# Fluid Mechanics local acceleration and convective acceleration

• yrael
In summary, the velocity of water in a pipe with a larger input end at v1=.5t m/s and a smaller output end with v2=1tm/s results in a local acceleration of .5 m/s^2 at point 1 and 1 m/s^2 at point 2. The average convective acceleration between the two points is positive, as the fluid particles must speed up due to the decrease in area. This holds true for a steady flow, where there is only convective acceleration.
yrael

## Homework Statement

The velocity of the water in the pipe is given by v1=.5t m/s and v2=1tm/s, where t is in seconds. Determine the local acceleration at points 1 and 2. Is the average convective acceleration between these two points negative, zero, or positive?

## Homework Equations

A figure of pipe (funnel like) that is larger at the input end with v1 and smaller end without put speed of v2.

## The Attempt at a Solution

I don't really know how to start answering this question, I don't have the text with me (still in delivery) and don't have any notes that's on this topic.

My try: d (v1)/dt=0.5t so a=d(v1)/dt=.5 m/s^2
d(v2)/dt=1t so a2=d(v2)/dt=1 m/s^2

The local accn changes because the flow is not steady and time dependent, and the values are as you have derived.

The convective accn is positive because a particle of fluid has to speed up due to the area at point 2 being smaller than area at point 1.

For a steady flow, there would be convective accn only.

## What is fluid mechanics?

Fluid mechanics is a branch of physics that deals with the study of fluids (liquids and gases) and the forces that act on them. It involves understanding the behavior of fluids at rest and in motion, and how they interact with their surroundings.

## What is local acceleration in fluid mechanics?

Local acceleration in fluid mechanics refers to the change in velocity at a specific point in a fluid. It is caused by the forces acting on the fluid at that point, such as pressure gradients and viscosity. Local acceleration can be described using the continuity equation and the Navier-Stokes equations.

## What is convective acceleration in fluid mechanics?

Convective acceleration in fluid mechanics is the change in velocity due to the movement of a fluid from one point to another. It is caused by the fluid's inertia and its tendency to resist changes in its motion. Convective acceleration can be described using the advection term in the Navier-Stokes equations.

## How are local acceleration and convective acceleration related?

Local acceleration and convective acceleration are both components of the total acceleration of a fluid. Local acceleration is caused by the forces acting at a specific point, while convective acceleration is caused by the movement of the fluid. They are both important factors in understanding the behavior of fluids in motion.

## What are some practical applications of fluid mechanics and its concepts of local acceleration and convective acceleration?

Fluid mechanics and its concepts of local acceleration and convective acceleration have a wide range of practical applications. They are used in designing and optimizing pumps, turbines, and other fluid machinery. They are also important in understanding and predicting weather patterns, ocean currents, and air flow in aircraft. Additionally, fluid mechanics is crucial in fields such as chemical and biomedical engineering, where fluids play a critical role in processes and systems.

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