# Determine the acceleration field for a three-dimensional flow with velocity components

Determine the acceleration field for a three-dimensional flow with velocity components u= -x, v = 4x^2y^2, and w = x-y

## General guidance

Concepts and Reason

Velocity of a fluid particle is a function of location and time. Velocity is a vector which has both magnitude and direction. The acceleration of a fluid particle is the time rate of change of velocity.

Fundamentals

The velocity vector for a fluid particle, The acceleration vector for a fluid particle in three dimensional flow, The scalar components of acceleration vector,

## Step-by-step

### Step 1 of 2

The x-component of acceleration, The y-component of acceleration, The z-component of acceleration,

Find the components of acceleration along the three Cartesian coordinate axes using the spatial and time derivatives of velocity components.

### Step 2 of 2

Find the acceleration field using the relation,

The acceleration field is .

Write the acceleration field vector using the components of acceleration of the fluid particle.