Mechanics of liquids (MEC215)

Hydrotronics can be use in some automation and robotic applications complementing electronic and electronics resources. In this article, from my book Mechatronics and Robotics (out os print), we describe some formulas and applications of liquids devices in mechatronics.

When using hydraulics or hydronics in mechatronics projects the designer must know how the devices work and this implies to know the fundamentals concepts and laws of the mechanics of liquids. In the next lines we will give to the reader some formulas, tables, applications and basic concepts involving hydrotronics (*).

 

(*) We can define "hydrotronics" the science derived of the application at the same time of electronics and hydraulics.

 

 

Pressure

a) Pressure is the amount of force for unit of area..

 

Formula

P = F/S

 

Where:

P is the pressure

F is the force

S is the area where the force is applied

 

b) Pressure of a column of liquid.

 

Formula

 

P = ρ x g x h

 

Where:

P is the pressure

ρ is the density of the liquid

g is the acceleration of gravity (9.8 m/s2)

h is the height of the column

 

c) Pressure in determinated depth of water:

Formula

 

P = h x D

 

Where:

P is the pressure

h is the depth of the considered point

D is the density of the water (or other liquid)

 

 

Table

Density of Water in Different Temperatures

T (°C) D (g/mL)
0 0.999 87
1 0.999 93
2 0.999 97
3 0.999 99
4 1.000 00
5 0.999 99
6 0.999 97
7 0.999 93
8 0.999 88
9 0.999 81
10 0,999 73
11 0.999 63
12 0.999 52
13 0.999 40
14 0.009 27
15 0.999 13
16 0.998 97
17 0.998 80
18 0.998 62
19 0.998 43
20 0.998 23
21 0.997 02
22 0.997 80
23 0.997 57
24 0.997 32
25 0.997 07
26 0.996 81
27 0.996 52
28 0.996 22
29 0.995 92
30 0.995 61

 

Table

Density of Some Liquids

(at 20o C)

Liquid Density (g/cm3)
Acetic acid 1.049
Acetone 0.791
Aniline 1.02
Benzene 0.879
Benzine 0.68 - 0.72
Chloroform 1.489
Crude Oil 0.76 - 0.86
Ethyl Alcohol 0.79
Formic acid 1.22
Glycerine 1.26
Heavy Water 1.108 6
Heptane 0.684
Hexane 0.660
Machine oil 0.8 - 0.9
Mercury 13.55
Methyl Alcohol 0.792
Milk (average) 1.03
Nitric acid 1.51
Nitroglycerine 1.6
Sea water 1.01 - 1.03
Water 0.998 23

 

Archimedes' Principle

A body, immersed in a liquid is buoyed up by a force equal to the weight of the liquid displaced.

 


 

 

 

Communicating vessels

The heigths of columns in communicating vessels are inversely proportional to their densities.

 


 

 

 

Formula

 

h1/h2 = d2/d1

 

Where:

h1 and h2 are the heigths of columns

d1, d2 are the denseities of the liquids

 

Flow of Liquids from Containers

The speed of the liquid in the outlet depends on several factor as shape, liquid density, position of the outlet in the container, etc. Figure 3 shows some cases with the associated formulas bellow.

 

 


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a) Base Aperture

 

Formula

 

 


 

 

 

b) Small Lateral Aperture

 

Formula

 

 


 

 

 

c) Excess Pressure on Surface of Liquid

 

Formula

 

 


 

 

 

d) Excess of pressure applied to na outlet point

 

Formula

 

 


 

 

 

Where:

v is the velocity in the outlet

Cv is the velocity coefficient (0.97 for water)

g is the gravity acceleration (9.8 m/s2)

h is the heith of the container filled with water

Pex /? is pressure in excess by area unit

 

 


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