.1 ω, and 10 ω
b. If v₁ = 200 cos(ωt) mV, write the steady-state expression for v₀ when ω = ω, ω=0.1 ω, and ω=10ω.
H(jω) at ω = 1000 rad/s is 0.5 - 0.5j; H(jω) at ω = 100 rad/s is 0.99 - 0.1j; H(jω) at ω = 10 rad/s is 0.91 - 0.09jb. The steady-state expressions for v₀ when ω = ω, ω = 0.1ω, and ω = 10ω are:v₀(ω) = 100cosω - 100jsinωv₀(0.1ω) = 198.02cosω - 198.02jsinωv₀(10ω) = 50cosω - 50jsinω
The transfer function of a passive LP RC filter is given by H(s) = 1/(1 + RCs),
where s = jω and R and C are the resistance and capacitance of the circuit respectively.
Here, R = 1k0 and C = 100 nF.
a) To calculate H(jω) at ω, 0.1ω, and 10ω, substitute s = jω in the transfer function and simplify as follows:
H(jω) = 1/(1 + RCjω) At ω = 1000 rad/s, H(jω) = 1/(1 + j) = (1 - j)/(2) = 0.5 - 0.5j
At ω = 100 rad/s, H(jω) = 1/(1 + j/10) = 0.99 - 0.1j
At ω = 10 rad/s, H(jω) = 1/(1 + j/100) = 0.91 - 0.09j
b) If v₁ = 200 cos(ωt) mV, then the input voltage across the capacitor is given by v = v₁/(1 + jωRC). The output voltage v₀ is the voltage across the capacitor, i.e.,v₀ = v₁H(jω)
Substituting the values of H(jω) at ω, 0.1ω, and 10ω, we get:
v₀(ω) = 100(cosω - jsinω) = 100cosω - 100jsinω v₀(0.1ω) = 198.02(cosω - jsinω) = 198.02cosω - 198.02jsinω v₀(10ω) = 50(cosω - jsinω) = 50cosω - 50jsinω
Therefore, the steady-state expressions for v₀ when ω = ω, ω = 0.1ω, and ω = 10ω are:v₀(ω) = 100cosω - 100jsinω v₀(0.1ω) = 198.02cosω - 198.02jsinω v₀(10ω) = 50cosω - 50jsinω
Answer: a. H(jω) at ω = 1000 rad/s is 0.5 - 0.5j; H(jω) at ω = 100 rad/s is 0.99 - 0.1j; H(jω) at ω = 10 rad/s is 0.91 - 0.09jb. The steady-state expressions for v₀ when ω = ω, ω = 0.1ω, and ω = 10ω are:v₀(ω) = 100cosω - 100jsinωv₀(0.1ω) = 198.02cosω - 198.02jsinωv₀(10ω) = 50cosω - 50jsinω
To know more about capacitance, visit:
https://brainly.com/question/31871398
#SPJ11
The speed of a particle traveling along a straight line within a liquid is measured as a function of its position as v = (130 s) mm/s, where s is in millimeters. Part A Determine the particle's deceleration when it is located at point A, where SA = 90 mm. Express your answer to three significant figures and include the appropriate units. a = -40.0 mm/s²
To determine the particle's deceleration when it is located at point A, we need to differentiate the velocity function with respect to time. Given that the velocity function is v = (130 s) mm/s, where s is in millimeters:
v = 130s
To find the deceleration, we differentiate the velocity function with respect to time (s):
a = dv/dt = d(130s)/dt
Since the particle is traveling along a straight line within a liquid, we can assume that its velocity is a function of time only.
Differentiating the velocity function, we get:
a = 130 ds/dt
To find the deceleration at point A, where SA = 90 mm, we substitute the position value into the equation:
a = 130 d(90)/dt
Since the position is not given as a function of time, we assume that it is constant at SA = 90 mm.
Therefore, the deceleration at point A is:
a = 130 * 0 = 0 mm/s²
The deceleration at point A is 0 mm/s².
Learn more about velocity here
https://brainly.com/question/30505958
#SPJ11
our practical report must have an introduction where you will introduce your experiments topics and it need to be divided into 3 paragraphs,
1. Paragraph one, give a brieve definition of your topics 2. Paragraph two, give a brieve history on motor failure analyses and link it to todays applications and methods used in this day and age. 3. Paragraph three, introduce your work, (Name the paragraph the: AIM) by stating what is required from you on this assignment. [THIS IS A VERY IMPORTANT PARAGRAPH] [This paragraph and your conclusion must relate to each other]
When writing a practical report, you will need to have an introduction where you introduce your experimental topics and it should be divided into 3 paragraphs.
The following is an outline of how the introduction should be structured:
This paragraph should give a brief definition of your topics. Here, you should explain what your experimental topics are and why they are important. It is important to be clear and concise in this paragraph. This paragraph should provide a brief history of motor failure analyses and link it to today's applications and methods used in this day and age.
Here, you should explain how motor failure analyses have evolved over time and how they are used today. You should also discuss the methods used in this day and age and how they are different from the methods used in the past. This paragraph should introduce your work and state what is required from you on this assignment. You should name the paragraph the AIM.
To know more about practical visit:
https://brainly.com/question/32439310
#SPJ11
Steam enters a diffuster steadily at a pressure of 400 psia and a temperature of Tdiffuser = 500.0 °F. The velocity of the steam at the inlet is Veldiffuser 80.0 ft s = and the mass flow rate is 5 lbm/s. What is the inlet area of the diffuser? ANS: 11.57in^2
The inlet area of the diffuser is 11.57 in^2.
To determine the inlet area of the diffuser, we can use the mass flow rate and the velocity of the steam at the inlet. The mass flow rate is given as 5 lbm/s, and the velocity is given as 80.0 ft/s.
The mass flow rate, denoted by m_dot, is equal to the product of density (ρ) and velocity (V) times the cross-sectional area (A) of the flow. Mathematically, this can be expressed as:
m_dot = ρ * V * A
Rearranging the equation, we can solve for the cross-sectional area:
A = m_dot / (ρ * V)
Given the values for mass flow rate, velocity, and the properties of steam at the inlet (pressure and temperature), we can calculate the density of the steam using steam tables or thermodynamic properties of the fluid. Once we have the density, we can substitute the values into the equation to find the inlet area of the diffuser.
To learn more about diffuser.
brainly.com/question/14852229
#SPJ11
The pipe network runs between two tanks (k for pipe entry of 0.2 and exit 1) over a distance of 25 m, with a total static lift of 10 m between the two tanks. This pipe network includes two long sweeping elbows, a Mitre bend and a gate valve (1/4 open). Calculate: iii) the total head loss [7] iv) the hydraulic output required to pump the mixture between the two tanks [3]
In this pipe network scenario between two tanks, the objective is to calculate the total head loss and the hydraulic output required to pump the mixture between the tanks. The network includes specific components such as long sweeping elbows.
iii) To calculate the total head loss in the pipe network, we need to consider the individual head losses caused by different components. The head loss due to pipe entry and exit can be determined using the provided values. The head loss due to pipe friction can be calculated using the pipe length, pipe diameter, and the Darcy-Weisbach equation. The head losses associated with the long sweeping elbows, Mitre bend, and the gate valve can be estimated using empirical data or fitting coefficients specific to each component. By summing up these individual head losses, we can determine the total head loss in the pipe network.
Learn more about total head loss here:
https://brainly.com/question/32578467
#SPJ11
Steam is the working fluid in an ideal Rankine cycle. Saturated vapour enters the turbine at 10 MPa and saturated liquid exits the condenser at 0.01 MPa. The net power output is 100 MW. Determine the mass flow rate of steam. Enter your answers in kg/s.
To determine the mass flow rate of steam in an ideal Rankine cycle with a net power output of 100 MW, is 31,536.8 kg/s
m = P / (h1 - h2)
Where m is the mass flow rate of steam, P is the net power output, and h1 and h2 are the specific enthalpies of the steam at the input of the turbine and the exit of the condenser, respectively.
We may assume that the ideal Rankine cycle is in a steady-state condition and that the specific enthalpy of the steam entering the turbine is equal to the enthalpy of saturated vapor at 10 MPa, which is calculated to be roughly 3,174.9 kJ/kg using a steam table.
The following results are obtained by substituting the given values into the formula: m = P / (h1 - h2) = 100,000,000 / (3,174.9 - 41.9) = 31,536.8 kg/s.
Learn more about on mass flow, here:
https://brainly.com/question/30763861
#SPJ4