(a) The value of function f(y) for which the laplacian of F is zero.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 8, Problem 8.5P

To determine

(a)

The value of function f(y) for which the laplacian of F is zero.

Expert Solution

Answer to Problem 8.5P

The value of function f(y) for which the laplacian of F is zero.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z):

F=2x² +y³ -4xz+f(y)

Concept Used:

First, we must find the suitable f(y) which makes ∇2F=0

Calculation:

∇2F=∂2F∂x2+∂2F∂y2+∂2F∂z2=∂2(2x2+y3−4xz+f(y))∂x2+∂2(2x2+y3−4xz+f(y))∂y2+∂2(2x2+y3−4xz+f(y))∂z2=(4+0+0)+(0+6y−0)+(0+0−0)+f"(y)=4+6y+f"y⇒f"(y)=−4−6y for ∇2F=0on solving for f(y) we get:f'(y)=−4y−3y2+cf(y)=−2y2−y3+c'on putting f(y) we get:F=2x2+y3−4xz−2y2−y3+c'=2x2−2y2−4xz+c'f(y) is not a harmonic function.

Conclusion:

The value of function f(y) for which the laplacian of F is zero is F=2x² -2y² -4xz+ c'

Here c' is integration constant. The function f(y) is not a harmonic function.

To determine

(b)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function can be served as a velocity potential function as ∇2F=0.

Explanation of Solution

Given Information:

A harmonic function F(x, y,z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be velocity potential the required condition is:

∇2F=0

Calculation:

Conclusion:

The given function can be served as a velocity potential function as ∇2F=0

But the given function may not be a realistic flow pattern.

To determine

(c)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function cannot be served as a stream function due to having three dimensional function.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be stream function the required condition is that the function should not be three dimensional.

Calculation:

Conclusion:

The given function is not a stream function as it is three dimensional.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

a ship 125m long and 17.5m beam floats in seawater of 1.025 t/m3 at a draught of 8m. the waterplane coefficient is 0.83, block coefficient 0.759 and midship section area coefficient 0.98. calculate i) prismatic coefficient ii) TPC iii) change in mean draught if the vessel moves into water of 1.016 t/m3

c. For the given transfer function, find tp, ts, tr, Mp . Plot the resulting step response. G(s) = 40/(s^2 + 4s + 40) handplot only, and solve for each

A ship of 9000 tonne displacement floats in fresh water of 1.000 t/m3 at a draught 50 mm below the sea water line. The waterplane area is 1650 m2. Calculate the mass of cargo which must be added so that when entering seawater of 1.025 t/m3 it floats at the seawater line.

Answer 2

Question

Chapter 8, Problem 8.5P

To determine

(a)

The value of function f(y) for which the laplacian of F is zero.

Expert Solution

Answer to Problem 8.5P

The value of function f(y) for which the laplacian of F is zero.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z):

F=2x² +y³ -4xz+f(y)

Concept Used:

First, we must find the suitable f(y) which makes ∇2F=0

Calculation:

∇2F=∂2F∂x2+∂2F∂y2+∂2F∂z2=∂2(2x2+y3−4xz+f(y))∂x2+∂2(2x2+y3−4xz+f(y))∂y2+∂2(2x2+y3−4xz+f(y))∂z2=(4+0+0)+(0+6y−0)+(0+0−0)+f"(y)=4+6y+f"y⇒f"(y)=−4−6y for ∇2F=0on solving for f(y) we get:f'(y)=−4y−3y2+cf(y)=−2y2−y3+c'on putting f(y) we get:F=2x2+y3−4xz−2y2−y3+c'=2x2−2y2−4xz+c'f(y) is not a harmonic function.

Conclusion:

The value of function f(y) for which the laplacian of F is zero is F=2x² -2y² -4xz+ c'

Here c' is integration constant. The function f(y) is not a harmonic function.

To determine

(b)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function can be served as a velocity potential function as ∇2F=0.

Explanation of Solution

Given Information:

A harmonic function F(x, y,z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be velocity potential the required condition is:

∇2F=0

Calculation:

Conclusion:

The given function can be served as a velocity potential function as ∇2F=0

But the given function may not be a realistic flow pattern.

To determine

(c)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function cannot be served as a stream function due to having three dimensional function.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be stream function the required condition is that the function should not be three dimensional.

Calculation:

Conclusion:

The given function is not a stream function as it is three dimensional.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 8, Problem 8.5P

To determine

(a)

The value of function f(y) for which the laplacian of F is zero.

Expert Solution

Answer to Problem 8.5P

The value of function f(y) for which the laplacian of F is zero.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z):

F=2x² +y³ -4xz+f(y)

Concept Used:

First, we must find the suitable f(y) which makes ∇2F=0

Calculation:

∇2F=∂2F∂x2+∂2F∂y2+∂2F∂z2=∂2(2x2+y3−4xz+f(y))∂x2+∂2(2x2+y3−4xz+f(y))∂y2+∂2(2x2+y3−4xz+f(y))∂z2=(4+0+0)+(0+6y−0)+(0+0−0)+f"(y)=4+6y+f"y⇒f"(y)=−4−6y for ∇2F=0on solving for f(y) we get:f'(y)=−4y−3y2+cf(y)=−2y2−y3+c'on putting f(y) we get:F=2x2+y3−4xz−2y2−y3+c'=2x2−2y2−4xz+c'f(y) is not a harmonic function.

Conclusion:

The value of function f(y) for which the laplacian of F is zero is F=2x² -2y² -4xz+ c'

Here c' is integration constant. The function f(y) is not a harmonic function.

To determine

(b)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function can be served as a velocity potential function as ∇2F=0.

Explanation of Solution

Given Information:

A harmonic function F(x, y,z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be velocity potential the required condition is:

∇2F=0

Calculation:

Conclusion:

The given function can be served as a velocity potential function as ∇2F=0

But the given function may not be a realistic flow pattern.

To determine

(c)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function cannot be served as a stream function due to having three dimensional function.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be stream function the required condition is that the function should not be three dimensional.

Calculation:

Conclusion:

The given function is not a stream function as it is three dimensional.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 8, Problem 8.5P

To determine

(a)

The value of function f(y) for which the laplacian of F is zero.

Expert Solution

Answer to Problem 8.5P

The value of function f(y) for which the laplacian of F is zero.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z):

F=2x² +y³ -4xz+f(y)

Concept Used:

First, we must find the suitable f(y) which makes ∇2F=0

Calculation:

∇2F=∂2F∂x2+∂2F∂y2+∂2F∂z2=∂2(2x2+y3−4xz+f(y))∂x2+∂2(2x2+y3−4xz+f(y))∂y2+∂2(2x2+y3−4xz+f(y))∂z2=(4+0+0)+(0+6y−0)+(0+0−0)+f"(y)=4+6y+f"y⇒f"(y)=−4−6y for ∇2F=0on solving for f(y) we get:f'(y)=−4y−3y2+cf(y)=−2y2−y3+c'on putting f(y) we get:F=2x2+y3−4xz−2y2−y3+c'=2x2−2y2−4xz+c'f(y) is not a harmonic function.

Conclusion:

The value of function f(y) for which the laplacian of F is zero is F=2x² -2y² -4xz+ c'

Here c' is integration constant. The function f(y) is not a harmonic function.

To determine

(b)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function can be served as a velocity potential function as ∇2F=0.

Explanation of Solution

Given Information:

A harmonic function F(x, y,z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be velocity potential the required condition is:

∇2F=0

Calculation:

Conclusion:

The given function can be served as a velocity potential function as ∇2F=0

But the given function may not be a realistic flow pattern.

To determine

(c)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function cannot be served as a stream function due to having three dimensional function.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be stream function the required condition is that the function should not be three dimensional.

Calculation:

Conclusion:

The given function is not a stream function as it is three dimensional.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 8, Problem 8.5P

To determine

(a)

The value of function f(y) for which the laplacian of F is zero.

Expert Solution

Answer to Problem 8.5P

The value of function f(y) for which the laplacian of F is zero.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z):

F=2x² +y³ -4xz+f(y)

Concept Used:

First, we must find the suitable f(y) which makes ∇2F=0

Calculation:

∇2F=∂2F∂x2+∂2F∂y2+∂2F∂z2=∂2(2x2+y3−4xz+f(y))∂x2+∂2(2x2+y3−4xz+f(y))∂y2+∂2(2x2+y3−4xz+f(y))∂z2=(4+0+0)+(0+6y−0)+(0+0−0)+f"(y)=4+6y+f"y⇒f"(y)=−4−6y for ∇2F=0on solving for f(y) we get:f'(y)=−4y−3y2+cf(y)=−2y2−y3+c'on putting f(y) we get:F=2x2+y3−4xz−2y2−y3+c'=2x2−2y2−4xz+c'f(y) is not a harmonic function.

Conclusion:

The value of function f(y) for which the laplacian of F is zero is F=2x² -2y² -4xz+ c'

Here c' is integration constant. The function f(y) is not a harmonic function.

To determine

(b)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function can be served as a velocity potential function as ∇2F=0.

Explanation of Solution

Given Information:

A harmonic function F(x, y,z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be velocity potential the required condition is:

∇2F=0

Calculation:

Conclusion:

The given function can be served as a velocity potential function as ∇2F=0

But the given function may not be a realistic flow pattern.

To determine

(c)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function cannot be served as a stream function due to having three dimensional function.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be stream function the required condition is that the function should not be three dimensional.

Calculation:

Conclusion:

The given function is not a stream function as it is three dimensional.

Answer 6

Chapter 8, Problem 8.5P

To determine

(a)

The value of function f(y) for which the laplacian of F is zero.

Expert Solution

Answer to Problem 8.5P

The value of function f(y) for which the laplacian of F is zero.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z):

F=2x² +y³ -4xz+f(y)

Concept Used:

First, we must find the suitable f(y) which makes ∇2F=0

Calculation:

∇2F=∂2F∂x2+∂2F∂y2+∂2F∂z2=∂2(2x2+y3−4xz+f(y))∂x2+∂2(2x2+y3−4xz+f(y))∂y2+∂2(2x2+y3−4xz+f(y))∂z2=(4+0+0)+(0+6y−0)+(0+0−0)+f"(y)=4+6y+f"y⇒f"(y)=−4−6y for ∇2F=0on solving for f(y) we get:f'(y)=−4y−3y2+cf(y)=−2y2−y3+c'on putting f(y) we get:F=2x2+y3−4xz−2y2−y3+c'=2x2−2y2−4xz+c'f(y) is not a harmonic function.

Conclusion:

The value of function f(y) for which the laplacian of F is zero is F=2x² -2y² -4xz+ c'

Here c' is integration constant. The function f(y) is not a harmonic function.

Answer 7

Chapter 8, Problem 8.5P

To determine

(a)

The value of function f(y) for which the laplacian of F is zero.

Answer 8

Expert Solution

Answer to Problem 8.5P

The value of function f(y) for which the laplacian of F is zero.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given Information:

A harmonic function F(x, y, z):

F=2x² +y³ -4xz+f(y)

Concept Used:

First, we must find the suitable f(y) which makes ∇2F=0

Calculation:

∇2F=∂2F∂x2+∂2F∂y2+∂2F∂z2=∂2(2x2+y3−4xz+f(y))∂x2+∂2(2x2+y3−4xz+f(y))∂y2+∂2(2x2+y3−4xz+f(y))∂z2=(4+0+0)+(0+6y−0)+(0+0−0)+f"(y)=4+6y+f"y⇒f"(y)=−4−6y for ∇2F=0on solving for f(y) we get:f'(y)=−4y−3y2+cf(y)=−2y2−y3+c'on putting f(y) we get:F=2x2+y3−4xz−2y2−y3+c'=2x2−2y2−4xz+c'f(y) is not a harmonic function.

Conclusion:

The value of function f(y) for which the laplacian of F is zero is F=2x² -2y² -4xz+ c'

Here c' is integration constant. The function f(y) is not a harmonic function.

Answer 13

To determine

(b)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function can be served as a velocity potential function as ∇2F=0.

Explanation of Solution

Given Information:

A harmonic function F(x, y,z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be velocity potential the required condition is:

∇2F=0

Calculation:

Conclusion:

The given function can be served as a velocity potential function as ∇2F=0

But the given function may not be a realistic flow pattern.

Answer 14

To determine

(b)

The given function can be served as velocity potential function.

Answer 15

Expert Solution

Answer to Problem 8.5P

The given function can be served as a velocity potential function as ∇2F=0.

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given Information:

A harmonic function F(x, y,z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be velocity potential the required condition is:

∇2F=0

Calculation:

Conclusion:

The given function can be served as a velocity potential function as ∇2F=0

But the given function may not be a realistic flow pattern.

Answer 20

To determine

(c)

The given function can be served as velocity potential function.

Expert Solution

Answer to Problem 8.5P

The given function cannot be served as a stream function due to having three dimensional function.

Explanation of Solution

Given Information:

A harmonic function F(x, y, z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be stream function the required condition is that the function should not be three dimensional.

Calculation:

Conclusion:

The given function is not a stream function as it is three dimensional.

Answer 21

To determine

(c)

The given function can be served as velocity potential function.

Answer 22

Expert Solution

Answer to Problem 8.5P

The given function cannot be served as a stream function due to having three dimensional function.

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given Information:

A harmonic function F(x, y, z): F=2x² +y³ -4xz+f(y)

Concept Used:

For a function to be stream function the required condition is that the function should not be three dimensional.

Calculation:

Conclusion:

The given function is not a stream function as it is three dimensional.

Answer 27

Ch. 8 - Prob. 8.1P Ch. 8 - The steady plane flow in Fig. P8.2 has the polar...Ch. 8 - P8.3 Using cartesian coordinates, show that each...Ch. 8 - P8.4 Is the function 1/r a legitimate velocity...Ch. 8 - Prob. 8.5P Ch. 8 - An incompressible plane flow has the velocity...Ch. 8 - Prob. 8.7P Ch. 8 - For the velocity distribution u=By,=+Bx , evaluate...Ch. 8 - Prob. 8.9P Ch. 8 - Prob. 8.10P

(a) The value of function f(y) for which the laplacian of F is zero.

Videos

(a)

The value of function f(y) for which the laplacian of F is zero.

Answer to Problem 8.5P

Explanation of Solution

(b)

The given function can be served as velocity potential function.

Answer to Problem 8.5P

Explanation of Solution

(c)

The given function can be served as velocity potential function.

Answer to Problem 8.5P

Explanation of Solution

Want to see more full solutions like this?

Chapter 8 Solutions

(a) The value of function f(y) for which the laplacian of F is zero.

Videos

(a) The value of function f(y) for which the laplacian of F is zero.

Answer to Problem 8.5P

Explanation of Solution

(b) The given function can be served as velocity potential function.

Answer to Problem 8.5P

Explanation of Solution

(c) The given function can be served as velocity potential function.

Answer to Problem 8.5P

Explanation of Solution

Want to see more full solutions like this?

Chapter 8 Solutions

(a)

The value of function f(y) for which the laplacian of F is zero.

(b)

The given function can be served as velocity potential function.

(c)

The given function can be served as velocity potential function.