using the conservation equations in radial co-ordinates, please derive an expression for the pressure distribution in the gap between cylinders chegg
Answers
Conservation equations in radial co-ordinates. The expression for the pressure distribution in the gap between cylinders is given by P = (1/2)ρω²r² + C.
To derive an expression for the pressure distribution in the gap between cylinders using conservation equations in radial coordinates, we can start by considering the radial momentum equation, which states that the radial pressure gradient is balanced by the centrifugal force and the viscous force.
In this case, we assume steady flow and neglect any axial variations. Using these assumptions, the radial momentum equation can be expressed as: ρv(dv/dr) = ρω²r - (1/ r)(dP/dr) - τ
Where ρ is the fluid density, v is the radial velocity, r is the radial distance, ω is the angular velocity, P is the pressure, and τ is the viscous stress term. For a gap between cylinders, we can assume that the angular velocity is constant and the viscous stress term is negligible.
Thus, the equation simplifies to: (1/ r)(dP/dr) = ρω²r Integrating both sides with respect to r, we get: P = (1/2)ρω²r² + C Where C is a constant of integration.
Therefore, the expression for the pressure distribution in the gap between cylinders is given by P = (1/2)ρω²r² + C.
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Related Questions
The owner of a health food store is developing a new product that consists of peanuts and raisins. Raisins cost \$2.50$2.50dollar sign, 2, point, 50 per pound and peanuts cost \$3.50$3.50dollar sign, 3, point, 50 per pound. The owner wants to create 202020 pounds of the product that cost \$3.03$3.03dollar sign, 3, point, 03 per pound. Which of the following systems of equations can be used to determine the number of pounds of peanuts, ppp, and the number of pounds of raisins, rrr, that should be combined?
Answers
Answer:
9.4 pound of raisin and 10.6 pound of peanut is required to make 20 pound of product
Step-by-step explanation:
The cost of raisins is $2.5 per pound and the cost of peanut per pound is $3.50.
Let r represent the number of raisin pound and p represent the number of peanut pound. Since 20 pounds of a new product that consists of peanuts and raisins need to be produced, it can be represented by the equation:
p + r = 20 (1)
The new product would cost $3.03, therefore:
3.5p + 2.5r = 3.03(20)
3.5p + 2.5r = 60.6 (2)
We have to solve equation (1) and (2) simultaneously. First multiply (1) by 2.5 to get 2.5p + 2.5r = 50. Subtract 2.5p + 2.5r = 50 from equation (2):
p = 10.6 pound
Put p = 10.6 in equation (1)
10.6 + r = 20
r = 20 - 10.6 = 9.4
r = 9.4 pound
9.4 pound of raisin and 10.6 pound of peanut is required to make 20 pound of product
Answer:
p + r = 20
\(\frac{3.50p+2.50r}{20}\) = 3.03
Step-by-step explanation:
The total cost of the product when the peanuts and raisins are combined is:
3.50p + 2.50r
To obtain the per pound cost, this expression needs to be divided by the number of total pounds, 20.
\(\frac{3.50p+2.50r}{20} =3.03\)
**KA's explanation**
find the coordinates of the orthocenter for XYZ with X(-5,-1) Y(-2,4), Z(3,-1)
Answers
9514 1404 393
Answer:
(-2, 2)
Step-by-step explanation:
The orthocenter is the intersection of the altitudes. The altitude lines are not difficult to find here. Each is a line through the vertex that is perpendicular to the opposite side.
Side XZ is horizontal, so the altitude to that side is the vertical line through Y. The x-coordinate of Y is -2, so that altitude has equation ...
x = -2
__
Side YZ has a rise/run of -1/1 = -1, so the altitude to that side will be the line through X with a slope of -1/(-1) = 1. In point-slope form, the equation is ...
y -(-1) +(1)(x -(-5))
y = x +4 . . . . . . . . subtract 1 and simplify
The orthocenter is the point that satisfies both these equations. Using the first equation to substitute for x in the second, we have ...
y = (-2) +4 = 2
The orthocenter is (x, y) = (-2, 2).
how to make a percent into a decimal
Answers
Answer:
Divide a percent by 100 and remove the percent sign to convert from a percent to a decimal. The shortcut way to convert from a percentage to a decimal is by removing the percent sign and moving the decimal point 2 places to the left.
Step-by-step explanation:
5.25% = .0525
Kono Dio Da
Answer:
Divide a percent by 100 and remove the percent sign to convert from a percent to a decimal.
Step-by-step explanation:
f(x) = x2 + 1 and g(x) = x2 - 1.Step 1 of 3: Find five ordered pairs that satisfy the function, f(x) = x2 + 1.AnswerHow to enter your answer (opens in new window){(1,0)(C).O.O.O).O.O.O.O.O.O)})C
Answers
To get the ordered pairs that satisfy the function x, we will assign any value to x in order to get corresponding values of f(x).
Since there is no restriction on the values to assign to x from the question,
let x = -4, -2, 0, 2, 4
\(\begin{gathered} when\text{ x = -4} \\ f(x)\text{ = \lparen-4\rparen}^2\text{ + 1} \\ f(x)\text{ = 16 + 1 = 17} \\ \\ when\text{ x = -2} \\ f(x)\text{ = \lparen-2\rparen}^2\text{ + 1} \\ f(x)\text{ = 4+ 1 = 5} \end{gathered}\)\(\begin{gathered} when\text{ x = 0} \\ f(x)\text{ = 0}^2\text{ + 1} \\ f(x)\text{ = 0 +1 = 1} \\ \\ when\text{ x = 2} \\ f(x)\text{ = 2}^2\text{ + 1} \\ f(x)\text{ = 4+ 1 = 5} \\ \\ when\text{ x = 4} \\ f(x)\text{ = 4}^2\text{ + 1 } \\ f(x)\text{ = 16+ 1 = 17} \end{gathered}\)The ordered pair will be written in form: (x, f(x))
\(\lbrace(-4,\text{ 17\rparen, \lparen-2, 5\rparen, \lparen0, 1\rparen, \lparen2, 5\rparen, 4, 17\rparen\textbraceright}\)NEED HELP WITH THIS?
Answers
can see picture but i tried sorry
Solve with elimination please
Answers
Answer:
x = 6
Step-by-step explanation:
6x - 3y = -21 => 6x = 3y - 21
4x = 3y - 9 => 4x = 3y - 9
-2x = -12
-2x/-2 = -12/-2
x = 6
Hope this works
How many km is 1.8 • 10^5 m
Answers
Answer:
180000
by multiplying 1.8 by 10^5 you have to move the decimal point 5 spots to the right since the power is a positive number. 1.8 turns into 180000
What does the data above tell you about the difference in haircut costs between women and men? You may want to discuss similarities or differences in the shape, center, and spread of the data. Explain your reasoning and give mathematical evidence to support any claim that you make.
Answers
The difference shows that woman on average pays higher than men.
What is mean/ average?
Mean is that the average of the given ranges and is calculated by dividing the add of given numbers by the whole number of numbers.
Main body:
The wider range in prices may be due to the higher number of observation.
females have a bigger spread and overall higher cost. 50% of females spend between $20-$75 on a haircut, while 50% of men only spend between $9.25-$20. The median for Female is also significantly higher.
The mean is higher due to the high max valves that are bringing the mean up.
Hence from observing we can say that woman on average pays higher than men.
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acid solution a has a 50% acid concentration, and acid solution b has a 20% acid concentration. how many ounces each of solution a and solution b must be mixed to produce 100 ounces of an acid solution with a 41% acid concentration?
Answers
Solution a needed 70 ounces and solution b needed 50 ounces
What does "1 ounce" mean?
One ounce weighs 437.5 grains or 28.349 grams and is a sixteenth of a pound (avoirdupois) of weight.
One ounce, abbreviated "oz," equals 480 grains, or 31.103 grams, and is one-twelfth of a Troy or Apothecaries' pound in weight. abbreviation for fluid ounce. a tiny amount or percentage.
So, let x=the of ounces of the 50% acid solution. The total volume after both are mixed is 100 ounces so the amount of the 20% solution will be 120-X. The equation will therefore be:
50% * x + 20% * (100-x) = 41% * 100
Dropping the ‘%’ we get
50x + 2000 - 20x = 4100
30x = 2100
x = 2100/30 = 70
Hence 70 ounces will be needed
Solution a = 70 ounces
Solution b = 50 ounces
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with which measurement procedure is the target behavior recorded if it occurs at any point within the scoring interval?
Answers
If the target behavior is recorded whenever it occurs at any point within the scoring interval, the measurement procedure used is called continuous recording or event recording. This method involves observing and recording each instance of the behavior without considering its duration or intensity.
Continuous recording is typically used when the target behavior is discrete and occurs relatively infrequently or has a short duration. With this measurement procedure, each occurrence of the behavior is recorded as a separate event, regardless of when it starts or ends within the scoring interval. Examples of behaviors that can be measured using continuous recording include vocalizations, hand clapping, or instances of aggression.
Continuous recording provides a comprehensive account of the frequency or rate at which the behavior occurs, allowing for a detailed analysis of its occurrence patterns. This method is particularly useful when a precise count of behavior instances is needed and when the duration or intensity of the behavior is not a focus of measurement.
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What is the measure of <7?
Answers
Answer:
26
Step-by-step explanation:
∠5 = 154 {Corresponding angles}
∠5 + ∠7 = 180 {linear pair}
154 + ∠ 7= 180
∠7 = 180 - 154
∠7 = 26
What is the value of x?
Answers
Answer:
x = 68
Step-by-step explanation:
pls mark me as brainliest !!
Andrea bought some clothing on a department store credit card. Her total came to $250. She qualified for interest-free financing. She made a first payment of $35 and agreed to pay $25 twice a month until the $250 balance was paid. How long will it take for Andrea to pay off her bill? Show your work.
Answers
Answer:
A little over 4 months.
Step-by-step explanation:
First, we subtract the first payment she made from the total.
250 - 35 = 215
Now we have $215 left to pay off. She pays $25 off twice a month, so that's $50 a month.
215 ÷ 50 = 4 months, with a remainder of $15 to pay off.
Andrea will have paid it off 5 months later, or 4.5 months since she's paying twice a month, however, assuming this is an answer requiring work and is not multiple choice, my final answer would be a little over 4 months.
PLEASE HELP I WILL GIVE BRAINLIEST
Answers
Answer:
4x^2 B
-4x^2 A
1/4x^2 D
-1/4x^2 C
Step-by-step explanation:
1. Look at the concavity
up or down = negative or positive.
2. number before the x value
if N < 1, it will be wider. if N > 1, it will be thinner.
3. the two most right graphs would be -1/4x^2 and 1/4x^2
the one that is concave down is the - and the concave up is +
HELLLPPP PLEASE WILL GIVE BRAINLIEST
Answers
Answer:
-3
Step-by-step explanation:
Convert every fraction to an improper fraction just to make it easier.
43/10 - (12/5x + 11/2) = 1/2 (-18/5x + 6/10)
Distribute.
= 43/10 -12/5x - 11/2 = -18/10x + 6/10
Simplify using the common denominator, which is 10.
43/10 - 24/10x - 55/10 = -18/10 + 6/10
Isolate the x.
-24/10x + 18/10 = -43/10 + 55/10 + 6/10
Simplify.
-6/10x = 18/10
Multiply by the reciprocal (basically dividing fractions)
18/10 x -10/6
= -3
Answer:
x= -3
Step-by-step explanation:
43/10-12/5x-11/2=9/5x+3/5
-6/5=12/5x=-9/5x+3/5
-6-12x=-9x+3
-3x=9
x=-3
whats the balance point for 3,7,8
Answers
Answer:
The balance point is the,number in between your set of numbers so you need to find The middle of 3 and 7, and then when you get that answer you find the number in between 8 and the,number you just found
Step-by-step explanation:
I'm not good at figuring this out myself but, I know the steps
1.) Evaluate the expression for the given value of the variable. |2x +5|; x = −4
Answers
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
|2(-4)+5| = |-8+5| = |-3|
2. At a store, 3 cents on every dollar spent is charged as sales tax. How much is paid as sales tax on a costume which cost $196.00
Answers
0.3 multiplied by $196.00 gets you $58.8 as sales tax.
Adding that to the $196 dollars, gets you a total sum and amount of $254.80
They paid sales tax on a customer which cost $196.00 is 75 %.
We have given that,
At a store, 3 cents on every dollar spent is charged as sales tax.
What is the sale tax?A sales tax is a tax paid to a governing body for the sales of certain goods and services
0.3 multiplied by $196.00
0.3 *196=58.8
$58.8 as sales tax.
Adding that to the $196 dollars
$58.8+$196=$254.80
Therefore total sum and amount of
=$254.80
Therefore, they paid sales tax on a customer which cost $196.00 is 75%.
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As long as N is significanly less than K, logistic growth is indistinguishable from exponential O True O False if dN/dt > 0, then N O equals to zero O decreases O remains stable O increases
Answers
The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. If dN/dt > 0, then N increases.
The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. Logistic growth takes into account the carrying capacity of the environment, represented by K, which limits the growth of a population as it approaches this limit. In contrast, exponential growth assumes an unlimited supply of resources and no constraints on population growth. Therefore, as N approaches K, logistic growth begins to level off, while exponential growth continues to increase indefinitely.
If dN/dt > 0, then N increases. This means that the population size is growing at a positive rate. If dN/dt is equal to zero, then N remains stable, indicating that the population size is not changing. Finally, if dN/dt is negative, then N decreases, indicating that the population size is shrinking. Therefore, the correct answer to this question is "increases."
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Which of the following functions best describes this graph?
Answers
Answer:
Option D
Step-by-step explanation:
Looking at the graph each jump is 2 units on the x-axis and y-axis :
We are looking for a quadratic with x values of 3 and 6 when y=0
Solving the last quadratic gives us :
(x-3)(x-6)=0
x = 3 , x = 6
Our answer will be Option D
Hope this helped and have a good day
Answer:
D: \(y=x^{2} -9x+18\\\)
Step-by-step explanation:
x intercept of the curve is 3 and 6
meaning that when y=0, x is either 3 or 6
mathematically stated:
0 = (x - 3) (x - 6)
0=x(x-6)-3(x-6)
\(0=x^{2} -6x-3x+18\\therefore \ y=x^{2} -9x+18\\\)
Which formula is used to find a Centre of a circle?
Answers
A formula is used to find a Center of a circle with a (h, k) center and a radius of r has the equation:
\((x-h)^2 + (y-k)^2 = r^2\)
A circle is a collection of all points in a plane that are uniformly distanced from a fixed point. The radius of a circle is the difference between the center and any point itself along the perimeter.
A circle is a closed curve that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center. The equation for a circle with a (h, k) center and a radius of r is:
\((x-h)^2 + (y-k)^2 = r^2\)
This is the equation's standard form. So, if we know the radius and center coordinates of a circle, we can rapidly determine its equation.
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Simplify each of the expressions below. Which of the expressions have a value between 20 and 40? Select all that apply.
A)(6 −3)2+(5×3)
B)72 −(1×3)3
C)43 −5×8
D)102 −(5+2)2
Answers
Answer:
d
Step-by-step explanation:
Describe if the function is linear, exponential, or neither. Explain how you can tell
Answers
It is not linear because it does not follow a set pattern and it is not exponential because there are no exponents present.
The coach of a lacrosse team bought ice cream cones to celebrate a victory. A single-scoop cone was $3 and a double-scoop cone was $5. The coach bought 15 cones and paid $57. A system of equations describing this situation could be written in the form below where s represents the number of single cones and d represents the number of double cones. What is the sum of A, B, C and E?
Answers
Answer:
The number of
Single scoop cones = s = 9
Double scoop cones = d = 6
Step-by-step explanation :
Let t he number of
Single scoop cones = s
Double scoop cones = d
A single-scoop cone was $3 and a double-scoop cone was $5. The coach bought 15 cones and paid $57.
The system of equation
= s + d = 15.. Equation 1
s = 15 - d
3s + 5d = 57.... Equation 2
We substitute 15 - d for s
3(15 - d) + 5d = 57
45 - 3d + 5d = 57
Collect like terms
- 3d + 5d = 57 - 45
2d = 12
d = 12/2
d = 6
Solving for s
s = 15 - d
s = 15 - 6
s = 9
Therefore,
The number of
Single scoop cones = s = 9
Double scoop cones = d = 6
Determine whether each function is even, odd, or neither. g(x) = |x-3| neither g(x) = x + x² neither
Answers
Answer:
So, both the functions are neither even and nor odd.
Step-by-step explanation:
A function is even if g(x) = g(-x) and odd if g(x) = - g(x).
g(x) = |x-3|
g (-x ) = | -x -3 |
So, the function is neither even and nor odd.
g (x) = x + x²
g (- x) = (- x) + (- x) ² = - x + x²
So, the function is neither even and nor odd.
drop down box #1: $7.50 , $5.00, $1.50
Drop down box #2: $17.50, $15.50, $15,00
Answers
Solve for x. Round to the nearest tenth.
Answers
Using trigonometric function the value of x is 51.3°.
What is trigonometric function?
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Here Let us take the given right triangle as ABC.
∠A = x , ∠B = 90° and AB = 25 , AC= 40
Now using Cosine ratio then
Cos A = \(\frac{adjacent}{hypotenuse}\)
=> cos x = \(\frac{25}{40}\)
=> cos x = \(\frac{5}{8}\)
=> x = \(cos^{-1}\frac{5}{8}\)
=> x = 51.3°
Hence the value of x is 51.3°.
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If y = 2 and x = 5, Then solve
3x + 4 + 2y
A 20
B 61
C 23
D 0
Answers
Answer:
C
Step-by-step explanation:
Michael Hendrix earned $232.10 for working 27.5 hours. How much would he earn if he worked 40 hours? (Annex a zero to
the dividend to make the quotient come out even)
out even.)
Answers
Answer:
337.60
Step-by-step explanation:
I divided what he earned by what he worked and multiplied that number by 40
Solve Ax − By = C for x