The pressure difference, , across a partial blockage in an artery (called a stenosis) is approximated by the equation where is the blood velocity, the blood viscosity , the blood density , the artery diameter, the area of the unobstructed artery, and the area of the stenosis. Determine the dimensions of the constants and . Would this equation be valid in any system of units

Answers

Answer 1

The question is incomplete. The complete question is  :

The pressure difference, Δp, ac[tex]K_u[/tex]ross a partial blockage in an artery (called a stenosis) is approximated by the equation :

[tex]$\Delta p=K_v\frac{\mu V}{D}+K_u\left(\frac{A_0}{A_1}-1\right)^2 \rho V^2$[/tex]

Where V is the blood velocity, μ the blood viscosity {FT/L2}, ρ the blood density {M/L3}, D the  artery diameter, [tex]A_0[/tex] the area of the unobstructed artery, and A1 the area of the stenosis.  Determine the dimensions of the constants [tex]K_v[/tex] and [tex]K_u[/tex]. Would this equation be valid in any  system of units?

Solution :

From the dimension homogeneity, we require :

[tex]$\Delta p=K_v\frac{\mu V}{D}+K_u\left(\frac{A_0}{A_1}-1\right)^2 \rho V^2$[/tex]

Here, x means dimension of x. i.e.

[tex]$[ML^{-1}T^{-2}]=\frac{[K_v][ML^{-1}T^{-1}][LT^{-1}]}{[L]}+[K_u][1][ML^{-3}][L^2T^{-2}]$[/tex]

                    [tex]$=[K_v][ML^{-1}T^{-2}]+[K_u][ML^{-1}T^{-2}]$[/tex]

So, [tex]$[K_u]=[K_v]=[1 ]=$[/tex] dimensionless

So, [tex]K_u[/tex] and [tex]K_v[/tex]  are dimensionless constants.

This equation will be working in any system of units. The constants [tex]K_u[/tex] and [tex]K_v[/tex] will be different for different system of units.


Related Questions

What is average speed???​

Answers

Answer:

total distance dibide by total time

Two wires made of the same material are connected in parallel
across the mains. The length and radius of one wire is two
times that of the other wire. If heat produced in the shorter wire
is 100 J, then the heat produced in the longer wire is:-
O A. 100 J
B. 180 J
O C. 2003
O D. 420 J​

Answers

Answer:

The heat produced in the longer wire is 200 J.

Explanation:

When the two wires are connected in parallel then the voltage across both the wires is same.

Let the length of the second wire is L and the radius of the second wire is R.

The length of the first ire is 2L and the radius of the first wire is 2R.

Heat produced in the second wire is 100 J.

Let the heat produced in the first wire is H'.

The resistance of the wire is proportional to length of the wire and inversely proportional to the area of the wire.

[tex]\frac{R_2}{R_1}=\frac{L\times \pi\times 4R^2}{2L\times \pi\times R^2}\\\\\frac{R_2}{R_1}=2[/tex]

The heat produced is given by

[tex]H=\frac{V^2}{R}\\\\\frac{H_1}{H_2}=\frac{R_2}{R_1}\\\\\frac{H_1}{100}=2\\\\H_1=200 J[/tex]

An effort of 20N is applied to lift a load.If the load arm and effort arm are 15cm and 60cm respectively,calculate the load.​

Answers

Answer:

Load = 80 Newton

Explanation:

Given the following data:

Effort = 20 N

Load arm = 15 cm

Effort arm = 60 cm

Conversion:

100 cm = 1 meters

15 cm = 15/100 = 0.15 meters

60 cm = 60/100 = 0.6 meters

To calculate the load, we would use the expression;

Effort * effort arm = load * load arm

Substituting into the expression, we have;

20 * 0.6 = load * 0.15

12 = load * 0.15

Load = 12/0.15

Load = 80 Newton

What is the position and kind of image produced by the lens below?

Complete the ray diagram to support your answer.​

Answers

The answer is convex image

Paco was driving his scooter west with an initial velocity of 4 m/s. He accelerates at 0.5 m/s2 for 30 seconds. What is his final velocity?

Answers

Answer:

19m/s

Explanation:

U= 4m/s

a = 0.5m/s²

t= 30s

V= U+at

= 4+15

=19m/s

which type of material is the best sound absorber?
a. glass
b. wood
c. concrete
d. carpet​

Answers

Explanation:

Glass is the best sound absorber material.

A car and a large are moving with the same velocity. Which of the two is more difficult to

slow down? Why?


(Serious Answers Please)​

Answers

Whichever object has more mass will need more energy to slow it down.

We don't know the mass of the car or the mass of the large.

None of this has anything to do with "difficult". We don't know what's difficult for you, and we don't know the SI unit of "difficult".

A 1500 kg truck travelling north at 60 km/hr collides with a 1200 kg car moving east at 15km/hr. If the two cars remain locked together after impact, with what velocity do they move immediately after the collision.​

Answers

Answer:

33.33j+6.67i km/hr

Explanation:

From the law of conservation of momentum,

Applying,

mu+m'u' = V(m+m')............... Equation 1

Where m = mass of the truck, m' = mass of the car, u = initial velocity of the truck, u' = initial velocity of the car, V = Final velocity.

Note: let j represent the north, and i  represent the east

From the question,

Given: m = 1500 kg, u = 60j, m' = 1200 kg, u' = 15i

Substitute these values into equation 1

1500*60j+1200*15i = V(1500+1200)

90000j+18000i = 2700V

V = (90000j+18000i)/2700

V = 33.33j+6.67i km/hr

True or false please help I’ll give brainliest

Answers

Answer:

1 is false 2 is true 3 is false

Mr. Tolman believes that our universe is expanding, but with all of the gravitational force from the celestial bodies of space, the universe will begin to contract. He believes in the _____.

A) oscillating universe theory
B) inflation theory
C) steady state theory
D) big bang theory

Answers

The correct answer is A I believe but I may not be correct. Either A or B

What is the difference between circular and rotatory motion?​

Answers

Answer:

In a circular motion, the object just moves in a circle. In rotational motion, the object rotates about an axis. ... For example, Earth rotating on its own axis.

Answer:

Its different

Explanation:

it's different because

What are the poles of a bar magnet.is it North West South or east.​

Answers

Answer:

One end of any bar magnet will always want to point north if it is freely suspended. This is called the north-seeking pole of the magnet, or simply the north pole. The opposite end is called the south pole.

Explanation:

Answer:

North Pole and South Poles

Explanation:

There is no east or west in a magnetic field of a magnet. The magnetic field lines comes from North pole to south pole.

VI. A student attaches four drawing pins to a copper rod using candle wax as shown in the diagram
The rod is then heated continuously at one end and the pins fall off in the order 4, 3, 2, 1​

Answers

Explanation:

[tex]C.) \: Conduction \: \\ \\ = > it \: is \: a \: process \: of \: transferring \: \\ \\ of \: heat \: from \: one \: object \: to \: another \\ \\ when \: they \: are \: in \: contact \: [/tex]

By the conduction process the heat reaches the pin.Option C is correct.

What is heat transfer?

The term "heat transfer" refers to the movement of heat. The flow of heat across a system's boundary is due to a temperature differential between the system and its surroundings.

Conduction is the type of heat transfer occurs mainly in solid or by contact.In the given condition the rod is then heated continuously at one end and the pins fall off in the order 4, 3, 2, 1​.

By the conduction process the heat reaches the pin.

Hence option C is correct.

To learn more about the heat transfer refer to the link;

https://brainly.com/question/13433948

#SPJ2

B
oc
OD
A metal has a specific heat capacity of 360J/(kg°C).
An object made of this metal has a mass of 2.0kg.
What is the thermal capacity (heat capacity) of the object?

Answers

Answer:

Thermal capacity of the object = 720 j/°C

Explanation:

Given:

Specific heat capacity of metal = 360J/(kg°C)

Mass of given object = 2 kg

Find:

Thermal capacity of the object

Computation:

Thermal capacity = Specific heat x Mass

Thermal capacity of the object = Specific heat capacity of metal x Mass of given object

Thermal capacity of the object = 360 x 2

Thermal capacity of the object = 720 j/°C

HELPPPPPPPP!!!!! PLZZZ

Answers

Answer:

1- 31.25

2-?

3-?

Explanation:

1. 31. 25m/s
2.200

Thanks me later..

The symbol for the hydroxide ion is
Он*
Оно
ОН(ОН)
ООН
NEXT QUESTION
ASK FOR HELP

Answers

It is OH and it has a charge of negative 1

Jenny is doing her homework when Jenny writes, the pencil exerts a force of 5N on the paper. The area of the pencil in contact with the paper is 0.5mm2 calculate the pressure of the pencil in the paper give the unit

Answers

Answer:

here is your answer

mark me as brainlist

Force=5N
Area(m)=0.0005
Pressure=1000Pa(m)
=100Pa(cm)

In an experiment, 120 g of ice at 0 °C is to be melted. The specific latent heat of
ice is 340 J/g. Assume that all the energy from the heater will be used to melt
the ice.
Q1) Calculate the expected time for which the 60 W heater is switched on.​

Answers

Answer:

[tex]680\; \rm s[/tex].

Explanation:

Start by finding the total amount of energy required for melting that much ice.

[tex]\begin{aligned}&\text{Energy required for melting ice sample} \\ &= \text{Mass of Ice} \times \text{Specific Latent Heat of Ice} \\ &= 120\; \rm g \times 340\; \rm J \cdot g^{-1} = 4.08 \times 10^{4}\; \rm J \end{aligned}[/tex].

Hence, the heater would need to supply (at least) [tex]4.08 \times 10^{4}\; \rm J[/tex] of energy.

The power of the heater is [tex]60\; \rm W[/tex], which is equivalent to [tex]60\; \rm J \cdot s^{-1}[/tex], In other words, the heater is rated to supply [tex]60\; \rm J[/tex] of energy every second.

Amount of time it takes for the heater to supply [tex]4.08 \times 10^{4}\; \rm J[/tex] at [tex]60\; \rm J \cdot s^{-1}[/tex]:

[tex]\begin{aligned}\frac{4.08 \times 10^{4}\; \rm J}{60\; \rm J \cdot s^{-1}} = 680\; \rm s\end{aligned}[/tex].

Hence, it would take [tex]680\; \rm s[/tex] for the heater to melt the ice if the heater is insulated, and all the energy from the heater went to the ice.

WILL MARK BRAINLIEST

Answers

Answer:

152,155 J

Explanation:

115,333 + 36,822 = 152,155J

if a current of 0.3 ampere flows through a conductor of resistance of 11.7 ohm's,the voltage across the ends of the conductor is what​

Answers

Here,

Resistance = 11.7

Ampere = 0.3

Voltage = ?

Now,

R = V/A

11.7 = V/0.3

11.7*0.3 =V

V = 3.51

I hope it's help you...

Mark me as brainliest...

The length of second hand of clock is 14cm, an ant sits on the top of second hand. find the following
i) speed of ant
ii) distance covered by ant in 150 seconds
iii) displacement in 150 seconds

Answers

Answer:

i) v = 1.47 cm/s

ii) distance = 219.8 cm

iii) displacement = 28cm

Explanation:

Remember that:

The motion of the tip of the second hand is a circular motion.

For something that rotates with an angular frequency ω, and a radius R, the velocity is given by:

v = ω*R.

i) We know that the second hand of a clock does a complete rotation each 60 seconds.

Then the period is:

T = 60s

And the frequency is the inverse of the period, so:

f = 1/T

f = (1/60s)

And the angular frequency is 2*pi times the normal frequency, thus:

ω = 2*pi*f

ω = 2*pi*(1/60s)  = (2*pi/60s)

And the radius will be 14 cm, the velocity of the ant is:

v = (2*pi/60s)*14cm

if we replace pi by 3.14 we get:

v =  (2*3.14/60s)*14cm = 1.47 cm/s

ii) The distance covered by the ant in 150 seconds:

Remember that the period of the clock is T = 60s

so in 150 seconds we have:

150s/60s = 2.5 revolutions.

Then the total distance covered is 2.5 times the perimeter of a circle of radius R = 14cm, this is:

distance = (2.5)*2*pi*14cm

              = (2.5)*2*3.14*14cm = 219.8 cm

iii) We want to know the displacement, this is, the difference between the final position and the initial position.

In 150 seconds, the ant does 2.5 revolutions.

So the ant will end in the opposite side of the circle where she started (if the ant started when the second hand was at the "3", then the final position is when the second hand is at the "9").

So the displacement will be equal to twice the radius, or the diameter of the circle.

if the radius is 14cm, the diameter is:

2*14cm = 28cm

the displacement is 28cm

In which of these media will mechanical waves travel the slowest in?
a Plastic
b Butter
C Ice
d Air
e Steel

Answers

Answer:

E

Explanation:

it has more mass

The medium in which mechanical waves will travel the slowest in is air which is gaseous medium.

What is mechanical wave?

A mechanical wave is a type of wave that requires material medium for its propagation.

An example of mechanical wave is sound wave because sound wave requires material medium for its propagation.

Sound waves travel fastest in solid, followed by liquid, then least in gasous medium.

Thus, the medium in which mechanical waves will travel the slowest in is air which is gaseous medium.

Learn more about mechanical waves here: https://brainly.com/question/9242091

A current of 17 A flows through a resistor of 10 2. What is the voltage
across the resistor

Answers

Ohms law V = IR

17 x 10 = 170V

En una sala de juntas hay mesas, sillas y otras personas. ¿Cuál de ellas tienen temperaturas
a) menores, b) mayores y d) iguales que la del aire?

Answers

Answer:

table and chair

Explanation:

In a meeting room there are tables, chairs, and other people. Which of them have temperatures

a) smaller, b) bigger and d) equal to that of air?

the temperature of tables and chairs is same as air.

a cell of EMF 1.5 volt is connected in series with a resistor of Resistance 3 ohms a high resistance voltmeter connected across the cell registers 0.9 volt calculate the internal resistance of the cell ​

Answers

Answer:

0.6 resistance

What is shunt resistance? How does it help in measuring current?​

Answers

Answer:

it helps me

Explanation:

:))) ...

....

Is it safe to travel to the moon in a total lunar eclipse ? If you answer I will mark you as BRAINLIEST​

Answers

Answer:

Yes. The area around you would be a bit red I think.

4. Alcohol of mass 21g and density 0.7gcm-3 is mixed with 10g of water. Determine the density
of the mixture. (density of water = 1.0g cm-3)

Answers

Answer:

The density of the mixture is 0.775 g/cm³

Explanation:

The given parameters are;

The mass of the alcohol, m₁ = 21 g

The density of the alcohol, ρ₁ = 0.7 g/cm³

The mass of the water with which the alcohol is mixed, m₂ = 10 g

The density of wate, ρ₂ = 1.0 g/cm³

The density of a substance is given by the ratio of the mass to the volume of the substance

The density of the mixture, ρ is given as follows;

[tex]\rho = \dfrac{m_1 + m_2}{\dfrac{m_1}{\rho_1} + \dfrac{m_2}{\rho_2} }[/tex]

Therefore;

[tex]\rho = \dfrac{21 + 10}{\dfrac{21}{0.7} + \dfrac{10}{1.0} } = 0.775[/tex]

The density of the mixture, ρ = 0.775 g/cm³.

Describe how the moment acts in each one of them.
1. Applying a force on the pedal of a bicycle​

Answers

Answer:

Moment is an expression involving the product of a distance and physical quantityA moment is due to a force not having an equal and opposite force directly along it's line of action. ... It is defined as the product of the force (F) and the moment arm (d). The moment arm or lever arm is the perpendicular distance between the line of action of the force and the center of moments.Moments act about a point in a clockwise or anticlockwise direction.

Answer: A ( how to pedal and balance )

Explanation:

A exerted by an object on another is a force

Answers

hope this helps

Answer:

If a person is pushing a desk across the room, then there is an applied force acting upon the object. The applied force is the force exerted on the desk by the person.

Other Questions
25.673 round off to the nearest hundredth An American tourist visits South Africa with $3000. The exchange rate when she arrives is$1 = 12.90. She changes all her dollars into rands and then spends R900 per day for sevendays. She changes the rands she has left back into dollars at a rate of $1 = R12.93. How muchdoes she get in dollars? show your working. you arrive in Mexico City with $360 how many pesos can you buy? Anime fans (sorry for grammar and spelling...) * One Piece fans= During the Dressrosa arc, why were the people being turned into toys, and how were they able to turn back into humans? * Naruto fans= How did Rin (Kakashi's teammate) die, and why? * Boku no Hr Akademia= Why did Kaa-chan (Bakugou) bully Deku (Izuku) when they were younger? At what age did it start?* That time I got reincarnated as a slime fans= How did Satoru Mikami (Rinmuru) die? Where does he wake up, and with whom?* The seven deadly sins fans= What happened to King's sister? And who did he blame? * Attack on titan fans= When was the first time Eren became a titan, and why did he? * Tokyo ghoul fans= What made kaneki's hair go white, and what happened afterward? * Death Note fans= How did Light find the Death note? Who was the first person he killed with it? PLEASE HELP WITH THIS GEOMETRY PROJECT IM GIVING ALL MY POINTS (45) Complete the sentence A _______ spans a geographic area like a city,is larger than a LAN and smaller than WAN describe 2 ways you could increase the efficiency of a household central heating system animais que dependem parcialmente da gua - necessitam de ambientes midos para evitar a dessecao da pele e para botar seus ovos, pois a casca no resistente a perda de gua. a descrio refere-se a qual grupo de vertebrados?a) avesb) mamferosc) rpteisd) anfbiose) peixes pfv ajudem Stomach acid is approximately 0.10 M HCl. How many mL of stomach acid can be neutralized by one regular antacid tablet that contains 500 mg of solid CaCO3 (100.09 g/mol)? Write a single Python regular expression for each of the following. Note: For each problem, you must use only ONE regular expression. Matches a string that has both the substring dog and cat in the string in either order. For instance, both of the following strings match: 'The dog chased the cat' and 'xxcatxxdogxx'. Explain one way that mutual respect is upheldcentral value underpinning life for UK citizens which one is it i thought it was Dictatorship but its not there Which crop did the English started to plant first What is the answer to -4 + 10.Negative 4 plus 10 2^5 + 10=????????????? Contrast how a depositor's account is classified by a bank compared to how it is classified by the account owner by completing the following sentence. A depositor's account is a(n) (liability/asset/expense) on the bank's records, but it is a(n) (liability/asset/expense) on the books of the account owner. Because of this, every time the account owner makes a deposit, the bank (debits/credits) the account owner's account. What sport are you most likely doing if you are in the mountains? el boliche la esgrima el alpinismo el paracaidismo Oregon Forest Products will acquire new equipment that falls under the five-year MACRS category. The cost is $500,000. If the equipment is purchased, the following earnings before depreciation and taxes will be generated for the next six years. Use Table and calculate your final answer using the formula and financial calculator methods. Earnings before DepreciationYear 1 $160,000 Year 2 215,000 Year 3 125,000 Year 4 89,000 Year 5 78,000 Year 6 44,000The firm is in a 20 percent tax bracket and has a 12 percent cost of capital. Calculate the net present value. 15. Which are the ending of the -er/ir verbs in the preterit?+1.i iste io imos ieron2.es iste io imos ieron3.i iste i imomos ieron In convergent evolution, unrelated species or different organisms evolve similar traits, even though they live in different parts of the world.