# Accelerated vertically

Fluid masses subjected to vertical acceleration

**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/s

^{2}(i) vertically upwards (ii) vertically downwards.Workings

Given,

- = 4 m
- = 2.5 m
- = 1.5 m
- = g/2 m/s
^{2} - 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,