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# Accelerated vertically

Fluid masses subjected to vertical acceleration
Contents

## Overview

Consider a tank open at top, containing a liquid and moving vertically upwards with a uniform acceleration. Since the tank is subjected to an acceleration in the vertical direction only, therefore the liquid surface will remain horizontal.

Now consider a small column of the liquid of height h and area dA in the tank as sown in fig-1.

Let, = Pressure due to vertical acceleration

We know that the forces acting on this column are :

1. Weight of the liquid column acting vertically downwards,

2. Acceleration force,

3. Pressure exerted by the liquid particles on the column.

Now resolving the forces vertically,

Example:

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##### Example - Fluid masses subjected to vertical acceleration
Problem
An open rectangular tank 4m long and 2.5m wide contains an oil of specific gravity 0.85 up to a depth of 1.5m. Determine the total pressure on the bottom of the tank, when the tank is moving with an acceleration of of g/2 m/s2 (i) vertically upwards (ii) vertically downwards.
Workings
Given,
• = 4 m
• = 2.5 m
• = 1.5 m
• = g/2 m/s2
• Specific gravity of liquid = 0.85

(i) Total pressure on the bottom of the tank, when it is vertically upwards

Specific weight of oil,

Intensity of pressure at the bottom of the tank,

Total pressure on the bottom of the tank,

(i) Total pressure on the bottom of the tank, when it is vertically downwards

Intensity of pressure at the bottom of the tank,

Total pressure on the bottom of the tank,