812 
APPENDIX 1. 
1) PIEZO-ELECTRIC GAUGE THEORY. 
The miniature gauge is connected to the input of the piezo-electric 
amplifier as shown below:- 
R=Z 
ete a erg 4 a 
| f : Amplifier 
CR 
Ca Ze Co 
The capacity of a n=ply gauge is given by 
k = dielectric constant of tourmaline (7.4) 
CGn = nkaA farads A = area of tourmaline disc in oms. 
4nd x 9 x 10" ad = thiokness of tourmaline disc in ams. 
k = 4.5 for Quartz 
= nA x 0.658 x 10712 farads. 5.6 for Roch Salt 
ad 
The charge developed by a n=ply gauge due to a pressure p dynes/om2 
is given by 
Qa, = nk! p A coulombs k! = piezo-electric constant for 
tourmaline (2.20 x 10717 coulombs/ 
dyne) 
PD = pressure in dynes/cm@. 
A = area in cms. 
= 1.518 n p A x 10712 cowlombs (P = pressure in lbs./in2). 
Q 
“ VG, = = = 2.31 Pd volts. P = pressure in lbs./in2 
Gy d = thickness of disc in cms. 
The special cable developed for use with piezo-electric gauges has a 
capacity of 18.5 x 10-12 farad per foot. Let total length of cable used 
with miniature gauge be L feet long. 
wel Cg iS) 18e5 Ts x 10712 farads. 
Hence vecltage Vp, developed across the amplifier input is given very 
closely by a 
DA x 0.658 x 10712 
Vp. = ol 5 
es Scot volcom (ominclnpe them shinnt 
18.5 L x 10712 capacity Cp) 
nAP 
0.0822 L volts. 
“ine 
number of pone ae discs 
pressure in lbs./in 
area of tourmaline disc in cms2. 
length of cable in feet. 
tun 
Heys 
EXAMPLE. 
Se 
Consider a two=ply miniature gauge, each tourmaline disc being #" in 
diameter and 1/16" thick. 
Mheny | Clve ply; 
, -@ 2ply 
oe V 2 ply 
10.5 micromicrofarads 
3.85 P micromicrocoulombs 
0.367 P volts. 
ow tt 
The voltage across the amplifier input is given by 
Vp 2 ply = 0.2086 P/;, 
LP Ti eeooee 
