Question

(b) Describe in your own words, what each of the terms in the acceleration equation represents (give and example of each): диди - +и + va + (Әt "дходу = pa, (1)

Answer 1

We know that in fluid flow the resultant velocity at any point is given as V=u i^ + v j^ +w k^.

In the question, we are given only the component of velocity in the x-direction only, i.e. u .

And, the acceleration of the particle in fluid flow in the direction of the x-axis is given as ax.$\rho( \frac{\partial u}{\partial t }+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z})=\rho\mathbf{ a_{x}}$

The term $\frac{\partial u}{\partial t }$ is defined as the rate of increase of velocity with respect to time at a given point in a flow field.This term is known as the Local Acceleration of the fluid particle and it occurs when the flow is unsteady.

The term  $\frac{\partial u}{\partial x }$ is the rate of change of velocity due to change of position of the fluid particle in the direction of x-axis in a fluid flow.

The term  $\frac{\partial u}{\partial y }$  is the rate of change of the velocity of fluid-particle due to change of its position in the direction of y-axis in a fluid flow.

The term $\frac{\partial u}{\partial z }$ is the rate of change of the velocity of fluid-particle due to change of its position in the direction of z-axis in a fluid flow.

The terms $\frac{\partial u}{\partial x} , \frac{\partial u}{\partial y} , \frac{\partial u}{\partial z}$ are known as Convective Acceleration of the fluid particle.

Convective acceleration results when the flow is non-uniform.