Fluid Kinematics

Chapter 4

Fluid Kinematics

After completing this chapter, you should be able to:

■ discuss the differences between the Eulerian and Lagrangian descriptions of

fluid motion.

■ identify various flow characteristics based on the velocity field.

■ determine the streamline pattern and acceleration field given a velocity field.

■ discuss the differences between a system and control volume.

■ apply the Reynolds transport theorem and the material derivative.

In this chapter we will discuss various aspects of fluid motion. consider the kinematics of the motion—the velocity and acceleration of the fluid, and the description and visualization of its motion.  

One of the most important fluid variables is the velocity field.

Useful mobile App:

The «Wind Tunnel» app is a software for Android devices. It turns your smartphone into a wind tunnel simulator. Draw obstacles and watch the fluid flow around (flow field and streamlines). Experiment with different sizes, shapes, aerodynamic profiles and observe what happens.

****************************************************************************

solution of book problems

*******************************************************************

Examples and Problems:

Question# 1:

A two-dimensional velocity field is given by    u=1+y   &  ν=1 

Determine the equation of the streamline that passes through the origin. On a graph, plot this streamline.

 Question# 2:

The velocity field of a flow is given by  V=(5z-3) i+(x+4) j+4y k   m/s Where x, y, and z are in meters. Determine the fluid speed at the origin ( x = y = z = 0 ) and on the x axis ( y = z = 0 ).

  Question# 3:

Determine the acceleration field for a tree-dimensional flow with velocity components   u = -x  ν = 4x2 y2 ,and  w = x - y