Concept explainers
A velocity field is given by
(a ) Is this flow steady or unsteady? Is it two- or three-dimensional?
(b ) At (x,y,z) = (3.2,-3), compute the velocity
(c) At (x.y.z) = (3,2,-3), compute the heal (i.e., unsteady part) of the acceleration vector.
(d) At (x,y,z) = (3,2,-3), compute the convective (or advective) part of the acceleration vector.(e) At (x,y,z) = (3,2,-3), compute the (total) acceleration vector.
(a)
That the flow is steady or unsteady and is it two or three dimensional.
Answer to Problem 121P
The flow is steady and two-dimensional.
Explanation of Solution
Given information:
The velocity field is
Write the expression for the streamline for three- dimensional flow.
Here, the derivative of
Substitute
Conclusion:
The flow is steady and two-dimensional.
(b)
The velocity vector at
Answer to Problem 121P
The velocity vector is
Explanation of Solution
Write the expression for the velocity vector.
Here,
Substitute
Here, the location points are x, and y.
Calculation:
Substitute
Conclusion:
The velocity vector is
(c)
The local (unsteady part) of the acceleration vector at
Answer to Problem 121P
The local (unsteady part) of the acceleration is
Explanation of Solution
Write the expression for the local acceleration of the flow in
Here, the time derivative of
Write the expression for the local acceleration of the flow in
Here, the time derivative of
Write the expression for the local acceleration of the flow in
Here, the time derivative of
Substitute
Substitute
Substitute
Conclusion:
The local (unsteady part) of the acceleration is
(d)
The convective (or advective) part of the acceleration vector at
Answer to Problem 121P
The convective part of acceleration in
Explanation of Solution
Given information:
The velocity field is
Write the expression for the convective part of acceleration in
Here, the velocity component in
Substitute
Here, the location points are
Write the expression for the convective part of acceleration in
Here, the velocity component in
Substitute
Write the expression for the convective part of acceleration in
Here, the velocity component in
Substitute
Calculation:
Substitute
Substitute
(e)
The (total) acceleration vector at
Answer to Problem 121P
The total acceleration is
Explanation of Solution
Write the expression for the total acceleration.
Here, acceleration in
Calculation:
Substitute
Conclusion:
The total acceleration is
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Chapter 4 Solutions
FLUID MECHANICS CONNECT ACCESS
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