Consider the steady, two-dimensional, velocity field V = (u,v)=(ax+b)i +(-ay+cx); where a, b, c are constants. The fluid density is p, viscosity is u. Is this flow field incompressible or compressible? Why? Calculate the acceleration; Find an expression for the pressure gradient in the y direction.

Answers

Answer 1

The flow field is incompressible and the acceleration is 0. The expression for the pressure gradient in the y direction is ∂p/∂y = $a^2$ρy + bcρx + μ($a^2 + c^2$).

To determine if the flow field is incompressible or compressible, we need to calculate the divergence of the velocity field.

Divergence of V = ∂u/∂x + ∂v/∂y

= a - a

= 0

Since the divergence of V is zero, the flow field is incompressible.

To find the acceleration, we take the time derivative of the velocity field:

a = ∂V/∂t = (∂u/∂t)i + (∂v/∂t)j

Since the flow is steady, there is no time variation and the acceleration is zero, i.e., a = 0.

To find the pressure gradient in the y direction, we apply the Navier-Stokes equation:

ρ(∂V/∂t + V·∇V) = -∇p + μ∇$^2V$

where ρ is the fluid density, μ is the viscosity, and ∇$^2$ is the Laplacian operator.

Since the flow is steady, the time derivative term is zero. Also, the Laplacian operator simplifies to ∇$^2V$ = (∂$^2u$/∂$x^2$ + ∂$^2u$/∂$y^2$)i + (∂$^2v$/∂$x^2$ + ∂$^2v$/∂$y^2$)j.

Thus, we have:

ρ(V·∇V) = -∇p + μ(∂$^2u$/∂$x^2$ + ∂$^2u$/∂$y^2$)i + μ(∂$^2v$/∂$x^2$ + ∂$^2v$/∂$y^2$)j

Expanding the dot product, we get:

ρ(u∂u/∂x + v∂u/∂y)i + ρ(u∂v/∂x + v∂v/∂y)j = -∇p + μ(∂$^2u$/∂$x^2$ + ∂$^2u$/∂$y^2$)i + μ(∂$^2v$/∂$x^2$ + ∂$^2v$/∂$y^2$)j

Taking the y-component of both sides, we get:

ρ(u∂v/∂x + v∂v/∂y) = -∂p/∂y + μ(∂$^2v$/∂$x^2$ + ∂$^2v$/∂$y^2$)

Simplifying this expression, we get:

∂p/∂y = -ρ(u∂v/∂x + v∂v/∂y) + μ(∂$^2v$/∂$x^2$ + ∂$^2v$/∂$y^2$)

Substituting the given velocity field, we get:

∂p/∂y = -ρ(-$a^2$y - bcx) + μ(-$a^2 - c^2$)

Simplifying further, we get:

∂p/∂y = $a^2$ρy + bcρx + μ($a^2 + c^2$)

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Related Questions

1+4d = 8.75(5-z) Help please I can't figure it out.

Answers

Answer:

d = -35z + 171 / 16

z = -16d - 171 / 35

Step-by-step explanation:

Let's find "d" first.

1 + 4d = 8.75(5 - z)

*100 *100

------------------------------------

100 + 400d = 875 (5 - z)

-100 -100

-------------------------------------

400d = -875z + 4275

/400 /400

-------------------------------------

d = -35z + 171 / 16

Now, let's find "z".

1 + 4d = 8.75(5 - z)

*100 *100

------------------------------------

100 + 400d = 875 (5 - z)

/875 /875

-------------------------------------

4(4d + 1) / 35 = 5 - z

-5 -5

--------------------------------------

4(4d + 1) / 35 - 5 = -z

/-1 /-1

---------------------------------------

-16d - 171 / 35 = z

Answer:

d = -35z + 171 / 16

z = -16d - 171 / 35

BEST ANSWER GETS BRAINLIEST, THANKS ON ANSWER, AND THANKS ON YOUR PROFILE!

Answers

shouldn’t it be the figures are similar? theyre the same size, along with the same measure of angles.

Step-by-step explanation:

Figure ABCD is similar to figure A'B'C'D'. is the correct awnser.

Figure ABCD is similar to figure A'B'C'D'. is the correct awnser.this is became ABCD is reflected over the y-axis so it is simular too A'B'C'D.

A is incorrect because the size of the shape doesn't change when getting reflected.

B and D is incorrect because just by looking at the shape D is not equal to A' or B'

Hope this helps!!

10. A shopkeeper bought 5 sets of sofa from a factory for $ 15800 (inclusive of a 10% value-added
tax). He then sold each set of sofa for $6794.
(a) Calculate the percentage profit made by the shopkeeper. [3]
(b) How much was the value-added tax for the 5 sets of sofa? [2]

Answers

(a).
Percentage profit made by the shopkeeper
= (5(6794)-15800)/15800 x 100
= (33970-15800)/15800 x 100
= 1.15 x 100
= 115 %

(b).
Value-added tax
= 10/100 x 15800
= $1580

Hope it helps : )

NEED HELP ASAP!!!! plssss

Answers

Answer:

Draw rise on y-axis from (0,0)-(0,3). Draw run from (0,3) to (4,3). Rise/run=3/4

Answer:

Draw rise on y-axis from (0,0)-(0,3). Draw run from (0,3) to (4,3). Rise/run=3/4

Step-by-step explanation:

Hope this helps:)

p2 — 6р + n
I can’t find the anywhere can someone help?

Answers

I believe the answer is -4p+n
hope this helped!

What is negative times a negative?

Answers

Answer:

positive

Negative x negative = positive.

Here is an example:

-2 x -4 = 8.

Hope it helps!

positive

Negative x negative = positive.

Here is an example:

-6 x -2 = 12

Hope it helps!

The table below shows the average annual salary of the workers at the Pearson
Corporation over the course of time since 1980. Let x represent the number of years
since 1980 with x = 0
representing the year 1980. Let y represent the average annual
salary of the workers. Complete the slope-intercept form of the equation for the line of
best fit below with the appropriate value for the slope.

Answers

Answer:

$y = 1164x + 14242$

Step-by-step explanation:

From the question, we understand that

x = 0, when year = 1980

First, we need to determine the slope of the table.

Pick any two corresponding values of year and average salary

year = 1982, average salary = 16570

year = 2002, average salary = 39850

Convert years to x values

year = 1982 implies that x = 2 i.e. 1982 - 1980

year = 2002 implies that x = 22 i.e. 2002 - 198-

So, we have:

$(x_1,y_1) = (2,16570)$

$(x_2,y_2) = (22,39850)$

Determine the slope.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{39850 -16570}{22 - 2}$

$m = \frac{23280}{20}$

$m = 1164$

The equation is calculated using:

$y - y_1 = m(x - x_1)$

Where

$m = 1164$

$(x_1,y_1) = (2,16570)$

So,

$y - y_1 = m(x - x_1)$

$y - 16570 = 1164(x - 2)$

$y - 16570 = 1164x - 1164*2$

$y - 16570 = 1164x - 2328$

Add 16570 to both sides

$y - 16570 + 16570 = 1164x - 2328 + 16570$

$y = 1164x - 2328 + 16570$

$y = 1164x + 14242$

Answer:

y = 1164x + 14,242

Step-by-step explanation:

find the solution to x′= y-x t, y'=y x(0) = 9 y(0) = 8

Answers

The solution to the given system of differential equations is x(t) = e^(t^2/2) * (8 - t^2/2) + e^(t^2/2) and y(t) = 8 * e^t. The initial conditions are x(0) = 9 and y(0) = 8.

To solve the system of differential equations x' = y - x*t and y' = y with initial conditions x(0) = 9 and y(0) = 8, we can use the method of integrating factors.

First, let's solve the second equation y' = y, which has the general solution y = C*e^t, where C is a constant determined by the initial condition y(0) = 8. Plugging in this value, we get C = 8.

Now, we can use this solution for y to find an integrating factor for the first equation x' = y - x*t. Multiplying both sides by e^(-t^2/2), we get

e^(-t^2/2)*x' - e^(-t^2/2)tx = e^(-t^2/2)*y - e^(-t^2/2)ty

The left-hand side can be simplified using the product rule

(d/dt)[e^(-t^2/2)*x] = e^(-t^2/2)*x' - e^(-t^2/2)tx

So, we can rewrite the equation as

(d/dt)[e^(-t^2/2)*x] = e^(-t^2/2)*y - e^(-t^2/2)ty

Integrating both sides with respect to t, we get

e^(-t^2/2)*x = ∫[e^(-t^2/2)*y - e^(-t^2/2)ty] dt + C

Using the solution for y we found earlier, we can simplify the integral

e^(-t^2/2)*x = e^t * (8 - t^2/2) + C

Now, we can use the initial condition x(0) = 9 to find C

e^0 * 9 = e^0 * (8 - 0/2) + C

C = 9 - 8 = 1

Therefore, the solution to the system of differential equations x' = y - x*t and y' = y with initial conditions x(0) = 9 and y(0) = 8 is:

x = e^(t^2/2) * (8 - t^2/2) + e^(t^2/2)

y = 8 * e^t

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Find the slope of the line through the given pair of points. (-7, 16), (-18, 18)

Answers

Answer: -2/11

Step-by-step explanation:

help will give brainliest asap

Answers

Answer:

476 and the top box is 5

Step-by-step explanation:

68×7

Multiply 68 and 7 to get 476.

476

Answer:

the bottom box is 476, the top one is 5

Step-by-step explanation:

Fill in the missing numbers to complete the linear equation that gives the rules for this tablex: 4, 5, 6, 7y: 56, 70, 84, 98y = ?x + ?

Answers

the two points are

A(4,56) and B(5,70)

so, the linear equation is

$y-70=\frac{70-56}{5-4}(x-5)$$\begin{gathered} y-70=\frac{14}{1}(x-5)_{} \\ y-70=14x-70 \end{gathered}$$y=14x$

thus, the equation is

y = 14x + 0

so we can put 14 in first place and 0 in second

Consider the arithmetic sequence.

16, 14, 12, 10, ...

Given that the sequence is represented by the function f(n), what are the values of f(1) and the common difference?

Answers

Answer:

Work shown below!

Step-by-step explanation:

f(n) = 16 - 2(n - 1)

f(1) = 16 - 2(1 - 1)

f(1) = 16 - 2(0)

f(1) = 16

Common difference is -2

write an equation whose graph is a line perpendicular to the graph of y=4 and which passes through the point (2, 5)

Answers

The equation whose graph is a line perpendicular to the graph of y=4 and which passes through the point (2, 5) is x = 2

How to determine the equation of the graph

From the question, we have the following parameters that can be used in our computation:

Perpendicular to the graph of y = 4

The above means that

The equation is a vertical line that passes through the x-axis

In the point (2, 5), we have

x = 2

This means that

The equation of the line is x = 2

Answers

$\left \{ {{f(x)=-3x+2} \atop {g(x)=x+1}} \right.$

To find g(f(x)), Substitute f(x) in g(x).

$g(-3x+2)$

Then substitute x = -3x+2 in g(x) = x+1

$g(-3x+2)=(-3x+2)+1\\g(-3x+2)=-3x+2+1\\g(-3x+2)=-3x+3$

Therefore, the answer is $g(f(x))=-3x+3$

Solve the exponential equation. Round your answer to the nearest hundredth:9n = 49

Answers

Answer:

$n=1.77$

Explanation: We have to solve the exponential equation, the equation provided is as follows:

$9^n=49$

We will resort to the logarithmic properties:

$\begin{gathered} \log_9(9^n)=\log_9(49) \\ \\ n\operatorname{\log}_9(9^)=\operatorname{\log}_9(49) \\ \\ n=\frac{\operatorname{\log}_9(49)}{\operatorname{\log}_9(9^)} \\ \\ n=\log_9(49) \\ \\ n=1.7712437491614 \\ \\ n=1.77 \end{gathered}$

the cuboid below is placed on a table.it exerts a pressure f 40 N/cm2. calculate the force exerted on the table.

Answers

Answer:

40 multiply by area of the table

Step-by-step explanation:

force = pressure * area of the table

Given that f(x)=2/x2 what is the value of f(x) when x=2?

A. 2.5
B. 2
C. 1
D. 0.5

Answers

Answer:

When x=2, we have:

f(2) = 2/2^2 = 2/4 = 0.5

Therefore, the value of f(x) when x=2 is 0.5.

The answer is (D) 0.5.

A company manufactures a special type of sensor, and packs them in boxes of 4 for shipment. Then a new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams. How much did each sensor weigh originally?

Answers

As the firm develops a specific sort of sensor and ships them in boxes of four, each sensor weighed 10 grams at first.

What is equation?

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

Let's call the original weight of each sensor "w". The total weight of 4 sensors would be 4w.

With the new design, each sensor weighs 9 grams more, so each sensor weighs w + 9 grams. The total weight of 4 sensors is 76 grams, so we can write an equation:

4(w + 9) = 76

Expanding the left-hand side and solving for w, we have:

4w + 36 = 76

4w = 40

w = 10

So each sensor originally weighed 10 grams as company manufactures a special type of sensor, and packs them in boxes of 4 for shipment.

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Can somebody answer these for me

Answers

Answer:

2) =22

3)= k> 18

Step-by-step explanation:

Find the distance between the points (5, - 4) and (5, 7)

Answers

11 units. It’s supaaaa easy

Refer to the following data set: What is the median?

Answers

Answer:

Step-by-step explanation:

8 the answer is c hope this helps

An online music company charges $15 per CD plus a flat fee of $4 per
order for downloading. Which equation best describes the relationship
between the total cost of an order (C) and the number of CDs that are
Ordered (x)

Answers

Answer:

Step-by-step explanation:

Your aunt and uncle took turns driving on a 580-mile trip that took 10 hours. Your uncle drove at a constant speed of 60 mph and your aunt drove a constant speed of 55 mph. How long did each person drive?

A. Write the two equations.

B Solve the equations and give both answers.

Answers

Answer:

Aunt drove 4 hours

Uncle drove 6 hours.

Step-by-step explanation:

Equations:

580 = 55/x + 60/y

600 = 55x + 60y

Happy Holidays!

The functions f(x)=−34x+214 and g(x)=(12)x+1 are shown in the graph. What are the solutions to −34x+214=(12)x+1? Select each correct answer.

Answers

The graphs cross at x=-1 and x=1. Those are the solutions to to the equation

How to explain the graph

We know that, If two functions are equal then there solution is the intersection point of the curves.

When we determine the graph the intersection points are (0,2) and (1,1.25).

The values of x of the intersection points are the solutions of the system

Using a graphing tool, there are two intersection points and therefore the solutions are x = -1 and x [ 1.

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rearrange the formulas to find r

I=Pr + t

Answers

The solution of the formula for the variable r is given as follows:

r = (I - t)/P.

How to solve the formula for the variable r?

The formula in this problem is defined as follows:

I = Pr + t.

To solve the formula for the variable r, we first must isolate the term with the variable r, as follows:

Pr = I - t.

Then we isolate the variable r applying the division operation, which is the inverse operation to the multiplication, giving the solution as follows:

r = (I - t)/P.

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Solve 5/6= 4/x

A. 7
B. 4.6
C. 5
D.4.8

Answers

Answer:

I think it's D, i might be wrong but im pretty sure it's D

u A store is having a sale where everything is 15% off. Which expression below does not represent the cost of an item in the store? Select all that apply85/100cc-0.15c15/100c0.85cc-0.85c

Answers

Given:

Percentage discount = 15%

Let's find the expression that does not represent the cost of an item in the store.

Let c represent the original cost of an item.

To find the c

$undefined$

PLEASE HELP!!! Julie is helping her mom carry groceries. The bag she is carrying has everything they need to make spaghetti for dinner tonight. It has 450 grams of spaghetti, 750 grams of tomato sauce, and 0.5 kilograms of ground beef. How many kilograms does her bag of groceries weigh?

Answers

Answer:

1.7 kilograms

Step-by-step explanation:

750 + 450 + 0.5kg ( 1kg = 1000) so 0.5 would be 500g.

=1,700g (1.7kg) :)

Help ASAP thank you!

Answers

This is D.5 units
…………….

The temperature rose 5 degrees from 6:00am to 12:00pm.

Answers

The average rate of change per hour in the temperature is 0.83 degrees.

What is the average rate of change per hour

To find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.

The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.

Therefore, the average rate of change per hour can be calculated as follows:

average rate of change per hour = total change in temperature / number of hours

So, we have

average rate of change per hour = 5 degrees / 6 hours

average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)

So, the average rate of change per hour is 0.83 degrees.