The pressure in a fluid flowing with laminar flow through a pipe is given by
Hagen-Poiseuille equation.
The correct responses are;
(a) If the pipe is horizontal, the flow rate is approximately 1.622 × 10⁻⁵ m³/s(b) If the pipe is inclined 8° upwards, the flow rate is approximately 1.003 × 10⁻³ m³/s(c) If the pipe is inclined 8° downwards, the flow rate is approximately 2.24 × 10⁻⁵ m³/sReasons:
When the flow is a steady incompressible flow through pipe, the flow rate
can be derived from the Hagen-Poiseuille equation as follows;
[tex]\displaystyle \dot V = \mathbf{\frac{\left[\Delta P - \rho \cdot g \cdot L \cdot sin\left(\theta \right) \right] \cdot \pi \cdot D^4 }{128 \cdot \mu \cdot L}}[/tex]
ΔP = 135 kPa - 88 kPa = 47 kPa
The density of the oil, ρ = 876 kg/m³
μ = 0.24 kg/(m·s)
L = 15 m
The diameter of the pipe, D = 1.5 cm = 0.015 m
(a) When the pipe is horizontal, we have;
θ = 0°
Which gives;
[tex]\displaystyle \dot V = \mathbf{\frac{\left[47 \times 10^3 - 876 \, kg/m^3 \times 9.81 \, m/s^2 \times 15 \, m \cdot sin\left(0^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m}}[/tex]
[tex]\displaystyle \dot V = \frac{\left[47 \times 10^3\, Pa - 128903.4\, Pa \cdot sin\left(0^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m}[/tex]
[tex]\displaystyle \dot V = \frac{\left[47 \times 10^3\, Pa - 128903.4 \, Pa \cdot sin\left(0^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m} =\frac{0.002379357\cdot \pi}{460.8}[/tex]
[tex]\displaystyle \dot V=\frac{0.002379357\cdot \pi}{460.8} = \mathbf{1.622 \times 10^{-5}}[/tex]
The flow rate when the pipe is horizontal, [tex]\displaystyle \dot V[/tex] = 1.622 × 10⁻⁵ m³/s(b) When the pipe is inclined 8°, we have;
[tex]\displaystyle \dot V = \mathbf{\frac{\left[47 \times 10^3\, Pa - 128903.4\, Pa \cdot sin\left(8^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m}} = 1.003 \times 10^{-5} \, m^3/s[/tex]
The flow rate of oil through the pipe if the pipe is inclined 8° upwards from the horizontal, [tex]\displaystyle \dot V[/tex] = 1.003 × 10⁻⁵ m³/s(c) If the pipe is inclined 8° downward from the horizontal, we have;
[tex]\displaystyle \dot V = \frac{\left[47 \times 10^3\, Pa - 128903.4\, Pa \cdot sin\left(-8^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m} = 2.24\times 10^{-5} \, m^3/s[/tex]
If the pipe is inclined 8° upwards from the horizontal, the flow rate of oil through the pipe is, [tex]\displaystyle \dot V[/tex] = 2.24 × 10⁻⁵ m³/sLearn more about flow through pipes here:
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Y= (3x-4)3
Y=(2-4x)3
Y=(3x6-2x4)4
Answer:
y=24
Step-by-step explanation:
The functionſ is defined by f(x) = x.
Write down the expression for h (x).
Answer:
h(x) = |x + 4| - 2
Step-by-step explanation:
Translation of functions:
- 4 on the x-axis ⇒ |x + 4|
- 2 on the y-axis ⇒ -2
Simplify. Solve as fast as possible.
Answer:
-5y
Step-by-step explanation:
[tex]\sqrt{y^2}[/tex] = y if x > 0
-5[tex]\sqrt{y^2}[/tex] = -5y
2+2 (I have been struggling on this for a long time)
What's The Interest Rate?
I = $200
P = $800
T = 24 months
Erin spent half of her weekly allowance at the movies. To earn more money her parents let her wash the car for
$7. What is her weekly allowance if she ended with $12?
Write an equation to represent this situation
which of the following angle measure combinations will form a triangle?
A. 47° degrees, 63 degrees, and 70 degrees
B. 160 degrees, 50 degrees, and 150 degrees
C. 90 degrees, 1 degrees, and 88 degrees
D. 182 degrees, 1 degrees, and 2 degrees
This year, a small business had a total revenue of $41,600 . If this is 28% more than their total revenue the previous year, what was their total revenue the previous year?
Answer:
Hey will you marry me? serious question
Pls Find the value of x
[tex]x + 104 + 28 = 180 \\ (140 + 28 = 132) \\ x = 132[/tex]
[tex]\sf\longmapsto x + 104 + 28 = 180[/tex]
[tex]\sf\longmapsto x = (104 + 28) = 132[/tex]
[tex]\sf\longmapsto x = 132[/tex]
help me please guys im being times and trying to get this done fast!
Answer:
C.
Step-by-step explanation:
You're trying to figure out how many more hours he needs to work in order to have worked for 240 hours.
3 movie tickets cost 36$. at this rate, the cost per ticket is $..
Answer: The cost per ticket is $12.
Step-by-step explanation:
the degree of the polynomial p³q²-6p²q⁵+p⁴q⁴
Answer:
idioet.
Step-by-step explanation:
Solve the equation logx = cosx to five decimal places by Newton Raphson method.
Answer:
OK okokokokokokokokokokokok
what is the rate of change for these data?
Answer:
-2 gallons per minute
Step-by-step explanation:
As we can clearly see, the water is continuously decreasing every 15 minutes by 30 gallons.
So, the rate of change is -30 gallons per 15 minutes
However, we can simplify this ratio by dividing both sides by 15, so we get
-2 gallons per minute
solve for x . Help me solve them
[tex]\\(1).\\\\(1.7898)^{2x} = (1.7898)^6\\\\\implies \ln(1.7898)^{2x} = \ln(1.7898)^6\\\\\implies 2x \ln(1.7898) = 6 \ln(1.7898)\\\\\implies 2x =6\\\\\implies x = \dfrac 62 =3\\\\(3).\\\\2^{5x -6} = 4^{x+9}\\\\\implies 2^{5x -6} = (2^2)^{x+9}\\\\\implies 2^{5x-6} = 2^{2x+18}\\\\\implies \ln(2^{5x-6}) = \ln(2^{2x+18})\\\\\implies (5x -6) \ln 2 = (2x +18) \ln 2\\\\\implies 5x -6 = 2x +18\\\\\implies 5x -2x = 18 +6\\\\\implies 3x = 24\\\\\implies x = \dfrac{24}3 =8[/tex]
A total of $4000 is invested: part at 10% and the remainder at 15%. How much is invested at each rate if the annual interest is $430?
3,400 at 10%
600 at 15%
This is the answer.
Which of the following describes exponential decay?
A. The amount at a given time can be calculated by multiplying the previous amount
by a value greater than 1.
B. The amount at a given time can be calculated by multiplying the previous amount by a value less than 1.
C. The amount at a given time can be calculated by adding an amount to the previous amount.
D. The amount at a given time can be calculated by subtracting an amount from the previous amount.
The amount at a given time can be calculated by multiplying the previous amount by a value less than 1, which represents exponential decay. Hence, option B is the right choice.
What does linear function mean?A quantity grows (or depreciates) linearly if it increases (or decreases) by the same amount per unit of time.
What does exponential function mean?A quantity grows (or depreciates) exponentially if the increase (or decrease) in the amount is a multiple of the previous amount.
How to solve the question?In the question, we are asked to identify the option that best describes an exponential decay.
We assess each option and try to identify the exponential decay among them.
A. The amount at a given time can be calculated by multiplying the previous amount by a value greater than 1: This is an exponential function as it is multiplied by the previous amount, but it shows exponential growth as the quantity multiplied is greater than 1.B. The amount at a given time can be calculated by multiplying the previous amount by a value less than 1: This is an exponential function as it is multiplied by the previous amount, and it shows exponential decay as the quantity multiplied is less than 1.C. The amount at a given time can be calculated by adding an amount to the previous amount: This is a linear function as a fixed quantity is added.D. The amount at a given time can be calculated by subtracting an amount from the previous amount: This is a linear function as a fixed quantity is subtracted.Therefore, the amount at a given time can be calculated by multiplying the previous amount by a value less than 1, which represents exponential decay. Hence, option B is the right choice.
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Which shows two triangles that are congruent by AAS
Answer:
answer A is the correct option.
Step-by-step explanation:
The triangles ( A ) are congruent by AAS theorem
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔABD
Now , AB is the common side of both the triangles
And , measure of ∠ACB = measure of ∠ADB
And , the measure of ∠ABC = measure of ∠ABD = 90°
So , Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Hence , the triangles are congruent
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Solve 2/3 (3x+14)=7x+6 by first multiplying both sides of the equation by 3 before applying the distributive property
[tex]\dfrac23 (3x +14) =7x+6\\\\\\\implies 3\left[\dfrac 23 (3x+14) \right] = 3(7x+6)\\\\\\\implies 2(3x+14) = 21x +18\\\\\implies 6x + 28 =21x +18\\\\\implies 21x -6x = 28-18\\\\\implies 15x = 10\\\\\implies x = \dfrac{10}{15} = \dfrac 23[/tex]
Simplify the expression 7h+(−8.3d)−13+6d−2.9h.
Answer:−2.3d+4.1h−13
Step-by-step explanation:
how much solutions does 2x = 2x + 1 have?
Answer:
no solution
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
PLEASE HELPPPP. I really need it
Answer:
Option 4: (0, 5]
Step-by-step explanation:
Given the inequality notation, 0 < x ≤ 5 :
Definitions:open- and closed-parenthesis "( )"We know that using the open- and closed-parenthesis, "( )" are used to express interval notation for which the endpoints are not included as part of the solution. Hence, the open- and closed-parenthesis are associated with the inequality symbols, less than (>) or greater than (<), as you do not include the endpoints when these inequality symbols are used.
open- and closed-brackets "[ ]"In contrast, the open- and closed-brackets, "[ ]" are used to express interval notation for which the endpoints are included as part of the solution. Hence, the open- and closed-parenthesis are associated with the inequality symbols, less than or equal to (≤), and greater than or equal to (≥).
Explanation:In the inequality notation, 0 < x ≤ 5, the endpoints are 0 and 5.
The inequality symbol between 0 and x is "<," which means that we must use an open parenthesis, " ( " for the endpoint, 0.
While the inequality symbol between x and 5 is "≤," which means that we must use an closed bracket, " ] " for the endpoint, 5.
Therefore, the correct answer is Option 4: (0, 5].
t•t•t•t•t•t•t rewrite using exponents
Answer:
t^7
Step-by-step explanation:
there are 7 ts so it is t to the power of 7
Mr. Herman's class is selling candy for a school fundraiser. The class has a goal of raising $500 by selling c
boxes of candy. For every box they sell, they make $2.75.
Write an equation that the students could solve to figure out
how many boxes of candy they need to sell.
Answer:
500=2.75c
Step-by-step explanation:
500= 2.75c
Isolate c by dividing 2.75 on each side
500/2.75 =181.818181818 which is about 181.8
So the students need to sell about 181.8 boxes of candy in order to reach their goal of $500.
Evan made a tower from 32 building blocks. Aisha made a tower using 5 times as many blocks. How many blocks did Aisha use to make her tower?
Answer:
160
Step-by-step explanation:
32×5 is 60 hope that helps
State the postulate or theorem you would use to prove each pair of triangles congruent.
a) SSS
b) SAS
c) ASA
d) AAS
e) HL
f) Not possible
Answer:
f) Not possible
Step-by-step explanation:
The triangles can be shown to be similar by SAS, but the corresponding sides are not marked as congruent. With the given information, it is not possible to show the triangles are congruent.
What is the slope of this line?
a.−23
b.−13
c.13
d.23
Answer:
D
Step-by-step explanation:
I think you meant to put the answers as a fraction
Answer:
if there were slashes in between every answer, the answer would be
D. 2/3
Step-by-step explanation:
m = y2-y1 / x2-x1 (slope formula) ⋅the two points i used were: (0,-3) and (3,-1)
m = -1-(-3) / 3-0 (plug in the points)
m = -1+3 / 3-0
m = 2/3 (Simplify to get your answer)
Tracey paid $150 for an item that was originally priced at $510. What percent of the original price did Tracey pay?
Answer:
29.4118%
Step-by-step explanation
510 * x = 150
x = .2941176
multiply by 100 to get percent
29.4118
which expression represents 100 less than 3 times the sum of 18 and 2
Answer: 3 times (18+ 2) - 100
3 (18+2) - 100 = -40
Step-by-step explanation:
What is the sign of the product (-5)(-3)(-8)(-6)? (5 points) Positive, because the products (-5)(-3) and (-8)(-6) are negative, and the product of two negative numbers is positive Positive, because the products (-5)(-3) and (-8)(-6) are positive, and the product of two positive numbers is positive Negative, because the products (-5)(-3) and (-8)(-6) are negative, and the product of two negative numbers is negative Negative, because the products (-5)(-3) and (-8)(-6) are positive, and the product of two positive numbers is negative
Positive, because the products (-5)(-3) and (-8)(-6) are positive, and the product of two positive numbers is positive
=======================================================
Explanation:
Recall we have these rules
positive times positive = positivepositive times negative = negativenegative times negative = positiveHere is one example for each rule
8*7 = 565*(-9) = -45-2*(-4) = 8So based on that, we know that (-5)(-3) is positive. The two negatives cancel each other out so to speak. The same goes for (-8)(-6). Then multiplying any two positive numbers produces another positive outcome.
