Answer:
c = kbs
Explanation:
The equation that best captures the following logic is ; C = kbs
because for the car to start all the outlined functions must be ON if any of the function is OFF the car won't start hence all functions have to be ON simultaneously . The equation that represents this is : C = kbs
The three-point suspension system of a powered industrial truck forms an imaginary triangle that represents the stability zone of the truck
Answer:
True.
Explanation:
The three-point suspension system can be found on all industrial trucks and this is what promotes stability to the truck. This system forms a triangle with imaginary lines, which represents the zone of stability as shown in the question above. This is because the truck's steering axle stabilizes on a pivot pin that is placed in the center of the axle, this being the first point of the suspension system. This point is projected through imaginary lines to two diagonal points, forming the center of stability.
6) A deep underground cavern Contains 980 cuft
of methane gas (CH4) at a pressure of 230
psia and temperature of 150°F. How many
(omllbmol of methane does this gas
deposit contain?
Answer:
15625 moles of methane is present in this gas deposit
Explanation:
As we know,
PV = nRT
P = Pressure = 230 psia = 1585.79 kPA
V = Volume = 980 cuft = 27750.5 Liters
n = number of moles
R = ideal gas constant = 8.315
T = Temperature = 150°F = 338.706 Kelvin
Substituting the given values, we get -
1585.79 kPA * 27750.5 Liters = n * 8.315 * 338.706 Kelvin
n = (1585.79*27750.5)/(8.315 * 338.706) = 15625
Ammonia enters the expansion valve of a refrigeration system at a pressure of 10 bar and a temperature of 20oC and exits at 3.0 bar. The refrigerant undergoes a throttling process. Determine the temperature, in oC, and the quality of the refrigerant at the exit of the expansion valve. Step 1 Determine the temperature of the refrigerant at the exit, in oC.
Answer:
[tex]T_{2}[/tex] = -9.24 °C
x = 0.1057
Explanation:
The tables used in this answer and explanation come from Fundamentals of Engineering Thermodynamics 9th Edition.
Using Table A-14: Properties of Saturated Ammonia (Liquid-Vapor): Pressure Table and the given [tex]P_{2}[/tex], [tex]T_{2}[/tex] can be determined by finding the temperature that corresponds with [tex]P_{2}[/tex] on the table. In this case, [tex]T_{2}[/tex] = -9.24 °C.
The quality of the refrigerant can be determined by using data from the same table and [tex]h_{2} =274.26[/tex] kJ/kg.
Necessary data (P=3bar):
[tex]h_{f}=137.42[/tex] kJ/kg
[tex]h_{g}=1431.47[/tex] kJ/kg
The formula to calculate quality is [tex]h_{2} =h_{f}+x(h_{g}-h_{f})[/tex].
Rearranging for x:
[tex]x=\frac{h_{2}-h_{f} }{h_{g}-h_{f} }= \frac{274.26-137.42}{1431.47-137.42}=0.1057[/tex]
20 points!!!! In this unit, we learned that, ideally, the reductionist and holistic approaches to engineering work together to ensure an optimal manufacturing process. We also discussed how problems may arise without a systems engineer to oversee the process. What if the tables were turned, however? What might happen if a systems engineer overlooked a detail that may have been discovered by a manufacturing engineer? Explain using an example.
Explanation:
When a problem is discovered in the system design or manufacturing process, it generally gets reported to all concerned (if the company has an appropriate culture). Depending on the nature of the problem, a "quick fix" may be found by the discoverer, or by someone to whom the discovery is reported. In some situations, what seems a simple problem requires a rethinking of the entire manufacturing process, possible product recalls, possible plant retrofits, and even larger ramifications. This can happen regardless of where along the line the problem is discovered.
__
Hypothetical example:
A test technician determines that a lithium battery charger sometimes gets confused and doesn't shut down properly--continuing to charge the battery when it should not. If the proximate cause is a wire harness routing or a component improperly installed, a manufacturing engineer may be called in to address the issue. The manufacturing engineer's investigation may determine that a number of battery chargers have been delivered with the problem. Further investigation may reveal a potential for fire in situations where injury or loss of life are possible outcomes.
Assessment of the design by manufacturing, process, and design engineers may reveal more than one potential cause of the shutdown/fire-hazard issue, and that the location and nature of any fire may release toxins or cause damage to systems and equipment beyond those in the immediate vicinity of the defective battery and/or charger.
Such ramifications may require the attention of one or more systems engineers and/or a rethinking of system failure modes and effects, including fire detection and suppression, throughout the product. The product may be effectively "grounded" (taken out of service), with possible customer revenue implications, until such time as the issues can be satisfactorily resolved.
(Note: 787 Dreamliner battery problems were caused by the physics of the battery construction, not the charger. The rest of the scenario above is not a bad match.)
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Answer:
what?????
Explanation:
A heat pump operates on a vapor-compression refrigeration cycle with R-134a as the working fluid. The refrigerant enters the compressor as saturated vapor at X kPa, and exits at 800 kPa and 60oC. The refrigerant leaves the condenser as saturated liquid at 800 kPa. The number of letters in your first name multiplied by 10 plus 50
Answer:
Hello your question has some missing information below are the missing information
The refrigerant enters the compressor as saturated vapor at 140kPa Determine The coefficient of performance of this heat pump
answer : 2.49
Explanation:
For vapor-compression refrigeration cycle
P1 = P4 ; P1 = 140 kPa
P2( pressure at inlet ) = P3 ( pressure at outlet ) ; P2 = 800 kPa
From pressure table of R 134a refrigerant
h1 ( enthalpy of saturated vapor at 140kPa ) = 239.16 kJ/kg
h2 ( enthalpy of saturated liquid at P2 = 800 kPa and t = 60°C )
= 296.8kJ/kg
h3 ( enthalpy of saturated liquid at P3 = 800 kPa ) = 95.47 kJ/kg
also h4 = 95.47 kJ/kg
To determine the coefficient of performance
Cop = ( h1 - h4 ) / ( h2 - h1 )
∴ Cop = 2.49
We have a credit charge that is trying to process but we do not remember signing up and email login is not working? Is there a way to check?
Answer:
Yes
Explanation:
In such a case, one way to check the credit charge is to contact your bank, doing so would allow the bank to check your account properly to determine where the transaction was originated from.
Another way you could check is to contact the online merchant where such a transaction was initiated.
A 20 mm diameter rod made of ductile material with a yield strength of 350 MN/m2 is subjected to a torque of 100 N.m, and a bending moment of 150 N.m. An axial tensile force is then gradually applied. What is the value of the axial force when yielding of the rod occurs using: a. The maximum-shear-stress theory b. The maximum-distortional-energy theory.
Answer:
a) 42.422 KN
b) 44.356 KN
Explanation:
Given data :
Diameter = 20 mm
yield strength = 350 MN/m^2
Torque ( T ) = 100 N.m
Bending moment = 150 N.m
Determine the value of the applied axial tensile force when yielding of rod occurs
first we will calculate the shear stress and normal stress
shear stress ( г ) = Tr / J = [( 100 * 10^3) * 10 ] / [tex]\pi /32[/tex] * ( 20)^4
= 63.662 MPa
Normal stress( Гb + Гa ) = MY/ I + P/A
= [( 150 * 10^3) * 10 ] / [tex]\pi /32[/tex] * ( 20)^4 + 4P / [tex]\pi * 20^2[/tex]
= 190.9859 + 4P / [tex]\pi * 20^2[/tex] MPa
a) Using MSS theory
value of axial force = 42.422 KN
solution attached below
b) Using MDE theory
value of axial force = 44.356 KN
solution attached below
A high-voltage discharge tube is often used to study atomic spectra. The tubes require a large voltage across their terminals to operate. To get the large voltage, a step-up transformer is connected to a line voltage (120 V rms) and is designed to provide 5000 V rms to the discharge tube and to dissipate 75.0 W. (a) What is the ratio of the number of turns in the secondary to the number of turns in the primary
Answer:
a. 41
b. i. 15 mA ii. 625 mA
c. 192 Ω
Explanation:
Here is the complete question
A high-voltage discharge tube is often used to study atomic spectra. The tubes require a large voltage across their terminals to operate. To get the large voltage, a step-up transformer is connected to a line voltage (120 V rms) and is designed to provide 5000 V (rms) to the discharge tube and to dissipate 75.0 W. (a) What is the ratio of the number of turns in the secondary to the number of turns in the primary? (b) What are the rms currents in the primary and secondary coils of the transformer? (c) What is the effective resistance that the 120-V source is subjected to?
Solution
(a) What is the ratio of the number of turns in the secondary to the number of turns in the primary?
For a transformer N₂/N₁ = V₂/V₁
where N₁ = number of turns of primary coil, N₂ =number of coil of secondary, V₁ = voltage of primary coil = 120 V and V₂ = voltage of secondary coil = 5000 V
So, N₂/N₁ = V₂/V₁
N₂/N₁ = 5000 V/120 V = 41.6 ≅ 41 (rounded down because we cannot have a decimal number of turns)
(b) What are the rms currents in the primary and secondary coils of the transformer?
i. The rms current in the secondary
We need to find the current in the secondary from
P = IV where P = power dissipated in secondary coil = 75.0 W, I =rms current in secondary coil and V = rms voltage in secondary coil = 5000 V
P = IV
I = P/V = 75.0 W/5000 V = 15 × 10⁻³ A = 15 mA
ii. The rms current in the primary
Since N₂/N₁ = V₂/V₁ = I₁/I₂
where N₁ = number of turns of primary coil, N₂ =number of coil of secondary, V₁ = voltage of primary coil = 120 V, V₂ = voltage of secondary coil = 5000 V, I₁ = current in primary coil and I₂ = current in secondary coil = 15 mA
So, V₂/V₁ = I₁/I₂
V₂I₂/V₁ = I₁
I₁ = V₂I₂/V₁
= P/V₁
= 75.0 W/120 V
= 0.625 A
= 625 mA
(c) What is the effective resistance that the 120-V source is subjected to?
Using V = IR where V = voltage = 120 V, I = current in primary = 0.625 A and R = resistance of primary coil
R = V/I
= 120 V/0.625 A
= 192 V/A
= 192 Ω
Diseña un mecanismo multiplicador con un engranaje motriz cuya relación de transmisión sea de 0.5 y que transmita el movimiento entre ejes distantes. Inserta una captura de pantalla indicando la relación entre los diámetros y la velocidad de giro del engranaje motriz.
What is being shown in the above Figure?
A. Camshaft is being aligned
B. Engine is being timed
C. Camshaft is being removed
D. Camshaft gear backlash is being checked
Solar azimuth is the horizontal angle of the sun as measured from a predetermined direction. For the northern hemisphere, the 0°
direction is due
Answer is in a photo. I couldn't attach it here, but I uploaded it to a file hosting. link below! Good Luck!
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3
Select the correct answer
Which statement is true about a corporation?
A
B.
The shareholders hold no liability for the corporation's debts.
The shareholders hold limited liability for the corporation's debts.
The shareholders hold complete liability for the corporation's debts.
C.
D.
There are no shareholders in a corporation.
OE.
A single individual owns the corporation,
Which industry does a shoe manufacturer belong?
When framing a wall, temporary bracing is
used to support, plumb, and straighten the wall.
used to support, level, and straighten the wall.
used to square the wall before it is erected.
removed before the next level is constructed.
A wind turbine designer is considering installing a horizontal axis wind turbine at a location in Michigan. To increase the power extracted from wind, the designer is debating between increasing the blade radius by 10% versus increasing the height from 40 m to 60 m, which would increase the average wind speed from 6 mph to 6.5 mph. Considering the only the impact on power extraction, the designer should go with the height increase.
a. True
b. False
Answer:
False ( B )
Explanation:
considering that the wind turbine is a horizontal axis turbine
Power generated/extracted by the turbine can be calculated as
P = n * 1/2 * p *Av^3
where: n = turbine efficiency
p = air density
A = πd^2 / 4
v = speed
From the above equation it can seen that increasing the Blade radius by 10% will increase the Blade Area which will in turn increase the value of the power extracted by the wind turbine
which statement best describes the velocity of a bus traveling along its route
Answer:
Option A is the correct answer. The bus traveled at 50 mph for 20 minutes
Explanation:
The complete question is
Which of the following choices best describes velocity of a bus traveling along its route? A. The bus traveled at 50 mph for 20 minutes. B. The airplane traveled southwest at 280 mph. C. The car went from 35 mph to 45 mph. D. The train made several stops, with an average rate of 57 mph.
Solution
In option A the bus is travelling at a speed of 50 miles per hour. This describes the velocity of bus along its route.
The other options are about the velocity of airplane, car and train
A long cylindrical black surface fuel rod of diameter 25 mm is shielded by a surface concentric to the rod. The shield has diameter of 50 mm, and its outer surface is exposed to surrounding air at 300 K with a convection heat transfer coefficient of 15 W/m2.K. Inner and outer surfaces of the shield have an emissivity of 0.05, and the gap between the fuel rod and the shield is a vacuum. If the shield maintains a uniform temperature of 335 K, determine the surface temperature of the fuel rod
Answer:
surface temp of fuel rod = 678.85 K
Explanation:
Given data :
D1 = 25 mm
D2 = 50 mm
T2 = 335 k
T∞ = 300 k
hconv = 0.15 w/m^2.k
ε2 = 0.05
ε1 = 1
Determine energy at Q23
Q23 = Qconv + Qrad
attached below is the detailed solution
Insert given values into equation 1 attached below to obtain the surface temperature of the fuel rod ( T1 )
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Garth is a recruitment executive in a firm and knows the eight stages of recruitment. What activity or incident should Garth carry out or
expect to occur at each stage of the process?
place an advertisement in a job portal
vacancyWhat activity should Garth
Here are the eight stages of the recruitment process and what Garth might expect to occur or carry out at each stage in the explanation part.
What is recruitment?The process of identifying, attracting, and selecting qualified candidates for a job opening in an organisation is known as recruitment.
Here are the eight stages of the recruitment process, as well as what Garth might expect to happen or do at each stage:
Identifying the Need for the Position: Garth should review the company's staffing needs and determine if a position needs to be filled. Once a decision has been made, he should create a job description and identify the position's requirements.Garth should create a recruitment plan that includes a timeline for the recruitment process, a list of recruitment sources, and an advertising strategy.Garth should actively seek qualified candidates through various recruitment channels such as job boards, social media, referrals, and recruiting events.Screening Candidates: Garth should go over resumes, cover letters, and other application materials to see if candidates meet the job requirements. Garth should conduct interviews with the most qualified candidates to assess their skills, experience, and fit for the position. Garth should review all of the information gathered during the recruitment process and choose the best candidate for the position. Garth should ensure that the new hire has all of the necessary information and resources to succeed in their new role.Evaluating the Recruitment Process: Garth should go over the recruitment process to see where he can improve.Thus, these are the stages of recruitment.
For more details regarding recruitment, visit:
https://brainly.com/question/30086296
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what technology has been used for building super structures
Answer: Advanced technologixal machines
Explanation: such as big cranes, multiple workers helping creat said structure, and big bull dozers
An electromagnet is formed when a coil of wire wrapped around an iron core is hooked up to a dry cell battery. The current traveling through the wire sets up a magnetic field around the wire. TRUE or FALSE
Answer:
true
Explanation:
true An electromagnet is formed when a coil of wire wrapped around an iron core is hooked up to a dry cell battery. The current traveling through the wire sets up a magnetic field around the wire. TRUE or FALSE
The irreversible losses in the penstock of a hydroelectric dam are estimated to be 7 m. The elevation difference between the reservoir surface upstream of the dam and the surface of the water exiting the dam is 140 m. If the flow rate through the turbine is 4000 L/min, determine (a) the power loss due to irreversible head loss, (b) the efficiency of the piping, and (c) the electric power output if the turbine-generator efficiency is 84 percent.
Answer:
a) the power loss due to irreversible head loss is 4.57 kW
b) the efficiency of the piping is 95%
c) the electric power output is 72.9918 kW
Explanation:
Given the data in the question below;
Irreversible loses [tex]h_L[/tex] = 7m
Total head, H = 140 m
flow rate Q = 4000 L/min = 0.0666 m³/s
Generator efficiency n₀ = 84% = 0.84
we know that density of water is 1000 kg/m³
g = 9.81 m/s²
a) power loss due to irreversible head loss [tex]P_L[/tex] is;
[tex]P_L[/tex] = p × Q × g × [tex]h_L[/tex]
we substitute
[tex]P_L[/tex] = 1000 × 0.0666 × 9.81 × 7
[tex]P_L[/tex] = 4573.422 W
[tex]P_L[/tex] = 4573.422 / 1000
[tex]P_L[/tex] = 4.57 kW
Therefore, the power loss due to irreversible head loss is 4.57 kW
b) the efficiency of the piping n is;
n = (Actual head / maximum head) × 100
n = (( H - [tex]h_L[/tex] ) / H) × 100
so we substitute
n = (( 140 - 7 ) / 140) × 100
n = (133/140) × 100
n = 0.95 × 100
n = 95%
Therefore, the efficiency of the piping is 95%
c) the electric power output if the turbine-generator efficiency is 84 percent;
n₀ = [tex]Power_{outpu[/tex] / [tex]power_{inpu[/tex]
[tex]Power_{outpu[/tex] = n₀ × [tex]power_{inpu[/tex]
[tex]Power_{outpu[/tex] = n₀ × ( pQg( H - [tex]h_L[/tex] ))
so we substitute
[tex]Power_{outpu[/tex] = 0.84 × ( 1000 × 0.0666 × 9.81( 140 - 7 ))
[tex]Power_{outpu[/tex] = 0.84 × 653.346( 133)
[tex]Power_{outpu[/tex] = 0.84 × 86895.018
[tex]Power_{outpu[/tex] = 72991.815 W
[tex]Power_{outpu[/tex] = 72991.815 / 1000
[tex]Power_{outpu[/tex] = 72.9918 kW
Therefore, the electric power output is 72.9918 kW
me that both a triaxial shear test and a direct shear test were performed on a sample of dry sand. When the triaxial test is performed, the specimen was observed to fail when the major and minor principal stresses were 100 lb/in2 and 20 lb/in2, respectively. When the direct shear test is performed, what shear strength can be expected if the normal stress is 3000 lb/ft2
Answer:
shear strength = 2682.31 Ib/ft^2
Explanation:
major principal stress = 100 Ib / in2
minor principal stress = 20 Ib/in2
Normal stress = 3000 Ib/ft2
Determine the shear strength when direct shear test is performed
To resolve this we will apply the coulomb failure criteria relationship between major and minor principal stress a
for direct shear test
use Mohr Coulomb criteria relation between normal stress and shear stress
Shear strength when normal strength is 3000 Ib/ft = 2682.31 Ib/ft^2
attached below is the detailed solution
An interest rate of norminal 12% per year , compounded weekly is
Answer: It is a nominal rate per year
What disadvantages can a resort come across
Answer:
the disadvantages can be people's thoughts about them and also a rival resort nearby which looks more posh pls mark brainliest i need 5 more for next rank thank you
Explanation:
Air enters a compressor operating at steady state at 1.05 bar, 300 K, with a volumetric flow rate of 30 m3/min and exits at 12 bar, 400 K. Heat transfer occurs at a rate of 5 kW from the compressor to its surroundings. Assuming the ideal gas model for air and neglecting kinetic and potential energy effects, determine the power input, in kW.
Answer:
power input = -66.2798 kW
Explanation:
Steady state pressure ( Cp ) = 1.05 bar,
Temperature ( T1 ) = 300 K
Volumetric flow rate = 30 m^3/min
exit pressure = 12 bar
exit temperature ( T2 ) = 400 K
Heat transfer rate ( Q ) = 5 kW
Calculate the power input in kW
p1v1 = m RT
m = p1v1 / RT1
= (1.05 * 10^2 * ( 30/60 )) / ( 0.287 * 300 )
= 0.60975 m^3/sec
also
h1 + Q = h2 + w
∴ w = m ( h1 - h2 ) + Q
= mCp ( t1 - t2 ) + Q ----- ( 1 )
where : ( Q ) = 5 kW , Cp = 1.05 bar, t1 = 300 K, t2 = 400 k ( input values into equation 1 )
w = -66.2798 kW
a) The initial moisture content of a food product is 77% (wet basis), and the critical moisture content is 30% (wet basis). If the constant drying rate in a fluidized bed dryer is 0.1 kg water removed/m2-s, determine the time required for the product to begin the falling-rate drying period. The product has a cube shape with 5-cm sides; the initial product density is 950 kg/m3.
Answer:
≈ 53 seconds
Explanation:
calculate Time required for the product to begin the falling-rate drying period
Initial moisture content = 0.77 kg water /kg of product
= 3.35 kg water /kg solids
Critical moisture content = 0.3 kg water / kg product
= 0.43 kg water / kg solids
∴ amount of water to be removed = 3.35 - 0.43 = 2.95kg water /kg solids
next: calculate surface are a of product during drying
= (0.05 * 0.05 ) * 6
= 0.015 m^3
Drying rate = 0.1 kg water m^2.s^-1 * 0.015 m^3 = 1.5 * 10^-3 kg water s^-1
applying product density
initial product mass = 0.11875 * 0.23 = 0.0273kg solid
hence total amount of water to removed = 2.92 * 0.0273 = 0.07972 kg
therefore : Time required for the product to begin the falling-rate drying period
= 0.07972 / 1.5 * 10^-3
= 53 seconds
A non-cold-worked 1040 steel cylindrical rod has an initial length of 100 mm and initial diameter of 7.50 mm. is to be deformed using a tensile load of 18,000 N. It must not experience either plastic deformation or a diameter reduction of more than 1.5 x 10-2 mm. Would the 1040 steel be a possible candidate for this application
Answer:
1040 steel will be a possible candidate for this application since : Yield strength > stress
Explanation:
The 1040 steel would be a possible candidate for this application because the stress experienced by the load is Lesser than its Yield strength
Given that 1040 steel has the following parameter values
Modulus of elasticity ( GPa ) = 205
Yield strength ( Mpa ) = 450
Poisson's ratio = 0.27
limitation of = 1.5 x 10^-2 mm.
stress = Tensile load / area of steel
= 18,000 N / 4.418 * 10^-5 m^2
= 407 .424 Mpa
g Three unequal point masses are attached to a vertical shaft with light rods. Two masses, m and 3m, are at a distance a from the shaft. The third mass, 2m, is at a distance 2a from the shaft. The three masses and the shaft rotate as a single unit about the vertical axis through the shaft. What is the moment of inertia of this system about the vertical axis
Answer:
12ma²
Explanation:
The moment of inertia I = ∑mr² where m = mass and r = distance from shaft
Since we have three masses,
So, I = m₁r₁² + m₂r₂² + m₃r₃² where m₁ = first mass = m, m₂ = second mass = 3m and m₃ = third mass = 2m. Also, r₁ = distance of first mass from shaft = a, r₂ = distance of second mass from shaft = a and r₃ = distance of third mass from shaft = 2a.
I = m₁r₁² + m₂r₂² + m₃r₃²
I = ma² + 3ma² + 2m(2a)²
I = ma² + 3ma² + 2m(4a²)
I = ma² + 3ma² + 8ma²
I = 12ma²
Fracture Mechanics: A specimen of a 4340 steel alloy having a plane strain fracture toughness of 45 MPa m ( ) is exposed to a stress of 1000 MPa (145,000 psi). Assume that the parameter Y has a value of 1.0. a) Calculate the critical stress for brittle fracture of this specimen if it is known that the largest surface crack is 0.75 mm (0.03 in.) long. b) Will this specimen experience fracture
Answer:
a) 927 MPa
b)The specimen will experience fracture
Explanation:
a) Calculate critical stress for brittle fracture
σ = fracture toughness / (y √ π * surface crack)
= 45 / ( 1 [tex]\sqrt{\pi * ( 0.75*10^-3)}[/tex] )
= 927 MPa
b) since critical stress( 927 MPa) < 1000 MPa
hence : The fracture will occur
2. The following segment of carotid artery has an inlet velocity of 50 cm/s (diameter of 15 mm). The outlet has a diameter of 11mm. The pressure at inlet is 110 mm of Hg and pressure at outlet is 95 mm of Hg. Determine the forces required to keep the artery in place (consider steady state, ignore the mass of blood in the vessel and the mass of blood vessel; blood density is 1050 kg/m3)
This question is incomplete, the missing diagram is uploaded along this answer below.
Answer:
the forces required to keep the artery in place is 1.65 N
Explanation:
Given the data in the question;
Inlet velocity V₁ = 50 cm/s = 0.5 m/s
diameter d₁ = 15 mm = 0.015 m
radius r₁ = 0.0075 m
diameter d₂ = 11 mm = 0.011 m
radius r₂ = 0.0055 m
A₁ = πr² = 3.14( 0.0075 )² = 1.76625 × 10⁻⁴ m²
A₂ = πr² = 3.14( 0.0055 )² = 9.4985 × 10⁻⁵ m²
pressure at inlet P₁ = 110 mm of Hg = 14665.5 pascal
pressure at outlet P₂ = 95 mm of Hg = 12665.6 pascal
Inlet volumetric flowrate = A₁V₁ = 1.76625 × 10⁻⁴ × 0.5 = 8.83125 × 10⁻⁵ m³/s
given that; blood density is 1050 kg/m³
mass going in m' = 8.83125 × 10⁻⁵ m³/s × 1050 kg/m³ = 0.092728 kg/s
Now, using continuity equation
A₁V₁ = A₂V₂
V₂ = A₁V₁ / A₂ = (d₁/d₂)² × V₁
we substitute
V₂ = (0.015 / 0.011 )² × 0.5
V₂ = 0.92975 m/s
from the diagram, force balance in x-direction;
0 - P₂A₂ × cos(60°) + Rₓ = m'( V₂cos(60°) - 0 )
so we substitute in our values
0 - (12665.6 × 9.4985 × 10⁻⁵) × cos(60°) + Rₓ = 0.092728( 0.92975 cos(60°) - 0 )
0 - 0.6014925 + Rₓ = 0.043106929 - 0
Rₓ = 0.043106929 + 0.6014925
Rₓ = 0.6446 N
Also, we do the same force balance in y-direction;
P₁A₁ - P₂A₂ × sin(60°) + R[tex]_y[/tex] = m'( V₂sin(60°) - 0.5 )
we substitute
⇒ (14665.5 × 1.76625 × 10⁻⁴) - (12665.6 × 9.4985 × 10⁻⁵) × sin(60°) + R[tex]_y[/tex] = 0.092728( 0.92975sin(60°) - 0.5 )
⇒ 1.5484 + R[tex]_y[/tex] = 0.092728( 0.305187 )
⇒ 1.5484 + R[tex]_y[/tex] = 0.028299
R[tex]_y[/tex] = 0.028299 - 1.5484
R[tex]_y[/tex] = -1.52 N
Hence reaction force required will be;
R = √( Rₓ² + R[tex]_y[/tex]² )
we substitute
R = √( (0.6446)² + (-1.52)² )
R = √( 0.41550916 + 2.3104 )
R = √( 2.72590916 )
R = 1.65 N
Therefore, the forces required to keep the artery in place is 1.65 N