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# Accelerated vertically

Fluid masses subjected to vertical acceleration
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Contents

### Key Facts

Gyroscopic Couple: The rate of change of angular momentum () = (In the limit).
• = Moment of Inertia.
• = Angular velocity
• = Angular velocity of precession.

Blaise Pascal (1623-1662) was a French mathematician, physicist, inventor, writer and Catholic philosopher.

Leonhard Euler (1707-1783) was a pioneering Swiss mathematician and physicist.

Henry Philibert Gaspard Darcy (1803-1858) was a French engineer who made several important contributions to hydraulics.

## 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,