Chapter 7, Problem 7.1P

(a)

Interpretation Introduction

Interpretation:

The fluid element deformation is to be sketched when $\frac{\partial v_x}{\partial y}$ is much larger than $\frac{\partial v_y}{\partial x}$ .

Concept Introduction:

Fluid element deformation occurs when the element changes its position with respect to its previous position. There are different types of deformation depending upon the aspect of change. These can be translation, rotation, angular, and volumetric deformations.

Answer to Problem 7.1P

The fluid element deformation when 1y $\frac{\partial v_x}{\partial y}$ is much larger than 13 $\frac{\partial v_y}{\partial x}$ is sketched as:

  

Explanation of Solution

Take a fluid element and plot it on a graph along x and y axis as shown below:

  

For a large change in $\frac{\partial v_x}{\partial y}$ as compared to $\frac{\partial v_y}{\partial x}$ , the fluid element shown in the above figure deforms over the x axis and remains unaltered over the y axis. Therefore, the deformation is sketched as:

  

(b)

Interpretation Introduction

Interpretation:

The fluid element deformation is to be sketched when $\frac{\partial v_y}{\partial x}$ is much larger than $\frac{\partial v_x}{\partial y}$ .

Concept Introduction:

Fluid element deformation occurs when the element changes its position with respect to its previous position. There are different types of deformation depending upon the aspect of change. These can be translation, rotation, angular, and volumetric deformations.

Answer to Problem 7.1P

The fluid element deformation when $\frac{\partial v_y}{\partial x}$ is much larger than $\frac{\partial v_x}{\partial y}$ is sketched as:

  

Explanation of Solution

Take a fluid element and plot it on a graph along x and y axis as shown below:

  

For a large change in $\frac{\partial v_y}{\partial x}$ as compared to $\frac{\partial v_x}{\partial y}$ , the fluid element shown in the above figure deforms over the y axis and remains unaltered over the x axis. Therefore, the deformation is sketched as: