An incompressible fluid is flowing through a vertical pipe with a constriction. The wide section is 2.00 cm in diameter and is at the top of the pipe. The pressure of the fluid in the wide section at the top is 200 kPa. The velocity of the fluid in the wide section is 4.00 m/s. The narrow section is located 8.00 m below the wide section. What is the diameter of the narrow section for the pressure of the fluid in the narrow section equal the pressure of the wide section? (density of the fluid is 680 kg/m^3)
1.10 cm
1.42 cm
1.31 cm
1.20 cm
1.55 cm
Answers
We can use the principle of continuity of flow to solve this problem. The diameter of the narrow section of the pipe for the pressure of the fluid in the narrow section to be equal to the pressure of the wide section is approximately 1.10 cm.
This principle states that the mass flow rate of an incompressible fluid is constant along a pipe, assuming that there are no sources or sinks of fluid along the pipe.
Let's first find the mass flow rate of the fluid in the wide section of the pipe. The mass flow rate is given by:
m₀ = rho ₓ A ₓ v
where rho is the density of the fluid, A is the cross-sectional area of the pipe, and v is the velocity of the fluid.
Substituting the given values, we have:
m₀ = 680 kg/m³ ₓ π ₓ (0.02 m / 2)² ₓ 4.00 m/s
m₀ = 0.0215 kg/s
Since the mass flow rate is constant along the pipe, we can use this to find the cross-sectional area of the narrow section of the pipe.
m₀ = rho ₓ A ₓ v
A ₓ v = m₀/ rho
The velocity of the fluid in the narrow section can be found using the Bernoulli's equation, which states that the pressure and kinetic energy of an incompressible fluid are related. The equation can be written as:
P + 1/2 ₓ rho ₓ v² = constant
Since the two sections are at the same height, the gravitational potential energy of the fluid is the same in both sections, and we can ignore it. Therefore, we have:
\(P_{wide}\) + 1/2 × rho × \(v_{wide}\)² =\(P_{narrow}\)+ 1/2 ₓ rho ₓ \(v_{narrow}\) ²
where \(P_{wide}\) is the pressure of the fluid in the wide section,\(P_{wide}\) is the velocity of the fluid in the wide section, \(P_{narrow}\) is the pressure of the fluid in the narrow section, and \(P_{narrow}\) is the velocity of the fluid in the narrow section.
Since we want to find the diameter of the narrow section for the pressure of the fluid in the narrow section to be equal to the pressure of the wide section, we can set \(P_{narrow}\) equal to \(P_{wide}\) and solve for v_narro\(v_{narrow}\)w:
\(v_{narrow}\) = \(\sqrt{}\)(\(v_{wide}\)² + 2 * (\(P_{wide}\) / rho))
Substituting the given values, we have:
\(v_{narrow}\) = √((4.00 m/s)+ 2 × (200 kPa / 680 kg/m³))
\(v_{narrow}\) = 5.73 m/s
Now we can solve for the cross-sectional area of the narrow section of the pipe:
\(A_{narrow}\) = m₀/ (rho * \(v_{narrow}\))
Substituting the given values, we have:
\(A_{narrow}\) = 0.0215 kg/s / (680 kg/m³ * 5.73 m/s)
\(A_{narrow}\) ≈ 6.50 * 10⁻⁵ m³
Finally, we can solve for the diameter of the narrow section of the pipe:
\(d_{narrow}\) = √(4 × \(A_{narrow}\) / π)
Substituting the calculated value of A_narrow, we have:
\(d_{narrow}\) = sqrt(4 * 6.50 * 10⁻⁵ m² / π)
\(d_{narrow}\) = 0.0110 m
\(d_{narrow}\) = 1.10 cm
Therefore, the diameter of the narrow section of the pipe for the pressure of the fluid in the narrow section to be equal to the pressure of the wide section is approximately 1.10 cm.
To know more about principle of continuity of flow
https://brainly.com/question/30890204
#SPJ4
Related Questions
Two children pull a 320 kg sled on an ice rink - Child A pulls with a force of 450 N [S 15° E]
while child B pulls with 380 N [W].
If the sled starts from rest, how far will it go in 2.0s, and in what direction?
Please add a diagram!
Answers
Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt. This allows you to measure how fast velocity changes in meters per second squared (m/s^2).
How do you calculate frictional force pulling?The resistive force of friction (Fr) divided by the normal or perpendicular force (N) pushing the objects together yields the coefficient of friction (fr), which is a numerical value. The formula fr = Fr/N serves as a representation of it.
The force of gravity acting on an object is known as its weight, and it can be determined using the formula w = mg, which equals the mass times the acceleration of gravity. The newton is the SI unit for weight since it is a force.
The formula F = m a, where F the is the force acting on the object, m is the object's mass, and an is the acceleration, can be used to express Newton's second equation of motion. This formula's subject, m, must be changed in order to get the object's mass.
To learn more about frictional force pulling refer to :
https://brainly.com/question/29441368
#SPJ1
HELP me need it asap
Answers
Answer:
D, D, A, C, D
Explanation:
A pitcher throws a baseball horizontally from the mound to home plate. The ball falls 0. 857 m (2. 81 ft) by the time it reaches home plate 18. 3 m (60 ft) away. How fast was the pitchers pitch.
Answers
Answer:
Baseball is commonly expressed in English units - we'll use that
(Rubber to home plate is 60' 6 '' but the ball is probably released at about 60 ft)
t = S / v time of fall and time to reach plate
H = 1/2 g t^2
t = (2 H / g)^1/2 we'll use 32.,2 ft / sec^2 for g
t = (2 * 2.81 / 32.2)^1/2 = .418 sec
v = 60 ft / .418 sec = 144 ft/sec
Since 60 mph = 88 ft/sec
v = 144 / 88 * 60 = 98 mph
How long would a simple pendulum need to be to have a period of 1. 0s.
Answers
Answer:
0.248 m
Explanation:
a stone is dropped from the top of a tower 400 m high and at the same time another stone is projected upward vertically from the ground with a velocity of 100 m/s. find where and when the two stones will meet.
Answers
Answer:The stones will be at the same height of 62.59 feets 4.4 seconds later.
Explanation:
An engineer is designing a runway for an airport. Several planes will use the runway and the
engineer must design it so that it is long enough for the largest planes to become airborne before the
runway ends. If the largest plane accelerates at 3.30 m/st and has a takeoff speed of 88.0 m/s, then
what is the minimum allowed length for the runway?
Answers
The minimum allowed length for the runway is 1170m.
a=3.30m/s2 is the acceleration of the plane
v=88.0 m/s is the final velocity of the plane
u=0m /s is the initial velocity of the plane
The acceleration of the object is the slope of the v-t graph, therefore,
Slope=Change in y component / Change in the x component
a = u- v / T f - T i
T f - T i = v/a
T f - T i = 88/3.3
T f - T i = 26.67 s
The displacement,
d=1/2 b h
d=1/2(T f - T i ) * v
d = 1/2 * 26.67 s * 88.0 m / s
d = 1173.33
= 1170m nearest three significant figures
Hence, the minimum allowed length for the runway is 1170m answers.
Learn more about length here:-https://brainly.com/question/2217700
#SPJ9
How do you think the switch controls the flow of current to the light?
Answers
Answer:
A switch interrupts the flow of current in a circuit.
Explanation:
7. The English Channel is 35 km wide at its narrowest point, which is where most swimmers attempt to cross north to south from England to France. The current across this portion of the English Channel runs at about 2 km/h east to west.
a. If a swimmer has a relative velocity to the shore of 3 km/h north to south, how long will it take her to cross the 35 km distance?
b. What must be her velocity relative to the water if she has a velocity of 3 km/h north to south relative to the shore?
Answers
Answer:
a. 10 hours
b. Approximately 4.03 km/h to shore
Explanation:
The width of the English Channel at the narrowest point = 35 km
The speed of the current across the English Channel across the narrowest point = 2 km/h
a. The relative velocity of the swimmer north to south = 3 km/h
Therefore, the the time it would take the swimmer to swim north to south will be given as follows;
Time = Distance/Velocity = 35 km/(3.5 km/h) =10 hours
The time it would take = 10 hours
It would take 10 hours for her to cross the 35 km distance
b. Given that she has a relative velocity of 3 km/h north to south, we have;
The magnitude of her relative velocity to shore = √((Her relative velocity north to south)² + (The velocity of the English Channel east to west)²)
∴ The magnitude of her relative velocity to shore = √(3.5² + 2²) = (√65)/2 km/h
The magnitude of her relative velocity to shore ≈ 4.03 km/h
a projectile is fired from a tank with initial speed 400 m/s. find two angles of elevation that can be used to hit a target 3000 m away
Answers
A projectile is fired from a tank with initial speed 400 m/s,the two angles of elevation that can be used to hit the target 3000 m away are approximately 0.144 radians (or 8.26 degrees) and 2.997 radians (or 171.74 degrees).
To find the two angles of elevation that can be used to hit a target 3000 m away, we can use the equations of projectile motion. The angles of elevation correspond to the launch angles at which the projectile will reach the target.
Let's denote the initial speed of the projectile as v0 = 400 m/s and the horizontal distance to the target as R = 3000 m.
The horizontal and vertical components of the projectile's velocity are given by:
Vx = v0 * cos(theta)
Vy = v0 * sin(theta)
where theta is the launch angle.
The time of flight, T, is determined by the vertical motion of the projectile and can be calculated using the equation:
T = (2 * Vy) / g
where g is the acceleration due to gravity (approximately 9.8 m/s²).
The horizontal range, R, is determined by the horizontal motion of the projectile and can be calculated using the equation:
R = Vx * T
Substituting the expressions for Vx and T, we have:
R = v0 * cos(theta) * [(2 * v0 * sin(theta)) / g]
Simplifying the equation, we get:
R = (2 * v0^2 * sin(theta) * cos(theta)) / g
Now we can solve this equation to find the launch angles theta that satisfy the given range R.
Rearranging the equation, we have:
sin(2 * theta) = (R * g) / (2 * v0^2)
Taking the inverse sine of both sides, we get:
2 * theta = arc sin((R * g) / (2 * v0^2))
theta = (1/2) * arc sin((R * g) / (2 * v0^2))
Now we can substitute the given values to calculate the two angles of elevation:
theta₁ = (1/2) * arc sin((R * g) / (2 * v0^2))
theta₂ = π - theta₁
where π is the value of pi (approximately 3.14159).
Substituting the values, we have:
theta₁ = (1/2) * arc sin((3000 * 9.8) / (2 * 400^2))
theta₂ = π - theta₁
Calculating the values, we find:
theta₁ ≈ 0.144 radians (or approximately 8.26 degrees)
theta₂ ≈ 3.141 - 0.144 ≈ 2.997 radians (or approximately 171.74 degrees)
Therefore, the two angles of elevation that can be used to hit the target 3000 m away are approximately 0.144 radians (or 8.26 degrees) and 2.997 radians (or 171.74 degrees).
To learn more about projectile visit: https://brainly.com/question/24216590
#SPJ11
. True/False mass is a fundamental Quantity
2. True/False the unit of density is g/cm3
3. True/False to convert from mm to cm, one must multiply by 10
4. True/False a micrometre screw gauge can measure the lengths greater than 3 cm
5. True/False the Vernier calliper can be used to measure small depths
6. True/False the mass of the bob affects the period of oscillation of a pendulum
7. True/False systematic error can be corrected by repeating the experiment
8. True/False a graph that rises from left to right would have a positive gradient
9. True/False gradient can be calculated using the formula rise over run
10. True/False acceleration is defined as the rate of change of displacemen
Answers
Answer:
truefalsefalsetruesorrtrue I really sorry I can't give answer because I don't know answer The fluid inside the hydraulic jack has a pressure of 30,000 Pa. If the surface of
the piston that is used to lift an object is 0.1 m’in area, how much weight can
the jack lift?
Answers
Explanation:
p = F /A
F = P×A
F = 30,000 Pa / 0.1 m²
F = 300,000 N
Dean Potter is known for slacklinging across a 915 metter deep ravine in Yosemite National Park with no safety gear. If his mass is 77 kg, how much potential energy did he have?
Answers
Explanation:
answer 689910
M x G x H
mass = 77
G= 9.8
Meter = 915 this is the height
77 x 9.8= 754.6
754.6 X 915 = 689910 J
Dean Potter is known for slacklining across a 915-metter deep ravine in Yosemite National Park with no safety gear. If his mass is 77 kg then he has the potential energy of 691163.55 Joules
What is mechanical energy?As total mechanical energy is the sum of all the kinetic as well as potential energy stored in the system.
ME = KE + PE
As given in the problem Dean Potter is known for slacklining across a 915-meter deep ravine in Yosemite National Park with no safety gear. If his mass is 77 kg,
m =77 kg
h = 915 m
the total potential energy of the dean potter can be calculated withe the help of the formula of the potential energy
PE = mgh
PE = 77*9.81*915
PE = 691163.55 Joules
Thus, he would have the potential energy of 691163.55 Joules
Learn more about mechanical energy from here
brainly.com/question/12319302
#SPJ2
Which of the following words BEST describes scientists’ current knowledge about the universe?
eternal
static
unpredictable
changing
Answers
Answer:
your answer is changing
Explanation:
which eletromagnetic waves have the lowest frequency radio waves micro waves x rays or gamma rays
Answers
Answer: Radio waves have the lowest energies, longest wavelengths, and lowest frequencies of any type of EM radiation. In order from highest to lowest energy, the sections of the EM spectrum are named: gamma rays, X-rays, ultraviolet radiation, visible light, infrared radiation, and radio waves.
Explanation:
What does the area of an acceleration time graph represent?
Answers
The area under the acceleration time graph represents change in velocity
The graph is plotted with acceleration on the vertical axis and time on the horizontal axis. The area under such graph represents change in velocity
The area of an acceleration- time graph represents the change in velocity. The pace at which a body's velocity varies is represented by acceleration, which is a vector quantity.
What is acceleration?The rate of change of velocity with respect to time is known as acceleration. According to Newton's second law, the eventual effect of all forces applied to a body is its acceleration.
The formula for acceleration is;
\(\rm a = \frac{v-u}{t}\)
u is the initial speed
v is the final speed
t is the time interval
a is the acceleration of a ball
Hence the area of an acceleration- time graph represents the change in velocity.
To learn more about the acceleration refer to the link;
https://brainly.com/question/2437624
#SPJ4
Why is the heliocentric model not correct
Answers
Answer:
Um, wrong.
Explanation:
The Helioentric model is correct. We orbit the sun. The GEOcentric model is incorrect. The Universe does not orbit the Earth. What are you learning?
Some environmental factors are studied by the use of: telescopes electroscopes astrolabes space satellites
Answers
Some environmental factors are studied by the use of space satellites.
Space satellites are used to study various environmental factors and phenomena from space. These satellites are equipped with advanced instruments and sensors that allow scientists to observe and collect data on different aspects of the Earth's environment.
Satellites provide valuable information about the Earth's atmosphere, weather patterns, climate change, land use, ocean currents, and many other environmental factors.
They can monitor changes over time, track pollution levels, measure temperature variations, and study the interactions between different components of the environment.
By orbiting the Earth, space satellites can capture high-resolution images, gather data on different wavelengths of light, measure atmospheric composition, and monitor the planet on a global scale.
The data collected by these satellites is crucial for understanding and managing various environmental issues, such as deforestation, air pollution, natural disasters, and climate change.
Telescopes, electroscopes, and astrolabes are not specifically designed for studying environmental factors. Telescopes are primarily used for astronomical observations, electroscopes measure electric charge, and astrolabes were historically used for celestial navigation.
While they have their own applications and significance, they are not primarily employed for studying environmental factors as space satellites are.
To learn more about electroscopes, refer below:
https://brainly.com/question/31030885
#SPJ11
Answer:
Space satellites
Explanation:
As I promised, this is the answer!! I have checked and reviewed to make sure this is the correct answer, and it is!! Good Luck to everyone who views this question in the future:)
pls help will mark brainliest
Answers
Answer: a!! Bc 10x2=20!
Explanation:
Answer:
20N
Explanation:
F=m*a
F=10*2
F=20N
.....
How many newtons does a 5-kg backpack weigh on Earth?
Answers
What is the formula for calculating mass?
Answers
Mass may be determined using the formula: mass = volume density. The gravitational force acting on a mass is quantified by its weight. The "kilogramme" is the kilogramme, which is the SI unit of mass. Weight in the SI is measured in Newtons (N).
With Newton's law, how do you calculate mass?If we are aware of the acceleration and force of the item, we may use Newton's Second Law of Motion to determine its mass. With this in mind, force is equal to mass times acceleration. We can thus calculate the mass of the item in issue by dividing the force by the acceleration.
The response force applied to a mass-containing object by the ground or a plane is known as the normal force.
learn more about gravitational force\
https://brainly.com/question/27943482
#SPJ4
The formula for calculating mass is Mass = volume × density
Mass = volume density is a formula that can be used to calculate mass. The weight of a mass serves as a measure of the gravitational force exerted on it. The SI unit of mass known as the kilogram is referred to as the "kilogramme". The SI uses Newtons to measure weight (N).
How do you determine mass using Newton's law?Newton's Second Law of Motion can be used to calculate an object's mass if we know its acceleration and force. In light of this, force is defined as mass times acceleration. Hence, by dividing the force by the acceleration, we can get the item's mass.
The reaction force applied to a mass-containing object by the ground or a plane is known as the normal force.
To learn more about mass from given link
https://brainly.com/question/28853889
#SPJ4
The amount of current produced by electromagnetic induction depends not only on the induced voltage but also on the resistance of the coil and the circuit to which it is connected.
True or False
Answers
True. The amount of current produced by electromagnetic induction depends on the induced voltage, the resistance of the coil, and the circuit to which it is connected.
The induced voltage is the voltage that is created in the coil by the changing magnetic field. The resistance of the coil is the opposition to the flow of current in the coil. The circuit to which the coil is connected determines the amount of current that can flow through the coil.
The current in the coil is given by the following equation:
I = E/R
where:
I is the current in the coil
E is the induced voltage
R is the resistance of the coil
The amount of current that can flow through the coil is limited by the resistance of the coil and the circuit to which it is connected. If the resistance of the coil is high, then the current will be low. If the circuit to which the coil is connected has a low resistance, then the current will be high.
The amount of current produced by electromagnetic induction can be increased by increasing the induced voltage, decreasing the resistance of the coil, or connecting the coil to a circuit with a low resistance.
To learn more about electromagnetic induction click here: brainly.com/question/32444953
#SPJ11
Table salt is made up of one sodium atom and one chlorine atom. Is table salt an element
Answers
An elevator accelerates from rest to a velocity of 12.0 m/sec as it rises 28.0 meters. What was its’ acceleration, and for what time did it travel while it was accelerating?
Answers
Answer:
given that
V = 12.0 m/s
U = 0 m/s
s = 28 m
Explanation:
using the equation of motion
V^2 = U^2 + 2as
12^2 = 0 + 2(28)a
144 = 56a
a = 5.5 m/s^2
v = u +at
12 = 0 + 5.5t
12 = 5.5t
t = 2.2s
Explain the mechanism that is responsible for the formation of snowflakes.
Answers
The mechanism that is responsible for the formation of snowflakes is the nucleation of ice crystals.
What is a Snowflake?This is defined as a piece of snow which falls from the sky as a result of an extremely cold climate condition and is common in the arctic regions of the world.
Snow flakes are formed when ice crystals stick together to form the flakes which usually has a dust or pollen being formed around the area being talked about.
This is also regarded as a type of precipitation such as rain etc and is therefore the most appropriate choice.
Reads more about Snowflake here https://brainly.com/question/15919831
#SPJ1
1.
If a truck that is traveling at 15 mph speeds up to 45 mph in 10 seconds, what is the truck’s acceleration? HELP me please!!!! this is a QUIZ!!!!
Answers
Answer:
3mph
Explanation:
a=v(final)-v(initial)/t
=45-15/10
=30/10
=3mph
Answer:
3mph
Explanation:
Rock B ha a ma of 100 kg and i travelling at 7 m/ in the ame direction a rock A. Rock B ha a momentum of 700 kg m/. Rock A and rock B collide and join together. Calculate the velocity of the two rock after the colliion. Show your working.
Answers
Velocity is 700kg.If you know the other values of an object's properties, you may determine its momentum or velocity using the momentum equation p is m•v.
After two objects collide, how can you determine their respective velocities?Equation v′=m1v1+m2v2m1+m2 m1 is the mass of object 1, v1 is the initial velocity of item 1, m2 is the mass of object 2, and v2 is the starting velocity of object 2, with v′ = m 1 v 1 + m 2 v 2 m 1 + m 2. v' is the final velocity of the two objects once they move as one unit following the collision.If you know the other values of an object's properties, you may determine its momentum or velocity using the momentum equation p = m•v.If a particle A with mass m is travelling toward a particle B that is stationary with velocities u from infinity, collides with B with final velocities v, and then deflects away with final velocities v, then VR=v- u is the particle's relative velocity.
Explanation:
m*v =100 * 7 = 700 kg.
To learn more about velocity refer to:
https://brainly.com/question/25749514
#SPJ4
Your best friend comes to you with a problem: He is not doing well in school because he has too much going on after school. He wants to improve his grades without giving up his after-school activities. What are the three general time-management techniques that you can suggest to him?
Answers
Answer:
1. Schedule your activities
2. Prioritize the more important tasks
3. Avoid procrastination
Explanation:
Time-management techniques are strategies or methods developed by people to help them effectively manage their time. My best friend in the scenario above cannot effectively manage his time because he has a lot of activities crowding up his time.
To get better in his grades, he should strike a balance between school work and extracurricular activities. He should make a workable schedule where only the most important tasks are prioritized. He should also learn to execute these tasks on time without postponing them.
Answer:
Sample Response: He should decide on a study time that works best for him, create a study schedule, and manage his study sessions by using a daily to-do list
Explanation:
got it right on edge 2021
Calculate the angular separation θ1 at which two point sources of wavelength 600 nanometers are just resolved when viewed through a circular aperture of diameter 1. 5 centimeters.
Answers
The angular separation is \(4.88 * 10^{-5} rad\)
What is angular distance formula?
The formula is θ=s/r, where, θ is Angular Displacement, s is the distance traveled by the body, and. r is the radius of the circle along which it is moving.
What is meant by angular resolution?
The angular resolving power (or resolution) of a telescope is the smallest angle between close objects that can be seen clearly to be separate. Resolution is limited by the wave nature of light.
The angular separation is calculated as given below.
θ = 1.220 λ/d
Where λ is the wavelength and d is the diameter of the lens aperture.
θ1 = \(1.220 * \frac{600 * 10^{-9} }{1.5 * 10^{-2} }\)
= 4.88 × \(10^{-5}\) rad
Therefore, The angular separation is 4.88 × \(10^{-5}\) rad.
Learn more about angular separation
brainly.com/question/14471998
#SPJ4
A 14 kg boulder is pushed off a cliff with velocity v = ( 14.0 m/s ) + ( 2.0m/s ) y . Will the object experience a larger vertical or horizontal acceleration?
Answers
The object will eventually experience a large vertical acceleration since the vertical velocity increases as the object moves downwards.
What is horizontal motion of a projectile?The horizontal motion of a projectile is the motion of the projectile along a horizontal path.
The horizontal distance of a projectile is not affected by gravity and hence the horizontal speed of a projectile remains constant. That is the initial horizontal velocity is equal to the final horizontal velocity of the projectile.
However, the during the vertical motion an object, the vertical velocity decreases as the object moves upwards and eventual becomes zero when the object reaches the maximum height.
As the object begins to move downwards the vertical velocity increase and eventually become maximum before the object hits the ground.
Learn more about vertical acceleration here: https://brainly.com/question/8564131
#SPJ1
An object travels 8 meters in the first second of travel, 8 meters again during the second second of travel, and 8 meters again during the third second. Its VELOCITY in meters per second is O 0 0 5 O 8 O 10 O more than 10 MARE
Answers
Answer:
V = (S2 - S1) / t
V = 8 m / 1 s = 8 meters /second