For the velocity fields given below, determine: (a) whether the flow field is one-, two-, or three-dimensional, and why. (b) whether the flow is steady or unsteady, and why. (The quantities a and b are constants.) 1 V → = [ ( a x + t ) e b y ] i ^ 2 V → = ( a x − b y ) i ^ 3 V → = a x i ^ + [ e b x ] j ^ 4 V → = a x i ^ + b x 2 j ^ + a x k ^ 5 V → = a x i ^ + [ e b t ] j ^ 6 V → = a x i ^ + b x 2 j ^ + a y k ^ 7 V → = a x i ^ + [ e b t ] j ^ + a y k ^ 8 V → = a x i ^ + [ e b y ] j ^ + a z k ^

Question

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Answer 1

Textbook Question

Chapter 2, Problem 1P

For the velocity fields given below, determine:

(a) whether the flow field is one-, two-, or three-dimensional, and why.
(b) whether the flow is steady or unsteady, and why.

(The quantities a and b are constants.)

1 V → = [ ( a x + t ) e b y ] i ^
2 V → = ( a x − b y ) i ^
3 V → = a x i ^ + [ e b x ] j ^
4 V → = a x i ^ + b x 2 j ^ + a x k ^
5 V → = a x i ^ + [ e b t ] j ^
6 V → = a x i ^ + b x 2 j ^ + a y k ^
7 V → = a x i ^ + [ e b t ] j ^ + a y k ^
8 V → = a x i ^ + [ e b y ] j ^ + a z k ^

1)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

Condition for checking the Flow dimensions:

The flow is dependent on a number of space coordinates such as x, y, and z. Depending on the number of coordinates, the flow is stated as one or two or three dimensional.

Condition for checking whether the flow is steady or unsteady:

When the flow is changing its velocity with respect to time, then the fluid is unsteady. If the flow is not changing its velocity with respect to time, then the fluid is steady.

Calculation:

The given velocity field is,

V→=[(ax+t)eby]i^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

2)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=(ax−by)i^

(a)

Here, the flow is dependent on one space coordinate x Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

3)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ehx]j^

(a)

Here, the flow is dependent on two space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

4)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+axk^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

5)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

6)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

7)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

8)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[eby]j^+azk^

(a)

Here, the flow is dependent on two space coordinates x , y, and z. Thus, the flow is three dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

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Students have asked these similar questions

1. Find the stream function for a parallel flow of uniform velocity V0 making an angle α with the x-axis. 2. A certain flow field is described by the stream function ψ = xy. (a) Sketch the flow field. (b) Find the x and y velocity components at [0, 0], [1, 1], [∞, 0], and [4, 1]. (c) Find the volume flow rate per unit width flowing between the streamlines passing through points [0, 0] and [1, 1], and points [1, 2] and [5, 3].

Home Work (steady continuity equation at a point for incompressible fluid flow: 1- The x component of velocity in a steady, incompressible flow field in the xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find the simplest y component of velocity for this flow field. 2- The velocity components for an incompressible steady flow field are u= (A x* +z) and v=B (xy + yz). Determine the z component of velocity for steady flow. 3- The x component of velocity for a flow field is given as u = Ax²y2 where A = 0.3 ms and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Assume incompressible steady two dimension flow

1. Stagnation Points A steady incompressible three dimensional velocity field is given by: V = (2 – 3x + x²) î + (y² – 8y + 5)j + (5z² + 20z + 32)k Where the x-, y- and z- coordinates are in [m] and the magnitude of velocity is in [m/s]. a) Determine coordinates of possible stagnation points in the flow. b) Specify a region in the velocity flied containing at least one stagnation point. c) Find the magnitude and direction of the local velocity field at 4- different points that located at equal- distance from your specified stagnation point.

Answer 2

Textbook Question

Chapter 2, Problem 1P

For the velocity fields given below, determine:

(a) whether the flow field is one-, two-, or three-dimensional, and why.
(b) whether the flow is steady or unsteady, and why.

(The quantities a and b are constants.)

1 V → = [ ( a x + t ) e b y ] i ^
2 V → = ( a x − b y ) i ^
3 V → = a x i ^ + [ e b x ] j ^
4 V → = a x i ^ + b x 2 j ^ + a x k ^
5 V → = a x i ^ + [ e b t ] j ^
6 V → = a x i ^ + b x 2 j ^ + a y k ^
7 V → = a x i ^ + [ e b t ] j ^ + a y k ^
8 V → = a x i ^ + [ e b y ] j ^ + a z k ^

1)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

Condition for checking the Flow dimensions:

The flow is dependent on a number of space coordinates such as x, y, and z. Depending on the number of coordinates, the flow is stated as one or two or three dimensional.

Condition for checking whether the flow is steady or unsteady:

When the flow is changing its velocity with respect to time, then the fluid is unsteady. If the flow is not changing its velocity with respect to time, then the fluid is steady.

Calculation:

The given velocity field is,

V→=[(ax+t)eby]i^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

2)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=(ax−by)i^

(a)

Here, the flow is dependent on one space coordinate x Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

3)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ehx]j^

(a)

Here, the flow is dependent on two space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

4)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+axk^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

5)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

6)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

7)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

8)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[eby]j^+azk^

(a)

Here, the flow is dependent on two space coordinates x , y, and z. Thus, the flow is three dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

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Answer 3

Textbook Question

Chapter 2, Problem 1P

For the velocity fields given below, determine:

(a) whether the flow field is one-, two-, or three-dimensional, and why.
(b) whether the flow is steady or unsteady, and why.

(The quantities a and b are constants.)

1 V → = [ ( a x + t ) e b y ] i ^
2 V → = ( a x − b y ) i ^
3 V → = a x i ^ + [ e b x ] j ^
4 V → = a x i ^ + b x 2 j ^ + a x k ^
5 V → = a x i ^ + [ e b t ] j ^
6 V → = a x i ^ + b x 2 j ^ + a y k ^
7 V → = a x i ^ + [ e b t ] j ^ + a y k ^
8 V → = a x i ^ + [ e b y ] j ^ + a z k ^

1)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

Condition for checking the Flow dimensions:

The flow is dependent on a number of space coordinates such as x, y, and z. Depending on the number of coordinates, the flow is stated as one or two or three dimensional.

Condition for checking whether the flow is steady or unsteady:

When the flow is changing its velocity with respect to time, then the fluid is unsteady. If the flow is not changing its velocity with respect to time, then the fluid is steady.

Calculation:

The given velocity field is,

V→=[(ax+t)eby]i^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

2)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=(ax−by)i^

(a)

Here, the flow is dependent on one space coordinate x Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

3)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ehx]j^

(a)

Here, the flow is dependent on two space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

4)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+axk^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

5)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

6)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

7)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

8)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[eby]j^+azk^

(a)

Here, the flow is dependent on two space coordinates x , y, and z. Thus, the flow is three dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

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Answer 4

Textbook Question

Chapter 2, Problem 1P

For the velocity fields given below, determine:

(a) whether the flow field is one-, two-, or three-dimensional, and why.
(b) whether the flow is steady or unsteady, and why.

(The quantities a and b are constants.)

1 V → = [ ( a x + t ) e b y ] i ^
2 V → = ( a x − b y ) i ^
3 V → = a x i ^ + [ e b x ] j ^
4 V → = a x i ^ + b x 2 j ^ + a x k ^
5 V → = a x i ^ + [ e b t ] j ^
6 V → = a x i ^ + b x 2 j ^ + a y k ^
7 V → = a x i ^ + [ e b t ] j ^ + a y k ^
8 V → = a x i ^ + [ e b y ] j ^ + a z k ^

1)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

Condition for checking the Flow dimensions:

The flow is dependent on a number of space coordinates such as x, y, and z. Depending on the number of coordinates, the flow is stated as one or two or three dimensional.

Condition for checking whether the flow is steady or unsteady:

When the flow is changing its velocity with respect to time, then the fluid is unsteady. If the flow is not changing its velocity with respect to time, then the fluid is steady.

Calculation:

The given velocity field is,

V→=[(ax+t)eby]i^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

2)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=(ax−by)i^

(a)

Here, the flow is dependent on one space coordinate x Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

3)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ehx]j^

(a)

Here, the flow is dependent on two space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

4)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+axk^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

5)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

6)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

7)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

8)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[eby]j^+azk^

(a)

Here, the flow is dependent on two space coordinates x , y, and z. Thus, the flow is three dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

1)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

Condition for checking the Flow dimensions:

The flow is dependent on a number of space coordinates such as x, y, and z. Depending on the number of coordinates, the flow is stated as one or two or three dimensional.

Condition for checking whether the flow is steady or unsteady:

When the flow is changing its velocity with respect to time, then the fluid is unsteady. If the flow is not changing its velocity with respect to time, then the fluid is steady.

Calculation:

The given velocity field is,

V→=[(ax+t)eby]i^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

2)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=(ax−by)i^

(a)

Here, the flow is dependent on one space coordinate x Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

3)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ehx]j^

(a)

Here, the flow is dependent on two space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

4)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+axk^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

5)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

6)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

7)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

8)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[eby]j^+azk^

(a)

Here, the flow is dependent on two space coordinates x , y, and z. Thus, the flow is three dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

Answer 8

1)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

Condition for checking the Flow dimensions:

The flow is dependent on a number of space coordinates such as x, y, and z. Depending on the number of coordinates, the flow is stated as one or two or three dimensional.

Condition for checking whether the flow is steady or unsteady:

When the flow is changing its velocity with respect to time, then the fluid is unsteady. If the flow is not changing its velocity with respect to time, then the fluid is steady.

Calculation:

The given velocity field is,

V→=[(ax+t)eby]i^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

Answer 9

1)

Expert Solution

Answer 10

1)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Answer 13

Explanation of Solution

Condition for checking the Flow dimensions:

The flow is dependent on a number of space coordinates such as x, y, and z. Depending on the number of coordinates, the flow is stated as one or two or three dimensional.

Condition for checking whether the flow is steady or unsteady:

When the flow is changing its velocity with respect to time, then the fluid is unsteady. If the flow is not changing its velocity with respect to time, then the fluid is steady.

Calculation:

The given velocity field is,

V→=[(ax+t)eby]i^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

Answer 14

2)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=(ax−by)i^

(a)

Here, the flow is dependent on one space coordinate x Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

Answer 15

2)

Expert Solution

Answer 16

2)

Expert Solution

Answer 17

Expert Solution

Answer 18

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Answer 19

Explanation of Solution

The given velocity field is,

V→=(ax−by)i^

(a)

Here, the flow is dependent on one space coordinate x Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

Answer 20

3)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ehx]j^

(a)

Here, the flow is dependent on two space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

Answer 21

3)

Expert Solution

Answer 22

3)

Expert Solution

Answer 23

Expert Solution

Answer 24

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Answer 25

Explanation of Solution

The given velocity field is,

V→=axi^+[ehx]j^

(a)

Here, the flow is dependent on two space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

Answer 26

4)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+axk^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

Answer 27

4)

Expert Solution

Answer 28

4)

Expert Solution

Answer 29

Expert Solution

Answer 30

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Answer 31

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+axk^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

Answer 32

5)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

Answer 33

5)

Expert Solution

Answer 34

5)

Expert Solution

Answer 35

Expert Solution

Answer 36

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Answer 37

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^

(a)

Here, the flow is dependent on space coordinates x only. Thus, the flow is one dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

Answer 38

6)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

Answer 39

6)

Expert Solution

Answer 40

6)

Expert Solution

Answer 41

Expert Solution

Answer 42

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Answer 43

Explanation of Solution

The given velocity field is,

V→=axi^+bx2j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

Answer 44

7)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

Answer 45

7)

Expert Solution

Answer 46

7)

Expert Solution

Answer 47

Expert Solution

Answer 48

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Answer 49

Explanation of Solution

The given velocity field is,

V→=axi^+[ebt]j^+ayk^

(a)

Here, the flow is dependent on two space coordinates x and y. Thus, the flow is two dimensional.

(b).

Here, the velocity of flow is changing with respect to time (t). Thus, the flow is unsteady flow.

Answer 50

8)

Expert Solution

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Explanation of Solution

The given velocity field is,

V→=axi^+[eby]j^+azk^

(a)

Here, the flow is dependent on two space coordinates x , y, and z. Thus, the flow is three dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

Answer 51

8)

Expert Solution

Answer 52

8)

Expert Solution

Answer 53

Expert Solution

Answer 54

To determine

(a) Whether the flow field is one-, two-, or three-dimensional, and why.

(b) Whether the flow is steady or unsteady, and why.

Answer 55

Explanation of Solution

The given velocity field is,

V→=axi^+[eby]j^+azk^

(a)

Here, the flow is dependent on two space coordinates x , y, and z. Thus, the flow is three dimensional.

(b).

Here, the velocity of flow is does not change with respect to time (t). Thus, the flow is steady flow.

Answer 56

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