Answer:
The correct answer is option 'b':0.25
Explanation:
By definition of strain we have
[tex]\epsilon =\frac{L_f-L_o}{L_o}[/tex]
where
[tex]\epsilon [/tex] is the strain
[tex]L_o[/tex] is the original length of specimen
[tex]L_f[/tex] is the elongated length of specimen
Applying the given values we get
[tex]\epsilon =\frac{12.5''-10''}{10''}=0.25[/tex]
Solar energy is the most widely available renewable energy source and it is sufficient to meet entire needs of the world. However, it is not used extensively. Why?
Answer:
Explanation:
Solar energy is one of the Renewable sources of energy and it is sufficient to meet the entire needs of the world.
But it is not used extensively because of the inconsistency. Inconsistency means that sun rays are not consistent throughout the year. If the weather is not good or in winters earth does not receive sun rays continuously.
And another reason to not to set up solar energy is that it is very expensive not everyone can afford it.
An engineer measures a sample of 1200 shafts out of a certain shipment. He finds the shafts have an average diameter of 2.45 inch and a standard deviation of 0.07 inch. Assume that the shaft diameter follows a Gaussian distribution. What percentage of the diameter of the total shipment of shafts will fall between 2.39inch and 2.60 inch?
Answer: 78.89%
Explanation:
Given : Sample size : n= 1200
Sample mean : [tex]\overline{x}=2.45 [/tex]
Standard deviation : [tex]\sigma=0.07[/tex]
We assume that it follows Gaussian distribution (Normal distribution).
Let x be a random variable that represents the shaft diameter.
Using formula, [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-value corresponds to 2.39 will be :-
[tex]z=\dfrac{2.39-2.45}{0.07}\approx-0.86[/tex]
z-value corresponds to 2.60 will be :-
[tex]z=\dfrac{2.60-2.45}{0.07}\approx2.14[/tex]
Using the standard normal table for z, we have
P-value = [tex]P(-0.86<z<2.14)=P(z<2.14)-P(z<-0.86)[/tex]
[tex]=P(z<2.14)-(1-P(z<0.86))=P(z<2.14)-1+P(z<0.86)\\\\=0.9838226-1+0.8051054\\\\=0.788928\approx0.7889=78.89\%[/tex]
Hence, the percentage of the diameter of the total shipment of shafts will fall between 2.39 inch and 2.60 inch = 78.89%
The condition of irrotationality for a two-dimensional flow is satisfied when rotation w everywhere is (less than — equal to — more than) zero.
Answer:
Zero.
Explanation:
Lets take velocity V is given as in 2 dimensional flow
V=u i +v j
V=f(x,y)
u=f(x,y)
v=f(x,y)
Rotational ability ω given as
[tex]\omega =\dfrac{1}{2}\left (\dfrac{\partial v}{\partial x}-\dfrac{\partial u} {\partial x}\right)[/tex]
If
ω=0 ,then flow will be irrotational.
ω ≠0 ,then flow will be rotational.
So we can say that , ω will be zero every where for irrotational two dimensional flow .
The horizontal component of acceleration, ay during a projectile motion is usually assumed to be_________ a)-9.81 m/s^2 b)-Zero c)- Constant d)- 32.2 m/s^2
Answer:
b) zero
Explanation:
The horizontal component of acceleration during projectile motion is usually assumed to be zero.Because in projectile motion horizontal component of velocity will remain the constant and we know that rate of change of velocity with time is called acceleration.So when velocity is constant then acceleration will be zero.
In projectile motion ,gravitational acceleration will be in only vertical direction.
What is the movement of the piston from top dead center (TDC) to bottom dead center (BDC) called?
Answer:
Piston movement of TDC to BDC is called stroke.
Explanation:
Step1
In any engine fuel is burned inside the cylinder and forces the piston to move from top dead center to bottom dead center. First piston is moved from top dead center to bottom dead center to allow the suction of fuel inside the cylinder. Then piston move toward top dead center and compresses the fuel. This process is called compression of fuel. Then fuel is burned with the spark inside the cylinder and the piston moves toward bottom dead center. This process is called expansion process. Last process is the expansion process that allows the exhaust out of the cylinder.
Step2
The piston reciprocates from bottom position of the cylinder to top position of the cylinder and vice versa. So, the motion of piston from top center to bottom center is called stroke. One movement of piston from TDC to BDC is called one stroke. There are total four strokes in petrol engine and diesel engine. So, two strokes are equal to one cycle or one rotation of crank and four strokes are equal to two rotation of crank.
Thus, piston movement of TDC to BDC is called stroke.
Answer:
The return stroke
Explanation:
Motion from top dead center to bottom dead center is called the return stroke because motion from the bottom to the top is the forward stroke.
The Reynolds number is a dimensionless group defined for a fluid flowing in a pipe as Re Durho/μ whereD is pipe diameter, u is fluid velocity, rho is fluid density, and μ is fluid viscosity.When the value of the Reynolds number is less than about 2100, the flow is laminar—that is, the fluid flows in smooth streamlines. For Reynolds numbers above 2100, the flow is turbulent, characterized by a great deal of agitation. Liquid methyl ethyl ketone (MEK) flows through a pipe with an inner diameter of 2.067 inches at an average velocity of 0.48 ft/s. At the fluid temperature of 20°C the density of liquid MEK is 0.805 g/cm3 and the viscosity is 0.43 centipoise [1 cP 1:00 103 kg/ m s]. Without using a calculator, determine whether the flow is laminar or turbulent. Show your calculations.
The Reynolds number is approximately 14,067, indicating turbulent flow of MEK through the pipe, as Re > 2100 denotes turbulence.
let's calculate the Reynolds number for the flow of liquid methyl ethyl ketone (MEK) through the pipe.
Given:
- Pipe diameter (D) = 2.067 inches = 0.0512 meters (converted from inches to meters)
- Fluid velocity (u) = 0.48 ft/s = 0.1463 meters/s (converted from feet per second to meters per second)
- Fluid density (ρ) = 0.805 g/cm³ = 805 kg/m³ (converted from grams per cubic centimeter to kilograms per cubic meter)
- Fluid viscosity (μ) = 0.43 centipoise = 0.43 x 10² kg/(m*s)(converted from centipoise to kg/(m*s))
The Reynolds number (Re) is calculated as:
[tex]\[ Re = \frac{(D \cdot u \cdot \rho)}{\mu} \][/tex]
Plugging in the values:
[tex]\[ Re = \frac{(0.0512 \, \text{m} \cdot 0.1463 \, \text{m/s} \cdot 805 \, \text{kg/m³})}{0.43 \times 10^{-3} \, \text{kg/(m*s)}} \][/tex]
[tex]\[\text{Re} = \frac{(0.0074991 \, \text{m}^2/\text{s}^2 \cdot 805 \, \text{kg/m}^3)}{0.43 \times 10^{-3} \, \text{kg/(m*s)}}\]\[\text{Re} = \frac{6.0498755 \, \text{kg/(m*s)}}{0.43 \times 10^{-3} \, \text{kg/(m*s)}}\]\[\text{Re} \approx \frac{6.0498755}{0.00043}\]\[\text{Re} \approx 14,067.35\][/tex]
Since the calculated Reynolds number is greater than 2100 (Re > 2100), the flow of MEK through the pipe is turbulent.
The energy conversion that takes place in an evaporative cooler is: a. thermal energy to chemical energy b. thermal energy to heat c. cooling of thermal energy d. heat energy to mechanical energy
Answer:
C.Cooling of thermal energy
Explanation:
In evaporative cooling liquid water convert into vapor by using thermal energy.In this out side air is used to evaporate the water.
Hot air enters from outside and this hot air gets contact with wet matrix .In wet matrix temperature of air will reduce and temperature of water will increases .After wet matrix heat transfer take place between air and water .After that by using force convection air pushed out and produce cooling.
The thermal conductivity of a sheet of rigid, extruded insulation is reported to be k= 0.029 W/ m K. The measured temperature difference across a 25-mm-thick sheet of the material is T1 - T2 = 12°C. a. What is the heat flux through a 3 mx 3 m sheet of the insulation? b. What is the rate of heat transfer through the sheet of insulation? c. What is the thermal resistance of the sheet due to conduction?
Answer:
a. The heat flux through the sheet of insulation is 19.92 W/m^2
b. The rate of heat transfer through the sheet of insulation is 125.28 W
c. The thermal resistance of the sheet due to the conduction is 0.86 Km^2/W.
Explanation:
From the heat conduction Fourier's law it can be state for a wall of width e and area A :
q = Q/ΔT = k*A* (T2-T1)/e
Where q is the rate of heat transfer, k the conductivity constant, and T2 and T1 the temperatures on the sides of the wall. Replacing the values in the correct units, we obtained the rate of heat transfer:
q = 0.029 W/*mK * (3m*3m) * (12°K) / (0.025m)
(The difference in temperatures in Kelvin is the same than in Celcius degres).
q = 0.029 W/*mK * (9 m^2) * (12°K) / (0.025m) = 125.28 W
The heat flux is calculated by dividing q by the area of the wall:
q/A = k* (T2-T1)/e = 0.029 W/*mK * (12°K) / (0.025m) = 19.92 W/m^2
The thermal resistance of the sheet is defined as:
R = e / k
Replacing the values in the proper units:
R = 0.025 m / 0.029 W/*mK = 0.86 Km^2/W
A car starts out from rest (zero velocity) at an elevation of 500 m and drives up a hill to reach a final elevation of 2000m and a final velocity of 20 m/s. At the same time the entire car heats up so the Internal Energy of the car increases by 100 kJ. What is the total energy change of the car if its mass is 2000 kg?
Answer:29,930 kJ
Explanation:
Given
Car starts with an initial elevation of 500 m and drives up a hill to reach a final elevation of 2000 m
Final velocity (V)=20 m/s
Energy of car increases by 100 kJ
mass of car(m)=2000 kg
[tex]Total Energy =\Delta PE+\Delta KE+\Delta U[/tex]
[tex]\Delta PE=mg(\Delta h)=2000\times 9.81\times (2000-500)[/tex]
[tex]\Delta PE=29,430 kJ[/tex]
[tex]\Delta KE=m\frac{v_2^2-v_1^2}{2}[/tex]
[tex]\Delta KE=2000\times \frac{20^2-0^2}{2}[/tex]
[tex]\Delta KE=400 kJ[/tex]
[tex]\Delta U=100 kJ[/tex]
Total Energy=29,430+400+100=29,930 kJ
Ignoring any losses, estimate how much energy (in units of Btu) is required to raise the temperature of water in a 90-gallon hot-water tank from 60°F to 110°F. The specific heat of water is approximated as a constant, whose value is 0.999 Btu/·lbmR at the average temperature of (60 + 110)/2 = 85ºF. In fact, c remains constant at 0.999 Btu/lbm·R (to three digits) from 60ºF to 110ºF. For this same temperature range, the density varies from 62.36 lbm/ft3 at 60ºF to 61.86 lbm/ft3 at 110ºF. We approximate the density as remaining constant, whose value is 62.17 lbm/ft3 at the average temperature of 85ºF.
Answer:
Q=36444.11 Btu
Explanation:
Given that
Initial temperature = 60° F
Final temperature = 110° F
Specific heat of water = 0.999 Btu/lbm.R
Volume of water = 90 gallon
Mass = Volume x density
[tex]1\ gallon = 0.13ft^3[/tex]
Mass ,m= 90 x 0.13 x 62.36 lbm
m=729.62 lbm
We know that sensible heat given as
Q= m Cp ΔT
Now by putting the values
Q= 729.62 x 0.999 x (110-60) Btu
Q=36444.11 Btu
I have a 500 L tank that can hold a fluid. How much heavier or lighter will the tank be if a. The tank holds water at 80C compared to if the water tank holds 5C water? b. The tank holds air at 80C compared to if the water tank holds 5C air? Assume the tank is vented in a way that the pressure remains at atmospheric pressure, given as 101.3 KPa.
Answer:
water=14.1 kg
air=0.1348kg
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 such as pressure and temperature.
To solve this exercise we must find the specific volume of water and air in the two states and then subtract them and multiply them by the volume of the tank to find the change in mass, the following equation is inferred
Δm=V(ρ2-ρ1)
Where V= tank volume=500L=0.5m^3
ρ2= density of fluid in state 2
ρ1=density of fluid in state 1
Δm=change of mass
for water
ρ1=971.8kg/m^3(80C)
ρ2=1000kg/m^3(5C)
Δm=0.5(1000-971.8)
Δm=14.1 kg
for air
ρ1=0.9994kg/m^3(80C)
ρ2=1.269kg/m^3(5C)
Δm=0.5(1.269-0.9994)
Δm=0.1348kg
Please define the coefficient of thermal expansion?
Answer:
The coefficient of thermal expansion tells us how much a material can expand due to heat.
Explanation:
Thermal expansion occurs when a material is subjected to heat and changes it's shape, area and volume as a result of that heat. How much that material changes is dependent on it's coefficient of thermal expansion.
Different materials have different coefficients of thermal expansion (i.e. It is a material property and differs from one material to the next). It is important to understand how materials behave when heated, especially for engineering applications when a change in dimension might pose a problem or risk (eg. building large structures).
Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) 354 mg (45 km) / (0.0356 kN), (b) (0.00453 Mg) (201 ms), and (c) 435 MN/23.2 mm.
The question requires calculating expressions using metric units and prefixes, converting them into SI units with appropriate prefixes, and ensuring these calculations are accurate to three significant figures.
Explanation:The question involves evaluating expressions with different units and converting them to SI units with appropriate prefixes, which requires a good understanding of metric prefixes and significant figures. Furthermore, examples of such conversions are provided to aid in this process.
Evaluations with SI Units and PrefixesFor part (a), you convert milligrams to kilograms, kilometers to meters, and kilonewtons to newtons, then perform the division ensuring that the answer is to three significant figures.For part (b), convert megagrams to kilograms and multiply by the given number of seconds, again reporting the answer to three significant figures.For part (c), convert meganewtons to newtons and millimeters to meters, divide, and round to three significant figures.Each conversion is an exercise in carefully applying metric prefixes and understanding how to manipulate them within calculations.
Describe the cartesain coordinate system.
Answer:
Cartesian coordinate system is used to specify any point on a plane.
In two dimensional plane,the two types of axes or coordinates are [tex]x[/tex] and [tex]y[/tex] axis.
Explanation:
Cartesian coordinate system specifies each point and every point on axes.
A Cartesian Coordinate system in two dimension also named as rectangular coordinate system.
The two types of axes or coordinates are [tex]x[/tex] and [tex]y[/tex] axis.
The horizontal axis is [tex]x[/tex]-axis and vertical axis is named as [tex]y[/tex]-axis.
The coordinate system specifies each point as a set of numerical coordinates in a plane which are signed from negative to positive. that is from ([tex]-\infty[/tex],[tex]\infty[/tex]).
In three dimensional plane, [tex]x[/tex], [tex]y[/tex] and [tex]z[/tex] coordinates are used and in two dimensional plane, [tex]x[/tex] and [tex]y[/tex]coordinates are used to address any point in the interval ([tex]-\infty[/tex],[tex]\infty[/tex]).
For defining both the coordinates, the two perpendicular directed lines [tex]x[/tex]- axis and [tex]x[/tex]-axis are drawn.
Now, for example [tex](3,4)[/tex] is a point in which indicates that the value of [tex]x[/tex] is [tex]3[/tex] and [tex]y[/tex] is [tex]4[/tex].
It is drawn by moving [tex]3[/tex] units right from the origin to positive [tex]x[/tex] axis and [tex]4[/tex] units upwards from the origin [tex](0,0)[/tex] to positive [tex]y[/tex]-axis.
Air is compressed slowly in a piston-cylinder assembly from an initial state where P1 = 1.4 bar, V1= 4.25 m^3, to a final state where P2= 6.8 bar. During the process, the relation between pressure and volume follows pv= constant. For the air as the closed system, determine the work, in kJ
Answer:
W=-940.36 KJ
Explanation:
Given that
[tex]P_1=1\ bar,V_1=4.25 {m^3}[/tex]
[tex]P_2=6.8\ bar[/tex]
Process follows pv=constant
So this is the isothermal process and work in isothermal process given as
[tex]W=P_1V_1\ln \dfrac{P_1}{P_2}[/tex]
Now by putting the values (1.4 bar =140 KPa)
[tex]W=P_1V_1\ln \dfrac{P_1}{P_2}[/tex]
[tex]W=140\times 4.25 \ln \dfrac{1.4}{6.8}[/tex]
W=-940.36 KJ
Negative sign indicates that this is a compression process and work will given to the system.
What is meant by the thickness to chord ratio of an aerofoil?
Answer:
Chord ratio:
It is the ratio of thickness to the chord.It is also knows as thickness ratio.
Chord ratio measure the performance of wing when it is operating at the transonic speed.
When the speed cross the speed of sound wave then that wave creates the shock wave and these shock leads to produce drag force on the aerofoil profile.When Mach number is one then it means that if Mach increase then it will leads increase then drag force.
When a 20-lb weight is suspended from a spring, the spring is stretched a distance of 1 in. Determine the natural frequency and the period of vibration for a 30-lb weight attached to the same spring
Answer:
natural frequency = 2.55 Hz
period of vibration = 0.3915 s
Explanation:
given data
weight = 20 lb
distance = 1 in = [tex]\frac{1}{12}[/tex] ft
weight = 30 lb
to find out
Determine the natural frequency and the period of vibration
solution
we first calculate here stiffness k by given formula that is
k = [tex]\frac{weight}{diatnace}[/tex] ..........1
k = [tex]\frac{20}{1/12}[/tex]
k = 240 lb/ft
so
frequency = [tex]\sqrt{\frac{k}{m} }[/tex] ..................2
put here value k and mass m = [tex]\frac{weight}{g}[/tex]
frequency = [tex]\sqrt{\frac{240}{30/32.2} }[/tex]
frequency = 16.05 rad/s
and
period of vibration = [tex]\frac{2* \pi }{frequency}[/tex]
period of vibration = [tex]\frac{2* \pi }{16.05}[/tex]
period of vibration = 0.3915 s
and
natural frequency = [tex]\frac{1 }{period of vibration}[/tex]
natural frequency = [tex]\frac{1 }{0.3915}[/tex]
natural frequency = 2.55 Hz
A galvanometer has a coil with a resistance of 24.0 Ω, and a current of 180 μA causes it to deflect full scale. If this galvanometer is to be used to construct an ammeter that can read up to 10.0 A, what shunt resistor is required? A galvanometer has a coil with a resistance of 24.0 , and a current of 180 μA causes it to deflect full scale. If this galvanometer is to be used to construct an ammeter that can read up to 10.0 A, what shunt resistor is required? 234 µΩ 123 µΩ 342 µΩ 423 µΩ 432 µΩ
Answer:
shunt resistor is 432µΩ
correct option is 432µΩ
Explanation:
given data
resistance R = 24.0 Ω
full scale deflection current Ig = 180 μA
galvanometer current I = 10.0 A
to find out
what shunt resistor is required
solution
we will apply here full scale deflection current formula that is
Ig = I × [tex]\frac{r}{r + R}[/tex] ...............1
here r is shunt current and R is resistance and I is galvanometer
put here all value
180 × [tex]10^{-6}[/tex] = 10 × [tex]\frac{r}{r + 24}[/tex]
r = 18 × [tex]10^{-6}[/tex] × 24
r = 432 × [tex]10^{-6}[/tex] Ω
so shunt resistor is 432µΩ
correct option is 432µΩ
Shunt resistor required for 10.0 A ammeter: approximately 432 μΩ.
To construct an ammeter using a galvanometer, a shunt resistor is connected in parallel to the galvanometer. The shunt resistor diverts most of the current, allowing only a fraction of the current to pass through the galvanometer, thus enabling it to measure higher currents.
The relationship between the current passing through the galvanometer and the shunt resistor can be expressed using the formula:
[tex]\[I_{\text{total}} = I_{\text{g}} + I_{\text{s}}\][/tex]
Where:
[tex]- \(I_{\text{total}}\)[/tex] is the total current (10.0 A)
[tex]- \(I_{\text{g}}\)[/tex] is the current passing through the galvanometer (180 μA)
[tex]- \(I_{\text{s}}\)[/tex] is the current passing through the shunt resistor
Given that the galvanometer resistance [tex]\(R_{\text{g}} = 24.0 Ω\)[/tex] and full-scale deflection current \[tex](I_{\text{g}} = 180 μA\),[/tex] we can calculate the shunt resistance required using Ohm's Law:
[tex]\[I_{\text{g}} = \frac{V_{\text{g}}}{R_{\text{g}}}\][/tex]
Where:
- [tex]\(V_{\text{g}}\)[/tex] is the voltage across the galvanometer
Since the galvanometer is designed to deflect full-scale at 180 μA, the voltage across it is:
[tex]\[V_{\text{g}} = I_{\text{g}} \times R_{\text{g}}\]\[V_{\text{g}} = (180 \times 10^{-6}) \times 24\]\[V_{\text{g}} = 0.00432 \, \text{V}\][/tex]
The current passing through the shunt resistor can be calculated using:
[tex]\[I_{\text{s}} = \frac{V_{\text{total}}}{R_{\text{s}}}\][/tex]
Since the total current is 10.0 A and the voltage across the shunt resistor is the same as the voltage across the galvanometer (as they are in parallel), we have:
[tex]\[I_{\text{s}} = \frac{10.0}{R_{\text{s}}}\][/tex]
Now, the total current equals the sum of the currents through the galvanometer and shunt resistor:
[tex]\[10.0 = 180 \times 10^{-6} + \frac{0.00432}{R_{\text{s}}}\][/tex]
Solving for [tex]\(R_{\text{s}}\):[/tex]
[tex]\[R_{\text{s}} = \frac{0.00432}{10.0 - 180 \times 10^{-6}}\]\[R_{\text{s}} ≈ \frac{0.00432}{10.0}\]\[R_{\text{s}} ≈ 432 \, \text{μΩ}\][/tex]
So, the required shunt resistor is approximately 432 μΩ. Therefore, the closest answer is 432 μΩ.
Polymers can be natural or synthetic. a)-True b)- false?
Answer:
TRUE
Explanation:
Polymers can be natural as well as synthetic
The polymer which are found in nature are called natural polymer tease polymer are not synthesized, they are found in nature
Example of natural polymers is cellulose, proteins etc
On the other hand synthetic polymers are not found in nature they are synthesized in market
There are many example of synthetic polymer
Example : nylon, Teflon etc
So it is a true statement
A storage tank, used in a fermentation process, is to be rotationally molded from polyethylene plastic. This tank will have a conical section at the bottom, right circular cylindrical mid-section and a hemispherical dome to cover the top. The radius of the tank is 1.5 m, the cylindrical side-walls will be 4.0 m in height, and the apex of the conic section at the bottom has an included angle of 60°. If the tank is filled to the top of the cylindrical side-walls, what is the tank capacity in liters?
Answer:
The volume up to cylindrical portion is approx 32355 liters.
Explanation:
The tank is shown in the attached figure below
The volume of the whole tank is is sum of the following volumes
1) Hemisphere top
Volume of hemispherical top of radius 'r' is
[tex]V_{hem}=\frac{2}{3}\pi r^3[/tex]
2) Cylindrical Middle section
Volume of cylindrical middle portion of radius 'r' and height 'h'
[tex]V_{cyl}=\pi r^2\cdot h[/tex]
3) Conical bottom
Volume of conical bottom of radius'r' and angle [tex]\theta [/tex] is
[tex]V_{cone}=\frac{1}{3}\pi r^3\times \frac{1}{tan(\frac{\theta }{2})}[/tex]
Applying the given values we obtain the volume of the container up to cylinder is
[tex]V=\pi 1.5^2\times 4.0+\frac{1}{3}\times \frac{\pi 1.5^{3}}{tan30}=32.355m^{3}[/tex]
Hence the capacity in liters is [tex]V=32.355\times 1000=32355Liters[/tex]
Sketch the velocity profile for laminar and turbulent flow.
Answer:
The laminar flow is generally given in high viscosity fluids such as honey or oil, it has the characteristic of flowing in an orderly manner, the walls of the tube have a zero speed while in the center it has a maximum speed.
turbulent flow is characterized by fluid velocity vectors presenting themselves in a disorderly manner and in all directions.
I attached the drawings for the velocity profile in laminar and turbulent flow.
The Danner process is used to make glass_____
Answer:
The Danner process is used to make glass tubes
Explanation:
In this process the molten glass passes from the feeder to a hollow ceramic cylinder that is tilted downward, so that the molten glass can "run"; This ceramic cylinder is spinning constantly.
As the molten glass passes through the Danner tube, compressed air is blown to prevent the glass from being damaged. On the opposite side of the feeder, i.e, on the other side of the tube a bubble is also formed so-called drawing onion, the glass tube is removed in a free buckling in a traction line from the onion.
When the stretching speed remains constant and an increase in the blowing pressure occurs, larger tube diameters are created and the wall thickness decreases.
This process allows tube diameters between 2 and 60 mm.
This is how glass bottles are made.
A steam piston system is heated by 72 Btu of heat. 7 Btu of heat is lost to the environment. The piston does 12 Btu of work as it rises. What is the change in the energy of the water steam in the system?
Answer:
ΔU = 53 BTU
Explanation:
In thermodynamics we consider heat entering a system as positive and heat leaving as negative.
Also, work performed by the system is positive and work applied to the system is negative.
The total heat applied to the system is:
Q = 72 - 7 = 65 BTU
The work is:
L = 12 BTU
The first law of thermodynamics states that:
Q = L + ΔU
Where ΔU is the change in internal energy.
Rearranging:
ΔU = Q - L
ΔU = 65 - 12 = 53 BTU
For a motor purchased for a tank project, it claims that at 12V it produces 6000 RPM. This motor is attached to a 50:1 gear reduction gearbox. The output of this gearbox is attached to a 2.5" wheel. Determine the speed of the tank under these conditions in miles/hour (mph).
Answer:
0.889 mph
Explanation:
Given:
Voltage = 12 V
RPM produced, N₁ = 6000
Gear reduction gearbox, G = 50:1
Diameter of the wheel = 2.5" = 2.5 × 0.0254 = 0.0635 m
Now,
The output speed = [tex]\frac{N_1}{\textup{G}}=\frac{6000}{50}[/tex] = 120 RPM
Thus,
The speed, v = [tex]\frac{\pi DN_2}{60}[/tex]
on substituting the respective values, we get
v = [tex]\frac{\pi\times0.0635\times120}{60}[/tex]
or
v = 0.39878 m/s
Also,
1 m/s = 2.23 mph
thus,
v = 0.39878 × 2.23 = 0.889 mph
The searchlight on the boat anchored 2000 ft from shore
isturned on the automobile, which is traveling along the
straightroad at a constant speed of 80 ft/s. Determine the
angularrate of rotation of the light when the automobile is r =
3000 ftfrom the boat.
The angular speed of a flywheel rotating at 300 revolutions per minute is calculated by converting revolutions to radians and minutes to seconds, resulting in an angular speed of 10π rad/s.
Explanation:The question asks to determine the angular rate of rotation of a searchlight on a boat when targeting an automobile that is 3000 ft away and moving at 80 ft/s. This involves understanding the relationship between linear velocity, radius, and angular velocity, which is a crucial concept in trigonometry and physics.
To find the angular speed of the flywheel rotating at 300 revolutions per minute, we first convert revolutions per minute (rpm) to radians per second, knowing that one revolution is 2π radians and there are 60 seconds in a minute. Therefore:
Angular speed = 300 rpm × (2π radians/revolution) × (1 minute/60 seconds) = 300 × 2π / 60 rad/s = 10π rad/s.
A power company desires to use groundwater from a hot spring to power a heat engine. If the groundwater is at 95 deg C and the atmosphere is at 20 deg C, what is the maximum power output for a mass flow of 0.2 kg/s? Assume the water is cooled to atmospheric temperature.
Answer:
W = 12.8 KW
Explanation:
given data:
mass flow rate = 0.2 kg/s
Engine recieve heat from ground water at 95 degree ( 368 K) and reject that heat to atmosphere at 20 degree (293K)
we know that maximum possible efficiency is given as
[tex]\eta = 1- \frac{T_L}{T_H}[/tex]
[tex]\eta = 1 - \frac{ 293}{368}[/tex]
[tex]\eta = 0.2038[/tex]
rate of heat transfer is given as
[tex]Q_H = \dot m C_p \Delta T[/tex]
[tex]Q_H = 0.2 * 4.18 8(95 - 20)[/tex]
[tex]Q_H = 62.7 kW[/tex]
Maximuim power is given as
[tex]W = \eta Q_H[/tex]
W = 0.2038 * 62.7
W = 12.8 KW
A 15-mm-diameter steel bar is to be used as a torsion spring. If the torsional stress in the bar is not to exceed 110 MPa when one end is twisted through an angle of 30°, what must be the length of the bar?
Answer:
The length of bar will be 2.82 m
Explanation:
Given that
d= 15 mm
r= 7.5 mm
Shear stress = 110 MPa
θ = 30° (30° = 30° x π/180° =0.523 rad)
θ = 0.523 rad
G for steel
G= 79.3 GPa
We know that
[tex]\dfrac{\tau}{r}=\dfrac{G\theta }{L}[/tex]
[tex]\dfrac{110}{7.5\times 10^{-3}}=\dfrac{79.3\times 10^3\times 0.523 }{L}[/tex]
L= 2. 82 m
The length of bar will be 2.82 m
an aluminum bar 125mm (5in) long and having a square cross section 16.5mm (.65in) on an edge is pulled in tension with a load of 66,700 N (15000lb) and experiences an elongation of .43mm (1.7*10^-2 in ). assuming that the deformation is entirely elastic, calculate the modulus of elasticity of the aluminum.
The modulus of elasticity for the aluminum bar is calculated using the relationship between stress and strain, given by Young's modulus formula. The given values are substituted in the formula to find that the modulus of elasticity for the aluminum is approximately 60 GPa.
Explanation:Calculating the Modulus of Elasticity for Aluminum
To calculate the modulus of elasticity (also known as Young's modulus) for the aluminum bar, we can use the relationship described by Hooke's Law for elastic deformation, where stress is directly proportional to strain. The formula to find Young's modulus (Y) is:
Y = (F \/ A) \/ (\u0394L \/ L0)
Here, F is the force applied, A is the cross-sectional area, \u0394L is the change in length, and L0 is the original length of the bar.
Using the given values:
Force (F) = 66,700 NCross-sectional area (A) = 16.5 mm x 16.5 mm = 272.25 mm2 (or 272.25 x 10-6 m2)Change in length (\u0394L) = 0.43 mm (or 0.43 x 10-3 m)Original length (L0) = 125 mm (or 0.125 m)The calculation is as follows:
Y = (66,700 N / 272.25 x 10-6 m2) / (0.43 x 10-3 m / 0.125 m)
When the calculations are done, we find that the modulus of elasticity for the aluminum bar is approximately 60 GPa (Gigapascals), which is within the typical range for aluminum.
Calculate the modulus of elasticity of aluminum given specific values for force, length, cross-sectional area, and elongation during tension.
Young's modulus is a measure of a material's stiffness and is calculated using the formula: Y = (F * Lo) / (A * AL). Substituting the given values, we can find the modulus of elasticity of aluminum to be approximately 68 GPa.
In an oscillating LC circuit, L ! 25.0 mH and C ! 7.80 mF. At time t 0 the current is 9.20 mA, the charge on the capacitor is 3.80 mC, and the capacitor is charging.What are (a) the total energy in the circuit, (b) the maximum charge on the capacitor, and (c) the maximum current? (d) If the charge on the capacitor is given by q ! Q cos(vt $ f), what is the phase angle f? (e) Suppose the data are the same, except that the capacitor is discharging at t ! 0.What then is f?
Answer:
a) 926 μJ
b) 3.802 mC
c) 8.61 A
d) 0.0721
e) 3.2137
Explanation:
The energy in the inductor is
[tex]El = \frac{1}{2}*L*I^2[/tex]
[tex]El = \frac{1}{2}*25*10^{-3}*(9.2*10^{-3})^2 = 1.06*10^{-6} J = 1.06 \mu J[/tex]
The energy store in a capacitor is
[tex]Ec = \frac{1}{2}*C*V^2[/tex]
The voltage in a capacitor is
V = Q/C
[tex]V = \frac{3.8*10^{-3}}{7.8*10^{-3}} = 0.487 V[/tex]
Therefore:
[tex]Ec = \frac{1}{2}*7.8*10^{-3}*0.487^2 = 9.256*10^{-4} J = 925.6 \mu J[/tex]
The total energy is Et = 925.6 + 1.1 = 926.7 μJ
At a certain point all the energy of the circuit will be in the capacitor, at this point it will have maximum charge
[tex]Ec = \frac{1}{2}*C*V^2[/tex]
V = Q/C
[tex]Ec = \frac{1}{2}*C*(\frac{Q}{C})^2[/tex]
[tex]Ec = \frac{1}{2}*\frac{Q^2}{C}[/tex]
[tex]Q^2 = 2*Ec*C[/tex]
[tex]Q = \sqrt{2*Ec*C}[/tex]
[tex]Q = \sqrt{2*926*10{-6}*7.8*10^{-3}} = 3.802 * 10{-3} C = 3.802 mC[/tex]
When the capacitor is completely empty all the energy will be in the inductor and current will be maximum
[tex]El = \frac{1}{2}*L*I^2[/tex]
[tex]I^2 = 2*\frac{El}{L}[/tex]
[tex]I = \sqrt{2*\frac{El}{L}}[/tex]
[tex]I = \sqrt{2*\frac{926.7*10^{-3}}{25*10^{-3}}} = 8.61 A[/tex]
At t = 0 the capacitor has a charge of 3.8 mC, the maximum charge is 3.81 mC
q = Q * cos(vt + f)
q(0) = Q * cos(v*0 + f)
3.8 = 3.81 * cos(f)
cos(f) = 3.8/3.81
f = arccos(3.8/3.81) = 0.0721
If the capacitor is discharging it is a half cycle away, so f' = f + π = 3.2137
2.4 kg of nitrogen at an initial state of 285K and 150 kPa is compressed slowly in an isothermal process to a final pressure of 600 kPa. Determine the work.
Answer:
W=-280.67 KJ
Explanation:
Given that
Initial pressure = 150 KPa
Final pressure = 600 KPa
Temperature T= 285 K
Mass m=2.4 Kg
We know that ,work in isothermal process given as
[tex]W=mRT\ ln\dfrac{P_1}{P_2}[/tex]
Gas constant for nitrogen gas R=0.296 KJ/kgK
Now by putting the values
[tex]W=mRT\ ln\dfrac{P_1}{P_2}[/tex]
[tex]W=2.4\times 0.296\times 285\ ln\dfrac{150}{600}[/tex]
W=-280.67 KJ
Negative sign indicates that it is compression process and work is done on the gas.