Answer:
7.05 Hz
Explanation:
The natural frequency of a mass-spring system is:
[tex]f = \frac{1}{2 \pi}\sqrt{\frac{k}{m}}[/tex]
To determine the constant k of the spring we use Hooke's law:
Δl = F / k
k = F / Δl
In the first case the force was the weight of the 20 kg mass and the Δl was 20 mm.
F = m * a
F = 2 * 9.81 = 19.6 N
Then:
k = 19.6 / 0.02 = 980 N/m
Therefore:[tex]f = \frac{1}{2 \pi}\sqrt{\frac{980}{0.5}} = 7.05 Hz[/tex]
The initial internal energy of a mug of coffee is known to be 168 Btu. The initial coffee temperature is approximately 200 F. The room temperature is 70 F. Time passes and the final amount of internal energy in the coffee is 68 Btu. How much heat flowed from the coffee to the room?
Answer:
100Btu
Explanation:
According to the First law of thermodynamics:
ΔQ = W + ΔU
Where,
ΔQ is the heat change
W is the amount of work done
ΔU is change in internal energy
Since, there is no work done on the system as heat is just passing from coffee mug to surroundings, So, W = 0
Thus,
Net heat change = change in internal energy.
Change in internal energy = [tex]U_f-U_i=(68-168)\ Btu=-100\ Btu[/tex]
Thus,
ΔQ = -100 Btu (negative sign indicates release of heat)
So,
Heat flown to the room = 100Btu
The physical arrangement of network equipment and cables is known as a network_________
Answer:
Network Topology
Explanation:
A network topology is the arrangement of nodes usually switches or routers, and connections in a network, often represented as a graph. The topology of the network, and the relative locations of the source and destination of traffic flows on the network, determine the optimum path for each flow and the extent to which redundant options for routing exist in the event of a failure.
There are two types of network topologies: physical and logical. Physical topology emphasizes the physical layout of the connected devices and nodes, while the logical topology focuses on the pattern of data transfer between network nodes.
I leave you an example in the next picture:
The International Space Station operates at an altitude of 350 km. Plans for the final construction show that material of weight 4.22 ✕ 106 N, measured at the Earth's surface, will have been lifted off the surface by various spacecraft during the construction process. What is the weight of the space station when in orbit?
Answer:
The weight of the station becomes [tex]3.756\times 10^{6}N[/tex]
Explanation:
Since the acceleration due to gravity decreases with increase in height we conclude that at a height of 350 kilometers the weight of the material will be lesser.
At the ground we have
[tex]W=mass\times g_{surface}\\\\\therefore mass=\frac{W}{g_{surface}}\\\\mass=\frac{4.22\times 10^{6}N}{9.81}\\\\\therefore mass=430173.292kg[/tex]
Now we know that the variation of acceleration due to gravity with height above surface of earth is given by
[tex]g(h)=g_{surface}(1-\frac{2h}{R})[/tex]
where R = 6371 km is Radius of earth
Applying values we get the value of 'g' at height of 350 kilometers equals
[tex]g(350)=9.81\times (1-\frac{2\times 350}{6371})=8.732ms^{-2}[/tex]
hence the weight in orbit becomes
[tex]W_{orbit}=mass\times g_{orbit}\\\\W_{orbit}=430173.292\times 8.732\\\\ \therefore W_{orbit}=3.756\times 10^{6}N\\[/tex]
An inventor claims that he wants to build a dam to produce hydroelectric power. He correctly realizes that civilization uses a lot more electricity during the day than at night, so he thinks he has stumbled upon a great untapped energy supply. His plan is to install pumps at the bottom of the dam so that he can pump some of the water that flows out from the generators back up into the reservoir using the excess electricity generated at night. He reasons that if he did that, the water would just flow right back down through the generators the next day producing power for free. What is wrong with his plan?
Answer:
The problem is that the pumps would consume more energy than the generators would produce.
Explanation:
Water has a potential energy associated with the height it is at. The higher it is, the higher the potential energy. When water flows down into the turbines that energy is converted to kinetic energy and then into electricity.
A pump uses electricity to add energy to the water to send it to a higher potential energy state.
Ideally no net energy woul be hgenerate or lost, because the generators would release the potential energy and pumps would store it again in the water. However the systems are not ideal, everything has an efficiency and losses. The losses would accumulate and the generator would be generating less energy than the pumps consume, so that system wastes energy.
What should be done is closing the floodgates to keep the water up in the dam at night producing only the power that is needed and releasing more water during the day.
the force acting on a particle of mass m is given by
F=kvx
in which k is a positive constant. The particle passes
throughthe origin with speed Vo at time t=0. Find x as a function
oft.
Answer with Explanation:
From newton's second law the acceleration produced by a force on a mass 'm' is given by
[tex]Acceleration=\frac{Force}{Mass}[/tex]
Applying the given values in the above equation we get
[tex]Acceleration=\frac{kvx}{m}[/tex]
Also we know that acceelration of a particle can ve mathem,atically written as
[tex]a=\frac{v\cdot dv}{dx}[/tex]
Applying the given values in the above equation we get
[tex]\frac{kvx}{m}=\frac{v\cdot dv}{dx}\\\\\Rightarrow {kx}\cdot dx=m\cdot dv\\\\\int kxdx=\int mdv\\\\\frac{kx^2}{2}=mv-c[/tex]
'c' is the constant of integration
whose value is found that at x =0 v= [tex]v_o[/tex]
Thus
[tex]c={mv_o}[/tex]
Thus the velocity as a function of position is
[tex]v=\frac{1}{m}(\frac{kx^2}{2}+c)[/tex]
Now by definition of velocity we have
[tex]v=\frac{dx}{dt}[/tex]
Using the function of velocity in the above relation we get
[tex]\frac{dx}{kx^{2}+\sqrt{2c}}=\frac{dt}{2m}\\\\\int \frac{dx}{(\sqrt{k})^2x^{2}+(\sqrt{2c})^2}=\int \frac{dt}{2m}\\\\\frac{1}{\sqrt{2kc}}\cdot tan^{-1}(\frac{(\sqrt{k})x}{\sqrt{2c}})=\frac{t}{2m}+\phi \\\\[/tex]
where
[tex]\phi [/tex] is constant of integration
Now it is given that at t = 0 ,x = 0
thus from the above equation of position and time we get [tex]\phi =0[/tex]
Thus the position as a function of time is
[tex]x(t)=\sqrt{\frac{2c}{k}}\cdot tan(\frac{kct}{\sqrt{2}m})[/tex]
where c=[tex]mv_o[/tex]
The atmospheric pressure reads "35.2". What is the "gage pressure"?
Answer:
No, it absolute pressure.
Explanation:
Gauge pressure is relative to the pressure of the atmosphere. It is the difference between the pressure measured and the pressure of the atmosphere. If it is measuring atmospheric pressure it will always read zero.
The measurement is an absolute pressure, which is the pressure above a total vacuum.
What are two advantages of forging when compared to machining a part from a billet?
Answer:
Less material waste and time.
Explanation:
Two advantages of forging vs machining would be that with forging there is much less waste of material. With machining you remove a large amount of material turning into not so valuable chips.
There is also a time factor, as machining can be very time intensive. This depends on the speed of the machining, newer machines tend to be very fast, and forging requires a lengthy heating, but for large parts the machining can be excessively long.
What's the monomer? Show the structure.
In order to understand a monomer let´s first see the structure of a polymer. As an example, in the first figure polyethylene (or polyethene) is shown. This polymer, like every other one, is composed of many repeated subunits, these subunits are called monomer. In the second figure, polyethylene's monomer is shown.
For turbulent now the friction factor is function of (Reynolds number —surface roughness -both the Reynolds number and the surface roughness) of the pipe.
Answer:
Both Reynolds and surface roughness
Explanation:
For turbulent flow friction factor is a function of both Reynolds and surface roughness of the pipe.But on the other hand for laminar flow friction factor is a function of only Reynolds number.
Friction factor for turbulent flow:
1. For smooth pipe
[tex]f=0.0032+\dfrac{0.221}{Re^{0.237}}[/tex]
[tex]5\times 10^4<Re<4\times 10^7[/tex]
2. For rough pipe
[tex]\dfrac{1}{\sqrt f}=2\ log_{10}\frac{R}{K}+1.74[/tex]
Where R/K is relative roughness
Friction factor for laminar flow:
[tex]f=\dfrac{64}{Re}[/tex]
Consider a system whose temperature is 18°C. Express this temperature in R, K, and °F.
Answer:
In Rankine 524.07°R
In kelvin 291 K
In Fahrenheit 64.4°F
Explanation:
We have given temperature 18°C
We have to convert this into Rankine R
From Celsius to Rankine we know that [tex]T(R)=(T_{C}+273.15)\frac{9}{5}[/tex]
We have to convert 18°C
So [tex]T(R)=(18+273.15)\frac{9}{5}=524.07^{\circ}R[/tex]
Conversion from Celsius to kelvin
[tex]T(K)=(T_{C}+273)[/tex]
We have to convert 18°C
[tex]T(K)=(18+273)=291K[/tex]
Conversion of Celsius to Fahrenheit
[tex]T(F)=T_{C}\times \frac{9}{5}+32=64.4^{\circ}F[/tex]
If the equation for the velocity profile is given by: v = 4y^2/3. Assuming v is in ft/s, what is the velocity gradient at the boundary and at y=0.25 ft and 0.5 ft from boundary?
The velocity gradients at y=0.25 ft and y=0.50 ft from the boundary are calculated by differentiating the velocity profile v = 4y^2/3 with respect to y and evaluating at the given points.
Explanation:The velocity profile given by v = 4y2/3 describes the velocity of a fluid at different distances from the boundary in a flow field. To find the velocity gradient at the boundary (y=0), and at y=0.25 ft and y=0.50 ft, we differentiate the velocity profile with respect to y to get the gradient, dv/dy.
At the boundary, y=0, but since we're dealing with a power of y, the derivative will be a term that includes y in the denominator, which would imply an infinite gradient at the boundary, although physically this would manifest as a very large but finite value. However, at y=0.25 ft and 0.50 ft, we calculate the gradient by inserting these y-values into the derivative
Let's calculate the velocity gradient at y = 0.25 ft and y = 0.50 ft:
For y = 0.25 ft: dv/dy = d/dy(4y2/3) = 8/3y-1/3 = 8/3(0.25)-1/3For y = 0.50 ft: dv/dy = 8/3(0.50)-1/3These calculations will give us the velocity gradients at the specified values of y, in ft/s2.
Engineering stress, strain vs true stress, strain.
Answer with Explanation:
Stress is defined as the force acting per unit area on a material.
Mathematically
[tex]\sigma =\frac{dF}{dA}[/tex]
where
[tex]\sigma [/tex] is the stress ,[tex]dF[/tex] is an infinitesimal force that acts on an infinitesimal area [tex]dA[/tex]
When a body is under stress it's dimensions change and this change in dimensions is known as strain.
Mathematically
[tex]\epsilon =\frac{\Delta x}{X}[/tex]
where
[tex]\epsilon=[/tex] strain in the object
[tex]\Delta x =[/tex] is the change in any dimension of the body
Now in the above relation of stress, the area involved also changes when the body is loaded as the load produces strain which changes the dimensions of the body.
Now while calculating the stress if we use the original area of the cross section of the body prior to loading the stress that we calculate is the engineering stress and the strain associated with it is the engineering strain.
On the other hand if we use the true cross section of the body when it is loaded the stress that we calculate is the true stress and the strain associated with it is the true strain.
Mathematically they are related as
[tex]\epsilon _{true}=ln(1+\epsilon _{engineering})}[/tex]
Thus the true stress is found to be larger than engineering stress.
A missile flying at high speed has a stagnation pressure and temperature of 5 atm and 598.59 °R respectively. What is the density of air at this point?
Answer:
[tex]5.31\frac{kg}{m^3}[/tex]
Explanation:
Approximately, we can use the ideal gas law, below we see how we can deduce the density from general gas equation. To do this, remember that the number of moles n is equal to [tex]\frac{m}{M}[/tex], where m is the mass and M the molar mass of the gas, and the density is [tex]\frac{m}{V}[/tex].
For air [tex]M=28.66*10^{-3}\frac{kg}{mol}[/tex] and [tex]\frac{5}{9}R=K[/tex]
So, [tex]598.59 R*\frac{5}{9}=332.55K[/tex]
[tex]pV=nRT\\pV=\frac{m}{M}RT\\\frac{m}{V}=\frac{pM}{RT}\\\rho=\frac{pM}{RT}\\\rho=\frac{(5atm)28.66*10^{-3}\frac{kg}{mol}}{(8.20*10^{-5}\frac{m^3*atm}{K*mol})332.55K}=5.31\frac{kg}{m^3}[/tex]
Two forces P and Q are applied as shown at point A of a
hooksupport. Knowing that P = 60 lb and
Q = 25 lb, determine graphically the magnitude and directionof
their resultant using the triangle rule.
The magnitude and direction of the resultant force from two applied forces, P and Q, at a point can be determined graphically using the triangle rule by forming a vector triangle, measuring the resultant vector, and calculating its angle.
Explanation:To determine the magnitude and direction of the resultant force using the triangle rule when two forces, P and Q, are applied at a point, you can follow a graphical method. Picture two vectors representing these forces originating from the same point. Since P = 60 lb and Q = 25 lb, you draw them to scale, with the tail of Q starting at the head of P to form a triangle. By connecting the tail of P to the head of Q, you form the resultant vector.
To find the magnitude of the resultant force, measure the length of the resultant vector using the same scale and apply trigonometry or the Pythagorean theorem if the angle is known. The direction of the resultant force is given by the angle it makes with either P or Q, which can be measured with a protractor in reference to a baseline, such as the horizontal.
Small droplets of carbon tetrachloride at 68 °F are formed with a spray nozzle. If the average diameter of the droplets is 200 um, what is the difference in pressure between the inside and outside of the droplets?
Answer:
the difference in pressure between the inside and outside of the droplets is 538 Pa
Explanation:
given data
temperature = 68 °F
average diameter = 200 µm
to find out
what is the difference in pressure between the inside and outside of the droplets
solution
we know here surface tension of carbon tetra chloride at 68 °F is get from table 1.6 physical properties of liquid that is
σ = 2.69 × [tex]10^{-2}[/tex] N/m
so average radius = [tex]\frac{diameter}{2}[/tex] = 100 µm = 100 ×[tex]10^{-6}[/tex] m
now here we know relation between pressure difference and surface tension
so we can derive difference pressure as
2π×σ×r = Δp×π×r² .....................1
here r is radius and Δp pressure difference and σ surface tension
Δp = [tex]\frac{2 \sigma }{r}[/tex]
put here value
Δp = [tex]\frac{2*2.69*10^{-2}}{100*10^{-6}}[/tex]
Δp = 538
so the difference in pressure between the inside and outside of the droplets is 538 Pa
The difference in pressure between the inside and outside of small droplets of carbon tetrachloride at 68 °F with a diameter of 200 um is calculated using the Laplace pressure equation and results in a difference of 2700 dyne/cm2.
Explanation:The relationship between the pressure inside and outside of small droplets is described by the Laplace pressure equation. The Laplace equation for the pressure difference is ΔP = 2σ/r, where ΔP is the pressure difference, σ is the surface tension, and r is the radius of the droplet. For carbon tetrachloride, the surface tension at 20°C (68°F) is approximately 27 dyne/cm. Therefore, the pressure difference (ΔP) would be 2 x 27 dyne/cm divided by the radius in cm. Given that 200 um = 0.02 cm, the pressure difference is ΔP = 2 x 27 dyne/cm / 0.02 cm = 2700 dyne/cm2. This means that the pressure inside the droplets is 2700 dyne/cm2 greater than the pressure outside the droplets.
Learn more about Laplace pressure equation here:https://brainly.com/question/31671639
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Increasing rake angle will decrease the tendency for Built-Up-Edge to form. a) True b) False
Answer:
a)True
Explanation:
While machining of ductile material and high feed and low cutting speed welding action take place between tool material and chip material this welding action is called built up edge. Built up edge action takes place due to high temperature.
To decrease the built up edge action
1. Increase the rake angle.
2. Increase the cutting speed
3. Decrease the feed rate
4. Use cutting fluid
a piston executes simple harmonic motion with an amplitude of 0.1m. If it passes through the center of it's motion with a speed of 0.5 m/s, what is the period of oscillation?
Answer:
Time period will be 1.26 sec
Explanation:
We have given amplitude A = 0.1 M
Speed [tex]\frac{dx}{dt}=0.5m/sec[/tex]
The displacement equation of simple harmonic motion is given by
[tex]x(t)=Asin\omega t[/tex]
Differentiating both side
[tex]\frac{dx}{dt}=A\omega cos\omega t[/tex]
In question it is given that at t=0, x=0 and [tex]\frac{dx}{dt}=0.5m/sec[/tex]
So [tex]0.5=0.1\omega cos0[/tex]
[tex]\omega =5sec^{-1}[/tex]
Now period of oscillation [tex]T=\frac{2\pi }{\omega }=\frac{2\times 3.14}{5}=1.26sec[/tex]
Calculate the density of a hydraulic oil in units of kg/m^3 knowing that the density is 1.74 slugs/ft^3. Then, calculate the specific gravity of the oil.
Answer:
Density of oil will be 897.292 kg[tex]m^3[/tex]
And specific gravity of oil will be 0.897
Explanation:
We have given density of oil is 1.74 slugs/[tex]ft^3[/tex]
We have to convert this slugs/[tex]ft^3[/tex] into kg/[tex]m^3[/tex]
We know that 1 slugs = 14.5939 kg
So 1.74 slug = 1.74×14.5939 = 25.3933 kg
And 1 cubic feet = 0.0283 cubic meter
So [tex]1.74slug/ft^3=\frac{1.74\times 14.5939kg}{0.0283m^3}=897.292kg/m^3[/tex]
Now we have to calculate specific gravity it is the ratio of density of oil and density of water
We know that density of water = 1000 kg/[tex]m^3[/tex]
So specific gravity of water [tex]=\frac{897.292}{1000}=0.897[/tex]
A has a mass of 7 kg, object B has a mass of 5 lbm, and object C has a mass of 0.5 slug. (a) Which object has the largest mass? Which object has the smallest mass? (b) Find the weights of objects A, B and C (in both N and lbf) on the surface of Mars.
Answer:
1) Object C has the largest mass.
2)Object has the smallest mass.
3) Weight of A = 26.6 Newtons
4)Weight of B = 8.6184 Newtons
5)Weight of C = 27.7286 Newtons
Explanation:
Since all the given masses have different unit's we shall convert them all into a same base unit for comparison. The base unit is selected to be kilogram.
Hence
1) Mass of object A = 7 kilogram
2) Mass of object B = 5 pounds
We know that 1 pound equals 0.4536 kilograms Hence 5 pounds equals
[tex]0.4536\times 5=2.268kg[/tex]
3) Mass of object C = 0.5 slug
We know that 1 slug equals 14.594 kilograms Hence 0.5 slug equals
[tex]14.594\times 0.5=7.297kg[/tex]
Upon comparing all the 3 masses we conclude that object C has the largest mass and object B has the smallest mass.
Part b)
Weight of an object is given by
[tex]Weight=mass\times g[/tex]
Now on Mars value of g equals [tex]3.8m/s^{2}[/tex]
Thus the corresponding weights are as under:
[tex]W_{A}=3.8\times 7=26.6N\\\\W_{B}=3.8\times 2.268=8.6184N\\\\W_{C}=3.8\times 7.297=27.7286N\\\\[/tex]
A light bulb is switched on and within a few minutes its temperature becomes constant. Is it at equilibrium or steady state.
Answer:
The temperature attains equilibrium with the surroundings.
Explanation:
When the light bulb is lighted we know that it's temperature will go on increasing as the filament of the bulb has to constantly dissipates energy during the time in which it is on. Now this energy is dissipated as heat as we know it, this heat energy is absorbed by the material of the bulb which is usually made up of glass, increasing it's temperature. Now we know that any object with temperature above absolute zero has to dissipate energy in form of radiations.
Thus we conclude that the bulb absorbs as well as dissipates it's absorbed thermal energy. we know that this rate is dependent on the temperature of the bulb thus it the temperature of the bulb does not change we can infer that an equilibrium has been reached in the above 2 processes i.e the rate of energy absorption equals the rate of energy dissipation.
Steady state is the condition when the condition does not change with time no matter whatever the surrounding conditions are.
Ammonia at 20 C with a quality of 50% and a total mass of 2 kg is in a rigid tank with an outlet valve at the bottom. How much saturated liquid can be removed from the tank in an isothermal process until there remains no more liquid?
Answer:
16.38L
Explanation:
Through laboratory tests, thermodynamic tables were developed, these allow to know all the thermodynamic properties of a substance (entropy, enthalpy, pressure, specific volume, internal energy etc ..)
through prior knowledge of two other properties.
Quality is defined as the ratio between the amount of steam and liquid when a fluid is in a state of saturation, this means that since the quality is 50%, 1kg is liquid and 1kg is steam.
then to solve this problem we find the specific volume for ammonia in a saturated liquid state at 20C, and multiply it by mass (1kg)
v(amonia at 20C)=0.001638m^3/kg
m=(0.01638)(1)=0.01638m^3=16.38L
Any change in the system from one equilibrium state to another is called: A) Path B) Process C) Cycle D) None of the above
Answer:
B) Process
Explanation:
In thermodynamics a process is a passage of a thermodynamic system from an initial to a final state of thermodynamic equilibrium.
A thermodynamic process path is the series of states through which a system passes from an initial to a final state.
Cycle is a process in which initial and final state are identical.
What is 30.25 inHg in psia?
Answer:
30.25 in Hg will be equal to 14.855 psi
Explanation:
We have given 30.25 Hg pressure
We have to convert the pressure of 30.25 Hg into psi
We know that 1 inch of Hg = 0.4911 psi
So to convert 30.25 inch Hg in psi we have to multiply with 0.4911
We have to convert 30.25 in Hg
So [tex]30.25inHg=30.25\times 0.4911=14.855775psi[/tex]
So 30.25 in Hg will be equal to 14.855 psi
Explain what is the young's modulus?
Answer and Explanation:
Young's modulus is a mechanical property that estimates the solidness of a strong material. If we have information about stress and strain the we can easily found the young's modulus.
Young's modulus gives us information that how hard or how easy to bend a solid material
Young's modulus is given by [tex]young's\ modulus=\frac{stress}{strain}[/tex]
Stress = [tex]\frac{force}{area}[/tex] and strain is [tex]=\frac{chane\ in\ length}{actual\ length}=\frac{\Delta L}{L}[/tex]
Air enters an adiabatic turbine at 800 kPa and 870 K with a velocity of 60 m/s, and leaves at 120 kPa and 520 K with a velocity of 100 m / s. The inlet area of the turbine is 90 cm2. What is the power output?
Answer:
The power output of the turbine is 603 KW.
Explanation:
Turbine is the thermodynamic open system in which fluid looses thermal energy into kinetic energy. Kinetic energy then converted into electric energy.
Here, fluid is air which passes through turbine at 800 Kpa and 870 K with a velocity of 60 m/s.
The turbine is an adiabatic turbine that means there is no heat transfer from the surrounding. Finally the air leaves the turbine at 120 Kpa and 520 K with a velocity of 100 m/s. The turbine inlet area is 90 cm2
Given:
Inlet pressure is [tex]P_{1}=800[/tex]kpa.
Inlet temperature is [tex]T_{1}=870[/tex]K.
Inlet velocity is[tex]V_{1}=60[/tex] m/s.
Outlet pressure is [tex]P_{2}=120[/tex]Kpa.
Outlet temperature is [tex]T_{2}=520[/tex]K.
Outlet velocity is [tex]V_{2}=100[/tex] m/s.
Inlet area of turbine is A=90 cm2.
Step1
Convert the area into SI unit as follows:
[tex]A=90 cm^{2}(\frac{1 m^{2}}{10^{4}cm^{2}})[/tex]
[tex]A=0.009 m^{2}[/tex]
Step 2
Consider air as an ideal gas. So, ideal gas equation is applicable. For air, gas constant is 287 j/kgK.
Ideal gas equation is expressed as follows:
[tex]P=\rho RT[/tex]
Here, P is pressure, T is temperature and \rho is density.
Density of air is calculated by ideal gas equation as follows:
[tex]\rho =\frac{P}{RT}[/tex]
[tex]\rho =\frac{800\times 10^{3}}{287\times870}[/tex]
[tex]\rho =3.2039 kg/m^{3}[/tex]
Step 3
Mass flow rate is calculated as follows:
[tex]\dot{m}=\rho AV_{1}[/tex]
[tex]\dot{m}=3.2039\times 0.009\times60[/tex]
[tex]\dot{m}=1.73 Kg/s[/tex]
Step 4
Steady state equation is the equation of first law of thermodynamics for the open system
Steady state equation for the turbine as follows:
[tex]h_{1}+\frac{v^{2}_{1}}{2000}+Z_{1}+Q=h_{2}+\frac{v^{2}_{2}}{2000}+Z_{2}+W[/tex]
Heat transfer is zero as the process is adiabatic. So value of Q is zero.
Turbine is taken as at the same level. So the value of [tex]Z_{1}[/tex] is equal to [tex]Z_{2}[/tex].
Substitute the value of Q as zero and tex]Z_{1}[/tex] is equal to [tex]Z_{2}[/tex] in steady state equation as follows:
[tex]h_{1}+\frac{v^{2}_{1}}{2}+Z_{1}+0=h_{2}+\frac{v^{2}_{2}}{2}+Z_{1}+W[/tex]
[tex]h_{1}+\frac{v^{2}_{1}}{2}+0=h_{2}+\frac{v^{2}_{2}}{2}+W[/tex]
[tex]W=(h_{1}-h_{2})+\frac{v^{2}_{1}-v^{2}_{2}}{2000}[/tex]
[tex]W=c_{p}(T_{1}-T_{2})+\frac{60^{2}-100^{2}}{2000}[/tex]
Specific heat at constant pressure is 1.005 kj/kgK for air.
Substitute the values of temperature and specific heat at constant temperature in the above simplified steady state equation as follows:
W=1.005(870-520)-3.2
W=351.75-3.2
W=348.55 Kj/kg.
Step 5
Power of the turbine is calculated as follows:
[tex]P=\dot{m}W[/tex]
[tex]P=1.73\times348.55[/tex]
P=603 KW
Thus, the power output of the turbine is 603 KW.
How is the principle of superposition used to determine the stress state for a combined loading?
Answer with Explanation:
For a linearly responsive system principle of superposition states that
"The cumulative response of the given system to forces of different magnitudes is the sum of the individual responses of the system to the individual forces"
In a less formal manner principle of superposition states that the effect of various forces acting together on any body is the sum of all the effects on the body produced when each force acts individually.
Now we know that
[tex]Stress=\frac{Force}{Area}[/tex]
Since stress at any point is in linear relation with the force hence we can conclude that the state of stress at any point due to different forces acting together is the sum of the individual stresses due to individual forces alone.
Mathematically
Let the stress due to a force [tex]F_i[/tex] be [tex]\sigma _i[/tex]
and the stress due to combined forces be [tex]\sigma _f[/tex]
thus according to principle of superposition we have
[tex]\sigma_f=\sum_{i=1}^{n}(\sigma_i)[/tex]
You are asked to build a digital logic circuit for a security alarm system. The system has four Motion Sensors which indicate the presence of an intruder. Each individual motion sensor should be able to trigger an alarm. The system should be completely disabled via a Master Switch. In addition, the siren, the lights and the automated call to the security company should have separate enable switches. The inputs and outputs are specified as follows:Inputs:S1, S2, S3, S4 : Motion Sensors (0 = no intrusion detected, 1 = intrusion detected)M : Master Switch (0 = security system disabled, 1 = security system enabled)A : Siren Enable Switch (0 = siren disabled, 1 = siren enabled)L : Light Enable Switch (0 = flashing light disabled, 1 = flashing light enabled)P : Phone Call Enable Switch (0 = call disabled, 1 = call enabled)Outputs:B : Buzzing SirenF : Flashing LightC : Call BoxDraw the logic circuit diagram of the digital logic using multi-input AND/OR/NOT gates.
Designing the digital logic circuit for a security alarm involves using AND, OR, and NOT gates to allow any motion sensor to trigger the system, with a master switch for overall control and separate switches for the siren, lights, and automated call.
Explanation:The question involves designing a digital logic circuit for a security alarm system with specific inputs and outputs. To achieve this configuration, one needs to employ AND, OR, and NOT gates to process signals from four motion sensors, a master switch, and individual enable switches for the siren, lights, and call function. The logic for this system requires that any motion sensor can trigger an alarm if the system is enabled, and each output (siren, lights, call) is individually controllable. Given the complexity of drawing a circuit diagram in text format, it's important to visualize the circuit as starting with OR gates to combine signals from the four motion sensors. These signals then pass through an AND gate along with the master switch to ensure the system is enabled. The outputs of this gate would then be directed to three separate AND gates, each also receiving input from their respective enable switch (for the siren, lights, and call functions). NOT gates may be used where necessary to invert signals, particularly for the enable/disable logic.
The rate of flow of water in a pump installation is 60.6 kg/s. The intake static gage is 1.22 m below the pump centreline and reads 68.95 kPa gage;the discharge static gage is 0.61 m below the pump centre line and reads 344.75 kPagage. The gages are located close to the pump as much as possible. The area of the intake and discharge pipes are; 0.093 m2 and 0.069 m2 respectively. The pump efficiency is 74%. Take density of water equals 1000 kg/m3. What is the hydraulic power in kW
Answer:
Pump power is 23.09 kW
Explanation:
Data
gravitational constant, [tex] g = 9.81 m/s^2 [/tex]
mass flow, [tex] \dot{m} = 60.6 kg/s [/tex]
flow density, [tex] \rho = 1000 kg/m^3 [/tex]
pump efficiency, [tex] \eta = 0.74 [/tex]
output gage pressure, [tex] p_o = 344.75 kPa [/tex]
input gage pressure, [tex] p_i = 68.95 kPa [/tex]
output pipe area, [tex] A_o = 0.069 m^2 [/tex]
input pipe area, [tex] A_i = 0.093 m^2 [/tex]
output height, [tex] z_o = 1.22 m - 0.61 m = 0.61 m [/tex] (considering that pump is at the maximum height, i.e., 1.22 m)
input height, [tex] z_i = 0 m [/tex]
pump hydraulic power,[tex] P = ? kW [/tex]
First of all, volumetric flow (Q) must be computed
[tex] Q = \frac{\dot{m}}{\rho}[/tex]
[tex] Q = \frac{60.6 kg/s}{1000 kg/m^3} [/tex]
[tex] Q = 0.0606 m^3/s[/tex]
Then, velocity (v) must be computed for both input and output
[tex] v_o = \frac{Q}{A_o}[/tex]
[tex] v_o = \frac{0.0606 m^3/s}{0.069 m^2}[/tex]
[tex] v_o = 0.88 m/s [/tex]
[tex] v_i = \frac{Q}{A_i}[/tex]
[tex] v_i = \frac{0.0606 m^3/s}{0.093 m^2}[/tex]
[tex] v_i = 0.65 m/s [/tex]
Now, total head (H) can be calculated
[tex] H = (z_o - z_i) + \frac{v_o^2 - v_i^2}{2 \, g} + \frac{p_o - p_i}{\rho \, g} [/tex]
[tex] H = (0.61 m - 0 m) + \frac{{0.88 m/s}^2 - {0.65 m/s}^2}{2 \, 9.81 m/s^2} + \frac{(344.75 Pa-68.95 Pa)\times 10^3}{1000 kg/m^3 \, 9.81 m/s^2} [/tex]
[tex] H = 28.74m [/tex]
Finally, pump power is computed as
[tex] P = \frac{Q \, \rho \, g \, H}{\eta}[/tex]
[tex] P = \frac{0.0606 m^3/s \, 1000 kg/m^3 \, 9.81 m/s^2 \, 28.74m}{0.74}[/tex]
[tex] P = 23.09 kW [/tex]
The hydraulic power in kW is mathematically given as
P = 23.09 kW
What is the hydraulic power?Generally the equation for the volumetric flow (Q) is mathematically given as
Q=m/p
Therefore
Q=60/1000
Q=0.0606
Generally the equation for the velocity (v) is mathematically given as
v=Q/A
Hence for input
[tex]v_i = \frac{Q}{A_i}\\\\v_i = \frac{0.0606 }{0.093 }[/tex]
v_i = 0.65 m/s
For input
[tex]v_o = \frac{Q}{A_o}\\\\v_o = \frac{0.0606 }{0.069}[/tex]
v_o = 0.88 m/s
Therefore, Total head (H)
[tex]H = (z_o - z_i) + \frac{v_o^2 - v_i^2}{2 \, g} + \frac{p_o - p_i}{\mu g}[/tex]
[tex]H = (0.61 0 ) + \frac{{0.88 }^2 - {0.65 }^}{2 *9.81 } + \frac{(344.75 Pa-68.95 Pa)*10^3}{1000* 9.81}[/tex]
H = 28.74m
Generally the equation for the pump power P is mathematically given as
[tex]P = \frac{Q * \rho*g*H}{\eta}[/tex]
[tex]P = \frac{0.0606 * 100*9.81*28.74}{0.74}[/tex]
P = 23.09 kW
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https://brainly.com/question/10203153
(a) Determine the dose (in mg/kg-day) for a bioaccumulative chemical with BCF = 103 that is found in water at a concentration of 0.1 mg/L. Calculate your dose for a 50 kg adult female who drinks 2 L lake water per day and consumes 30 g fish per day that is caught from the lake. Ans. 0.064 mg/kg-d (b) What percent of the total dose is from exposure to the water, and what percent is from exposure to the fish?
Answer:
0.064 mg/kg/day
6.25% from water, 93.75% from fish
Explanation:
Density of water is 1 kg/L, so the concentration of the chemical in the water is 0.1 mg/kg.
The BCF = 10³, so the concentration of the chemical in the fish is:
10³ = x / (0.1 mg/kg)
x = 100 mg/kg
For 2 L of water and 30 g of fish:
2 kg × 0.1 mg/kg = 0.2 mg
0.030 kg × 100 mg/kg = 3 mg
The total daily intake is 3.2 mg. Divided by the woman's mass of 50 kg, the dosage is:
(3.2 mg/day) / (50 kg) = 0.064 mg/kg/day
b) The percent from the water is:
0.2 mg / 3.2 mg = 6.25%
And the percent from the fish is:
3 mg / 3.2 mg = 93.75%
Determine if the following errors are systematic or random. Justify your response. (a) Effect of temperature on the circuitry of an electronic measurement device. (b) Effect of parallax on the reading of a needle-type analog voltmeter. (c) Effect of using an incorrect value of emissivity in the readings of an infrared thermometer.
Answer:
a) temperature: random error
b) parallax: systematic error
c) using incorrect value: systematic error
Explanation:
Systematic errors are associated with faulty calibration or reading of the equipments used and they could be avoided refining your method.