Answer:
b. inversely proportional to radius of curvature
Explanation:
In curvilinear motions, the normal acceleration which is also called the centripetal acceleration is always directed towards the center of the circular path of motion. This acceleration has a magnitude that is directly proportional to the square of the speed of the body undergoing the motion and inversely proportional to the radius of the curvature of the motion path. The centripetal or normal acceleration a, can be given by;
a = [tex]\frac{v^2}{r}[/tex]
Where;
v = speed of the body
r = radius of curvature.
You have accumulated several parking tickets while at school, but you are graduating later in the year and plan to return to your home in another jurisdiction. A friend tells you that the authorities in your home jurisdiction will never find out about the tickets when you re-register your car and apply for a new license. What should you do?
Answer:
pay off the parking tickets
Explanation:
In the scenario being described, the best thing to do would be to pay off the parking tickets. The parking tickets stay under your name, and if they are not paid in time can cause problems down the road. For starters, if they are not paid in time the amount will increase largely which will be harder to pay. If that increased amount is also not paid, then the government will suspend your licence indefinitely which can later lead to higher insurance rates.
When replacing a timing belt, many experts and vehicle manufacturers recommend that all of the following should be replaced except the
A. water pump
B. camshaft oil seal(s).
C. camshalt sprocket
D. tensioner assembly
Answer:
Correct Answer:
A. water pump
Explanation:
Timing belt in a vehicle helps to ensure that crankshaft, pistons and valves operate together in proper sequence. Timing belts are lighter, quieter and more efficient than chains that was previously used in vehicles.
Most car manufacturers recommended that, when replacing timing belt, tension assembly, water pump, camshaft oil seal should also be replaced with it at same time.
Consider atmospheric air at 25 C and a velocity of 25 m/s flowing over both surfaces of a 1-m-long flat plate that is maintained at 125 C. Determine the rate of heat transfer per unit width from the plate for values of the critical Reynolds number corresponding to 105 , 5 105 , and 106 .
Answer:
Explanation:
Temperature of atmospheric air To = 25°C = 298 K
Free stream velocity of air Vo = 25 m/s
Length and width of plate = 1m
Temperature of plate Tp = 125°C = 398 K
We know for air, Prandtl number Pr = 1
And for air, thermal conductivity K = 24.1×10?³ W/mK
Here, charectorestic dimension D = 1m
Given value of Reynolds number Re = 105
For laminar boundary layer flow over flat plate
= 3.402
Therefore, hx = 0.08199 W/m²K
So, heat transfer rate q = hx×A×(Tp – To)
= 0.08199×1×(398 – 298)
Armature reaction in a dc machine A) is due to an increase of the armature voltage. B) occurs when the motor is connected to an ac power source. C) occurs when the motor is connected to a dc power source. D) is due to an increase of the armature current.
Answer:
D) is due to an increase of the armature current.
Explanation:
Option D is correct because on the DC motor, when the load increases, it leads to an increase in the armature current.
The armature current then sets up a magnetic flux which opposes the main field flux. The net field flux gets reduced. It is at this point, the armature reaction occurs.
Armature reaction is seen as the effect of magnetic flux which is usually set up by an armature current. This occurs when there is the distribution of flux under the main poles.
There are two effects the armature flux causes on the main field flux.
1. The main field flux is distorted by the armature reaction.
2. The magnitude of the main field flux is reduced by the armature flux.
/ Air enters a 20-cm-diameter 12-m-long underwater duct at 50°C and 1 atm at a
mean velocity of 7 m/s, and is cooled by the water outside. If the average heat
transfer coefficient is 85 W/m2
°C and the tube temperature is nearly equal to the
water temperature of 5°C, determine the exit temperature of air and the rate of heat
transfer.
Answer:
A) EXIT TEMPERATURE = 14⁰C
b) rate of heat transfer of air = - 13475.78 = - 13.5 kw
Explanation:
Given data :
diameter of duct = 20-cm = 0.2 m
length of duct = 12-m
temperature of air at inlet= 50⁰c
pressure = 1 atm
mean velocity = 7 m/s
average heat transfer coefficient = 85 w/m^2⁰c
water temperature = 5⁰c
surface temperature ( Ts) = 5⁰c
properties of air at 50⁰c and at 1 atm
= 1.092 kg/m^3
Cp = 1007 j/kg⁰c
k = 0.02735 W/m⁰c
Pr = 0.7228
v = 1.798 * 10^-5 m^2/s
determine the exit temperature of air and the rate of heat transfer
attached below is the detailed solution
Calculate the mass flow rate
= p*Ac*Vmean
= 1.092 * 0.0314 * 7 = 0.24 kg/s
Q1: You have to select an idea developing an application like web/mobile or industrial, it should be based on innovative idea, not just a simple CRUD application. After selecting the idea do the following: 1) How your project will be helpful and what problem this project addresses. (10-Marks) 2) Write down the requirements. (10Marks) 3) List the functional and non-functional requirements of your project. (10marks) 4) Which process model you will follow for this project and why? (10marks) 5) Draw the Level 0, and level 1 DFD of your application. (20marks)
Answer:
Creating an app is both an expression of our self and a reflection of what we see is missing in the world. We find ourselves digging deep into who we are, what we would enjoy working on, and what needs still need to be fulfilled. Generating an app idea for the first time can be extremely daunting. Especially with an endless amount of possibilities such as building a church app.
The uncertainty has always spawned a certain fear inside creators. The fear of creating something no one will enjoy. Spending hundreds of dollars and hours building something which might not bring back any real tangible results. The fear of losing our investment to a poor concept is daunting but not random. But simple app ideas are actually pretty easy to come by.
Great app idea generation is not a gift given to a selected few, instead, it is a process by which any of us are able to carefully explore step by step methods to find our own solution to any problem. Whether you are a seasoned creator or a novice, we have provided a few recommendations to challenge and aid you as you create your next masterpiece.
if I am right then make me brainliest
The natural variation of a process relative to the variation allowed by the design specifications is known as
Answer:
"Process capability" is the correct answer.
Explanation:
The Process Capability seems to be a method of measuring of how and why the framework performs concerning something like the successful objectives. This same capacity is characterized as that of the client's voice over procedure speech.Through using functionality indicators it analyses the performance with an in-control process with the permissible range.Consider the thermocouple and convection conditions of Example 1, but now allow for radiation exchange with the walls of a duct that encloses the gas stream. If the duct walls are at 400℃ and the emissivity of the thermocouple bead is 0.9, calculate the steady-state temperature of the junction
Answer:
hello your question has some missing part attached below is the complete question
answer : steady state temperature = 419.713k ≈ 218.7⁰c
Time required to reach a junction ≈ 5 secs
Explanation:
The detailed solution of the given problem is attached below but the solution to the subsequent problem from which the question you asked is referenced to( problem 1 ), is not attached because it was not part of the question you asked
An air-conditioner which uses R-134a operates on the ideal vapor compression refrigeration cycle with a given compressor efficiency.
--Given Values--
Evaporator Temperature: T1 (C) = 9
Condenser Temperature: T3 (C) = 39
Mass flow rate of refrigerant: mdot (kg/s) = 0.027
Compressor Efficiency: nc (%) = 90
a) Determine the specific enthalpy (kJ/kg) at the compressor inlet.
Your Answer =
b) Determine the specific entropy (kJ/kg-K) at the compressor inlet
Your Answer =
c) Determine the specific enthalpy (kJ/kg) at the compressor exit
Your Answer =
d) Determine the specific enthalpy (kJ/kg) at the condenser exit.
Your Answer =
e) Determine the specific enthalpy (kJ/kg) at the evaporator inlet.
Your Answer =
f) Determine the coefficient of performance for the system.
Your Answer =
g) Determine the cooling capacity (kW) of the system.
Your Answer =
h) Determine the power input (kW)to the compressor.
Your Answer =
Answer:
A) 251.8 kj/kg
B) 0.9150 kj/kg-k
C) 155.4 kj/kg
F) 1.50
G) 3.95 kw
H) 2.6 kw
Explanation:
Given conditions :
air conditioner : R -134a
compressor efficiency (nc) = 90%.
T1 = 9⁰c, T3 = 39⁰c, mass flow rate = 0.027 kg/s
A) Specific enthalpy at the compressor inlet
at T = 9⁰c the saturated vapor (x) = 1
from the R-134a property table
h1 = 251.8 kj/kg
B ) specific entropy ( kj/kg-k) at the compressor inlet
at T = 9⁰c the saturated vapor (x) = 1
s = 0.9150 kj/kg-k ( from the R-134a property table )
C) specific enthalpy at the compressor exit
at T3 = 39⁰c , s2 = s1
has = 165.12 kj/kg
h2 = 155.4 kj/kg
attached below is the remaining solution to some of the problems
A four-cylinder four-stroke engine is modelled using the air standard Otto cycle (two engine revolutions per cycle). Given the conditions at state 1, total volume (V1) of each cylinder, compression ratio (r), rate of heat addition (Q), and engine speed in RPM, determine the efficiency and other values listed below. The gas constant for air is R =0.287 kJ/kg-K.
T1 = 300 K
P1 = 100 kPa
V1 = 500 cm^3
r = 10
Q = 60 kW
Speed = 5600 RPM
Required:
a. Determine the total mass (kg) of air in the engine.
b. Determine the specific internal energy (kJ/kg) at state 1.
c. Determine the specific volume (m^3/kg) at state 1.
d. Determine the relative specific volume at state 1.
Answer:
a) Mt = 0.0023229
b) = U1 = 214.07
c) = V₁ = 0.861 m³/kg
d) = Vr1 = 621.2
Explanation:
Given that
R = 0.287 KJ/kg.K, T1 = 300 K , P1 = 100 kPa , V1 = 500 cm³, r = 10 , Q = 60 kW , Speed N = 5600 RPM, Number of cylinders K = 4
specific heat at constant volume Cv = 0.7174 kJ/kg.K
Specific heat at constant pressure is 1.0045 Kj/kg.K
a) To determine the total mass (kg) of air in the engine.
we say
P1V1 = mRT1
we the figures substitute
(100 x 10³) ( 500 x 10⁻⁶) = m ( 0.287 x 10³) ( 300 )
50 = m x 86100
m = 0.00005 / 86100 = 0.0005807 ( mass of one cylinder)
Total mass of 4 cylinder
Mt = m x k
Mt = 0.0005807 x 4
Mt = 0.0023229
b) To determine the specific internal energy (kJ/kg) at state 1
i.e at T1 = 300
we obtain the value of specific internal energy U1 at 300 K ( state 1) from the table ideal gas properties of air.
U1 = 214.07
c) To determine the specific volume (m³/kg) at state 1.
we say
V₁ = V1/m
V₁ = (500 x 10⁻⁶) / 0.0005807
V₁ = 0.861 m³/kg
d) To determine the relative specific volume at state 1.
To obtain the value of relative specific volume at 300 K ( i.e state 1) from the table ideal gas properties of air.
At T1 = 300 k
Vr1 = 621.2
The structure of a house is such that it loses heat at a rate of 5400 kJ/h per degree Cdifference between the indoors and outdoors. A heat pump that requires a power input of 6 kW isused to maintain this house at 21 C. Determine the lowest outdoor temperature for which the heatpump can meet the heating requirements of this house
Answer: Tl = - 13.3°C
the lowest outdoor temperature is - 13.3°C
Explanation:
Given that;
Temperature of Th = 21°C = 21 + 273 = 294 K
the rate at which heat lost is Qh = 5400 kJ/h°C
the power input to heat pump Wnet = 6 kw
The COP of a reversible heat pump depends on the temperature limits in the cycle only, and is determined by;
COPhp = Th/(Th - Tl)
COPhp = Qh/Wnet
Qh/Wnet = Th/(Th -Tl)
the amount of heat loss is expressed as
Qh = 5400/3600(294 - Tl)
the temperature of sink
( 5400/3600(294 - Tl)) / 6 = 294 / ( 294 - Tl)
now solving the equation
Tl = 259.7 - 273
Tl = - 13.3°C
so the lowest outdoor temperature is - 13.3°C
1. Two types of superchargers include
A. turbine and piston.
B. roots-type and centrifugal.
C. double- and single-acting
D. rotary and reciprocating.
Input resistance of a FET is very high due to A) forward-biased junctions have high impedance B) gate-source junction is reverse-biased C) drain-source junction is reverse-biased D) none of the above
Answer:
B) gate-source junction is reverse-biased
Explanation:
FET is described as an electric field that controls the specific current and is being applied to a "third electrode" which is generally known as "gate". However, only the electric field is responsible for controlling the "current flow" in a specific channel and then the particular device is being "voltage operated" that consists of high "input impedance".
In FET, the different "charge carriers" tend to enter a particular channel via "source" and exits through "drain".
A rate of 0.42 minute per piece is set for a forging operation. The operator works on the job for a full eight-hour day and produces 1,500 pieces. Use a standard hour plan.
Required:
a. How many standard hours does the operator earn?
b. What is the operator's efficiency for the day?
c. If the base rate is 9.80 per hour, compute the earnings for the day.
d. What is the direct labor cost per piece at this efficiency?
e. What would be the proper piece rate (rate expressed in money) for this job, assuming that the above time standard is correct?
Answer:
b. What is the operator's efficiency for the day?
AND
e. What would be the proper piece rate (rate expressed in money) for this job, assuming that the above time standard is correct?
Explanation:
(A) Derive planar density expressions for BCC (100) and (110) planes in terms of the atomicradius R.
(B) Compute and compare planar density values for these same two planes for molybdenum (Mo).
Answer:
Explanation:
BCC structure can also be called Body-Centred Cubic. In BCC Structure, single atom is located at every corner of the cube, and one is also located at the centre of the structure.
Each of the four cube corners through which this (110) plane travels has an atom, which it shares with four neighboring unit The percentage of the entire crystallographic plane area that is occupied by atoms is known as planar density.
What is planar density ?The packing density of crystals is measured by planar density. A face-centered cubic unit cell's planar density may be determined by following a few straightforward procedures. Determine how many atoms are centered on a certain plane. An FCC crystal, for instance, has 2 atoms on a (1 1 0) plane.
The amount of atoms per unit area on an interest plane defines the planar density, a crucial aspect of a crystal structure.
The percentage of the entire crystallographic plane area that is occupied by atoms is known as planar density. Atomic packing factor analogs in one and two dimensions are linear and planar densities.
Thus, The center atom, however, is totally contained within the unit cell. This means that this BCC (110) plane has an equivalent of 2 atoms.
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Punctuate or edit the following sentences. Your punctuation and/or revisions should reflect best TW style and grammar writing practices.
1. The author an expert in cybersecurity will speak via Zoom this Wednesday.
2. Williams' book contains many illustrations, this makes it quick reading.
3. Based on the available evidence the university administrators have opted for a hybrid format for the fall quarter which begins September 20.
4. (Thesis statement) Free laptops should be offered to all students who need them.
I inferred you want literal editing of the text above.
Explanation:
Here's a correction of the sentences:
1. The author, an expert in cybersecurity will speak via Zoom on Wednesday.
In this sentence, punctuation mark ( , ) was added and the word 'this' was replaced with 'on'.
2. Williams' book contains many illustrations, which makes it easy to read.
Added punctuation and made a revision of the sentence.
3. Based on the available evidence, the university administrators have opted for a hybrid format for the fall, which begins September 20.
Mainly added punctuations to make the senstence clarer.
4. (Thesis statement) I believe Free laptops should be offered to all students who need them.
Made a few additions.
Consider an ideal gas undergoing a constant pressure process from state 1 to state
2 in a closed system. The specific heat capacities for this material depend on temperature in
the following way, cv = aT^b , cp = cT^d , where the constants a, b, c and d are known. Calculate
the specific entropy change, (s2 − s1), from state 1 to state 2.
Answer:
[tex]s_2-s_1=c\frac{T^d}{d}-Rg\ ln(\frac{P_2}{P_1})[/tex]
Explanation:
Hello,
In this case by combining the first and second law of thermodynamics for this ideal gas, we can obtain the following expression for the differential of the specific entropy at constant pressure:
[tex]ds=c_p\frac{dT}{T}-Rg\ \frac{dP}{P}[/tex]
Whereas Rg is the specific ideal gas constant for the studied gas; thus, integrating:
[tex]\int\limits^{s_2}_{s_1} {} \, ds=c\int\limits^{T_2}_{T_1} {T^{d-1}dT} \,-Rg\ \int\limits^{P_2}_{P_1} {\frac{dP}{P}} \,[/tex]
We obtain the expression to compute the specific entropy change:
[tex]s_2-s_1=c\frac{T^d}{d}-Rg\ ln(\frac{P_2}{P_1})[/tex]
Best regards.
In a typical transmission line, the current I is very small and the voltage V is very large. A unit length of line has resistance R. For a power line that supplies power to 10,000 households, we can conclude that:________
Answer:
IV > [tex]I^{2} R[/tex]
Explanation:
The current in the power line = I
The voltage in the power line = V
The resistance of the power line = R
Power supplied from the power house = P
power delivered to the households = [tex]p[/tex]
We know that the power supplied to a power line system is proportional to
P = IV ....1
we also know that according to Ohm's law, the relationship between the voltage, resistance, and current through an electrical system is given as
V = IR ....2
substituting equation 2 into equation 1, the power delivered to the households is proportional to the square of the current.
[tex]p[/tex] = [tex]I^{2} R[/tex] ....3
The problem is that when power is delivered across a transmission line, some of the power is loss due to Joules heating effect of the power lines. This energy and power loss is proportional to [tex]I^{2}[/tex] therefore, the electrical power delivered to the households will be less than the electrical power supplied from the power station. This means that
P > [tex]p[/tex]
equating these two powers from equations 1 and equation 3, we have
IV > [tex]I^{2} R[/tex]
What's the resistance in a circuit that has a voltage of 60 V and a current of 2 A? A. 10 Ω B. 60 Ω C. 120 Ω D. 30 Ω
Answer:
D. Resistance = 30 ohms
Explanation:
Using Ohm's law
V = I times R
Given:
V = 60 V
I = 2 A
Resistance = V / I = 60 V / 20 A
Resistance = 30 ohms
"The transistor base-emitter voltage (VBE) a. increases with an increase in temperature. b. is not affected by temperature change. c. decreases with an increase in temperature. d. has no effect on collector current."
Answer:
C) Decreases with an increase in temperature
Explanation:
As the temperature of a transistor increases, the thermal runaway property of the transistor becomes more significant and the transistors, conducting more freely as a result of the rise in temperature, causes an increase in the collector current or leakage current. The transistor base-emitter voltage decreases as a result.
With increased heating due to heavy current flow, the transistor is damaged.
Summary of Possible Weather and Associated Aviation Impacts for Geographic/Topographic Categories Common in the Western United States.
Geographic/Topographic Descriptive Summary of Potential Aviation Impacts
Category of a Possible Weather That Could Impact Based on Weather
of Airport Location Aviation Operations
Along the US West coast,
with steep mountains to the east
(An example of this category is
Santa Barbara Airport, located
on the Southern California Coast,
at an elevation of 10 feet).
Within a valley in elevated terrain
surrounded by high mountains
(An example of this category is
Friedman Memorial Airport, located
in Central Idaho, at an elevation of 5300 feet).
In elevated terrain on the leeside of
high mountains
(An example of this category is Northern Colorado
Regional Airport, located in northern Colorado,
at an elevation of 5000 feet, on the leeside
of the Rocky mountains).
Answer: answer provided in the explanation section.
Explanation:
Weather phenomenons that would impart Aviation Operations in Santa Barbara -
1. Although winters are cold, wet, and partly cloudy here. It is in general favorable for flying. But sometimes strong winds damage this pleasant weather.
2. The Sundowner winds cause rapid warming and a decrease in relative humidity. The wind speed is very high surrounding this area for this type of wind.
3. Cloud is an important factor that affects aviation operations. Starting from April, here the sky is clouded up to November. The sky is overcast (80 to 100 percent cloud cover) or mostly cloudy (60 to 80 percent) 44% on a yearly basis. Thus extra cloud cover can trouble aviation operations.
4. The average hourly wind speed can also be a factor. This also experiences seasonal variations, these variations are studied carefully in the aviation industry. The windier part of the year starts in January and ends in June. In April, the wind speed can reach 9.5 miles per hour.
This and more are some factors to look into when considering wheather conditions that would affect aviation operations.
I hope this was a bit helpful. cheers
The fins attached to a heat exchanger-surface are determined to have an effectiveness of 0.9. Do you think the rate of heat transfer from the surface has increased or decreased as a result of the addition of these fins?
Answer:
The rate of heat transfer has increased.
Explanation:
Heat transfer rate is the rate at which heat energy is dissipated to the ambient from a hot body. The rate of heat transfer is proportional to the available surface area for heat exchange. This means that the greater the exposed surface area for heat exchange, the greater the rate at which heat is lost to the ambient. In introducing the fins to the heat exchange system (fins have a large surface area to volume ratio for maximum exposure to the ambient), one maximizes the available surface area for heat exchange between the material and the ambient, increasing the rate of heat transfer.
A charge is distributed uniformly along a long straight wire. The electric field 2 cm from the wire is 36 N/C. The electric field 4 cm from the wire is:
Answer:
New electric field = 18 N/C
Explanation:
Given:
Length (E1) = 2 cm
New length (E2) = 4 cm
Electric field = 36 N/C
Find:
New electric field
Computation:
New electric field = 36 [2 / 4]
New electric field = 36 [1/2]
New electric field = 18 N/C
Conductivity is the reciprocal of what?
An ideal Diesel cycle has a compression ratio of 17 and a cutoff ratio of 1.3. Determine the maximum temperature of the air and the rate of heat addition to this cycle when it produces 140 kW of power and the state of the air at the beginning of the compression is 90 kPa and 578C. Use constant specific heats at room temperature.
Answer:
maximum temperature = 1322 k
rate of heat addition = 212 kw
Explanation:
compression ratio = 17
cut off ratio = 1.3
power produced = 140 Kw
state of air at the beginning of the compression = 90 kPa and 578 c
Determine the maximum temperature of air
attached below is the detailed solution
Two small balls A and B with masses 2m and m respectively are released from rest at a height h above the ground. Neglecting air resistance, which of the following statements are true when the two balls hit the ground?
(a) The kinetic energy of A is the same as the kinetic energy of B
(b) The kinetic energy of A is half the kinetic energy of B.
(c) The kinetic energy of A is twice the kinetic energy of B.
(d) The kinetic energy of A is four times the kinetic energy of B Explain your answer why.
What is the definition of General Plan Motion? What would be the effective methodology or approach to solve a rigid body kinematics problem?
Answer:
The kinetic energy of A is twice the kinetic energy of B
Explanation:
The true statement when the two balls hit the ground is, the kinetic energy of A is twice the kinetic energy of B. The correct option is (c).
What is kinetic energy?Kinetic energy is the energy of motion, which can be seen as an item or subatomic particle moving. Kinetic energy exists in every moving object and particle.
Kinetic energy is demonstrated by a person walking, a soaring baseball, a crumb falling from a table, and a charged particle in an electric field.
The definition of a General Plan of Motion is every point on the body has a different path. As a result, we must relate the forces to the acceleration of the body's center of mass, as well as the moments to the angular accelerations.
Therefore, the correct option is (c), The kinetic energy of A is twice the kinetic energy of B.
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After a capacitor is fully chargerd, a small amount of current will flow though it. what is this current called?
Answer:
leakage
Explanation:
That current is "leakage current."
When choosing building-construction materials, what kinds of materials would you choose, all other things being equal?
The building-construction materials are materials with a relatively large bulk modulus, would the choose of the constructor. Thus, option (e) is correct.
What is building?The term building refers to the large structure of the bricks. The building was the large structure made by the engineer and the architecture. There was the building are the people are the stay. The building was the used in the permanent basis. There are the different types of the building.
According to the building-construction materials are the engineers to the order of the bulk in the material. The bulk level of the material is the high discount rate of the order. The large amount of the material to the used in the building-construction, that are the order in the bulk of the production.
Therefore, option (e) is correct.
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Your question is incomplete, but most probably the full question was.
either materials with a large or a small bulk modulus.it doesn't matter as long as the building is not too tall.materials with a relatively small shear modulus.materials with a relatively small bulk modulus.materials with a relatively large bulk modulus.After clamping a buret to a ring stand, you notice that the set-up is tippy and unstable. What should you do to stabilize the set-up
Answer:
Move the buret clamp to a ring stand with a larger base.
Explanation:
A right stand is used for titration experiments in the laboratory. It holds the burette firmly during experiments so that accurate readings can be taken.
The right stand is made up of support base, vertical stainless steel, clamp with adjustable screw that holds on to the vertical rod.
The clamp is used to hold the burette in place.
If after clamping a buret to a ring stand, you notice that the set-up is tippy and unstable, the best action will be to move the buret clamp to a ring stand with a larger base.
The larger base provides a better center of gravity and stabilises the setup
An ideal turbojet engine is analyzed using the cold air standard method. Given specific operating conditions determine the temperature, pressure, and enthalpy at each state, and the exit velocity.
--Given Values--
T1 (K) = 249
P1 (kPa) = 61
V1 (m/s) = 209
rp = 10.7
rc = 1.8
Required:
a. Determine the temperature (K) at state 2.
b. Determine the pressure (kPa) at state 2.
c. Determine the specific enthalpy (kJ/kg) at state 2.
d. Determine the temperature (K) at state 3.
Answer:
a. the temperature (K) at state 2 is [tex]\mathbf{T_2 =270.76 \ K}}[/tex]
b. the pressure (kPa) at state 2 is [tex]\mathtt{ \mathbf{ p_2 = 81.79 \ kPa }}[/tex]
c. the specific enthalpy (kJ/kg) at state 2 is [tex]\mathbf{h_2 = 271.84 \ kJ/kg}}[/tex]
d. the temperature (K) at state 3 is [tex]\mathbf{ T_3 = 532.959 \ K}[/tex]
Explanation:
From the given information:
T1 (K) = 249
P1 (kPa) = 61
V1 (m/s) = 209
rp = 10.7
rc = 1.8
The objective is to determine the following:
a. Determine the temperature (K) at state 2.
b. Determine the pressure (kPa) at state 2.
c. Determine the specific enthalpy (kJ/kg) at state 2.
d. Determine the temperature (K) at state 3.
To start with the specific enthalpy (kJ/kg) at state 2.
By the relation of steady -flow energy balance equation for diffuser (isentropic)
[tex]h_1 + \dfrac{V_1^2}{2}=h_2+\dfrac{V^2_2}{2}[/tex]
[tex]h_1 + \dfrac{V_1^2}{2}=h_2+0[/tex]
[tex]h_2=h_1 + \dfrac{V_1^2}{2}[/tex]
For ideal gas;enthalpy is only a function of temperature, hence [tex]c_p[/tex]T = h
where;
[tex]h_1[/tex] is the specific enthalpy at inlet = [tex]c_pT_1[/tex]
[tex]h_2[/tex] is the specific enthalpy at outlet = [tex]c_pT_2[/tex]
[tex]c_p[/tex] = 1.004 kJ/kg.K or 1004 J/kg.K
Given that:
[tex]T_1[/tex] (K) = 249
[tex]V_1[/tex] (m/s) = 209
∴
[tex]h_2=C_pT_1+ \dfrac{V_1^2}{2}[/tex]
[tex]h_2=1004 \times 249+ \dfrac{209^2}{2}[/tex]
[tex]h_2 = 249996+21840.5[/tex]
[tex]\mathbf{\mathtt{h_2 = 271836.5 \ J/kg}}[/tex]
[tex]\mathbf{h_2 = 271.84 \ kJ/kg}}[/tex]
Determine the temperature (K) at state 2.
SInce; [tex]\mathtt{h_2 = c_pT_2 = 271.84 \ kJ/kg}[/tex]
[tex]\mathtt{ c_pT_2 = 271.84 \ kJ/kg}[/tex]
[tex]\mathtt{T_2 = \dfrac{271.84 \ kJ/kg}{ c_p}}[/tex]
[tex]\mathtt{T_2 = \dfrac{271.84 \ kJ/kg}{1.004 \ kJ/kg.K}}[/tex]
[tex]\mathbf{T_2 =270.76 \ K}}[/tex]
Determine the pressure (kPa) at state 2.
For isentropic condition,
[tex]\mathtt{ \dfrac{T_2}{T_1}= \begin {pmatrix} \dfrac{p_2}{p_1} \end {pmatrix} ^\dfrac{k-1}{k}}[/tex]
where ;
k = specific heat ratio = 1.4
[tex]\mathtt{ \dfrac{270.76}{249}= \begin {pmatrix} \dfrac{p_2}{61} \end {pmatrix} ^\dfrac{1.4-1}{1.4}}[/tex]
[tex]\mathtt{ 1.087389558= \begin {pmatrix} \dfrac{p_2}{61} \end {pmatrix} ^\dfrac{0.4}{1.4}}[/tex]
[tex]\mathtt{ 1.087389558 \times 61 ^ {^ \dfrac{0.4}{1.4} }}=p_2} ^\dfrac{0.4}{1.4}}[/tex]
[tex]\mathtt{ 3.519487255=p_2} ^\dfrac{0.4}{1.4}}[/tex]
[tex]\mathtt{ \mathbf{ p_2 = \sqrt[0.4]{3.519487255^{1.4}} }}[/tex]
[tex]\mathtt{ \mathbf{ p_2 = 81.79 \ kPa }}[/tex]
d. Determine the temperature (K) at state 3.
For the isentropic process
[tex]\mathtt{\dfrac{T_3}{T_2} = \begin {pmatrix} \dfrac{p_3}{p_2} \end {pmatrix}^{\dfrac{k-1}{k}}}[/tex]
where;
[tex]\mathtt{\dfrac{p_3}{p_2} }[/tex] is the compressor ratio [tex]\mathtt{r_p}[/tex]
Given that ; the compressor ratio [tex]\mathtt{r_p}[/tex] = 10.7
[tex]\mathtt{\dfrac{T_3}{T_2} = \begin {pmatrix} r_p \end {pmatrix}^{\dfrac{k-1}{k}}}[/tex]
[tex]\mathtt{\dfrac{T_3}{270.76} = \begin {pmatrix} 10.7 \end {pmatrix}^{\dfrac{1.4-1}{1.4}}}[/tex]
[tex]\mathtt{\dfrac{T_3}{270.76} = \begin {pmatrix} 10.7 \end {pmatrix}^{^ \dfrac{0.4}{1.4}}}[/tex]
[tex]\mathtt{{T_3}{} =270.76 \times\begin {pmatrix} 10.7 \end {pmatrix}^{^ \dfrac{0.4}{1.4}}}[/tex]
[tex]\mathbf{ T_3 = 532.959 \ K}[/tex]
