#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : MANOMETERS
# Example 1 # Page 329
D1=0.1 #('Enter the diameter of well =:')
D2=0.01 #('Enter the diameter of the tube =:')
g=9.81;
pho_air=1.23 #('Enter the density of air in kg/m**3 =:')
pho_liquid=1200. #('Enter the density of liquid in manometer =:')
h=1. #('Enter the height by which liquid decreases in smaller area arm when exposed to the nominal pressure of p2 =:')
# Let the pressure difference is represented by P=p1-p2
print("The pressure difference is given by:")
print("P=h*(1+((D2/D1)**2)*g*(pho_liquid-pho_air))")
P=h*(1+((D2/D1)**2)*g*(pho_liquid-pho_air))*10**-3;
print'So the pressure difference is given by kPa \n',round(P,3)
#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : MANOMETERS
# Example 2 # Page 329
pho_l=900.
print("pho_l=900 ") #('Enter the density of the fluid =:')
Pa= 500000.
print("Pa= 500000 ") #('Enter the air pressure =:')
t=298.
print("t=298 ") #('Air is at what temperature(in deg cent) =:')
R=287.;
print("R=287;")
g=9.81;
T=t+273;
print("pho_a=Pa/(R*T);")
pho_a=Pa/(R*T);
print'The density of air is d kg/m**3 \n',round(pho_a,3)
h=.2 #('Enter the difference in the height of the fluid in the manometer=:')
print("Pres_diff=(g*h)*(pho_l-pho_a)")
Pres_diff=(g*h)*(pho_l-pho_a)*10**-3
print'The differential pressure is kPa\n',round(Pres_diff,3)
#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : Elastic Transducers
# Example 3 # Page 337
Sa=1000.
print("Sa=1000") #('Enter the sensitivity of LVDT =:')
#Properties of diaphragm
E=200*10**9 #('Enter the value of modulus of elasticity=:')
print("E=200*10**9 ")
v=0.3 #('Enter the Poissons ratio=:')
print("v=0.3 ")
d=0.2 #('Enter the diameter of diaphragm=:')
print("d=0.2 ")
R=d*(1./2.);
P_max=2*10**6 #('What is the maximum pressure?')
print("P_max=2*10**6 ")
p=7800 #('What is the density of steel?')
print("Thickness is given by:")
print("t=(3*P_max*R**4*(1-v**4)/(4*E))**(1/4);")
t=(3*P_max*R**4*(1-v**4)/(4*E))**(1/4)
T=t*1000;
print'Thickness is mm\n',T
#To calculate the lowest pressure in kPa which may be sensed by this instrument , resolution and the natural frequency of the diaphragm
y=.001 #('Enter the l)east value of measurement=:')
p_min=(y*16*E*t**3)/(3*R**4*(1-v**2)*Sa)
print'So the minimum pressure and resolution is Pa \n',p_min
f=(10.21/R**2)*((E*t**2)/(12*(1-v**2)*p))**(1/2)
print'The natural frequency of diaphragm is d Hz',f
#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : Design of Pressure Transducers
# Example 4 # Page 338
p_max=10*10**6 #('Enter the capacity of the transducer=:')
D=.05 #('Enter the diameter of diaphragm=:')
R=D/2;
v=0.3; # poissons ratio
E=200*10**9;
# We know that
# y=3pR**4(1-v**2)/16t**3E
# if y<t/4, the non linearity is restricted to 0.3%
#So t is given by
t=(3*p_max*R**4*(1-v**2)/(4*E))**(1./4.)
print(t)
print'thickness comes out to be d m\n',t
Sr_max=(3*p_max*R**2)/(4*t**2)
print'So the max radial stress is d Pa\n',Sr_max
print'The given fatigue strength is 500MPa\n'
if (Sr_max > 500*10**6):
print("The diaphragm must be redesigned");
t1=((3*p_max*R**2)/(4*500*10**6))**(1./2.);
print'The required thickness is d m\n',t1
else:
print("The design is OK");
# Let the voltage ratio be represented by Err
Err=(820*p_max*R**2*(1-v**2))/(E*(t1**2))
print'The voltage ratio is d\n', Err
# For maximum power dissipation
PT=1.
RT=120.
Ei=2*(PT*RT)**(1./2.);
print("Let the sensitivity of the transducer be represented by ss")
ss=(820*R**2*(1-v**2)*Ei)/(E*t1**2)
print'sensitivity is d\n', round(ss)
# Part c
S_LVDT=(ss*16*t**3*E)/(3*R**4*(1-v**2)*Ei)
print'SENSITIVITY OF LVDT IS d \n',round(S_LVDT)
#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : Pressure Gage
# Example 5 # Page 347
from math import pi,sqrt
p_max=10*10**6 #('Enter the maximum differential pressure')
fn=20000. #(' Enter the frequency')
E=200*10**9; # modulus of elasticity
v=0.3; # poissons ratio
p=7800. # density of steel
print("Let t/R be represented by TR ")
TR=((3*p_max*(1-v**2))/(4*E))**(1/4)
# we know R**2/t = r2t=10.21(Et**2/12(1-v**2)p)**0.5/R**2 using it , we have
r2t=(10.21*sqrt(E/(12*(1-v**2)*p)))/fn
R=TR*r2t;
print'value of R is d m\n', R
t=R*TR;
print' value of t is d m \n',round(t,2)
eo=8.85*10**-12
er=1.0006;
d=.001 #('Enter the distance between the plates of capacitor=:')
S=-(eo*er*pi*R**2)/d**2;
# variation of capacitor distance with respect to pressure is given by
q=(3*R**4*(1-v**2))/(16*E*t**3)
# total sensitivity of the pressure transducer is given by
sensitivity=S*q*10**18;
print' So the total sensitivity of the pressure transducer is given by pF/MPa\n',round(sensitivity,2)
#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : High Pressure Measurement
# Example 6 # Page 357
R1=100 #(' Enter the resistance of Mangnin wire=:')
print("R1=100")
b=25*10**-12; # standard for mangnin
print("b=25*10**-12;")
print("u=0.5")
u=0.5 #(' enter the uncertainty in measuring pressure for gage=:')
# to calculate maximum uncertainty in differential pressure
udp=u*(10-0.1)*10**6/100;
uR=R1*b*udp;
print'So the maximum uncertainty in measuring resistance is d ohm \n',uR
#to calculate the output bridge voltage for 10 MPa
Ei=5 #('enter the input voltage=:')
print("p1=0.1*10**6")
print("R2=R1*(1+b*p1)")
print("p2=10*10**6 ")
p1=0.1*10**6 #('enter the pressure at which bridge is assumed to be balanced=:')
R2=R1*(1+b*p1)
p2=10*10**6 #('enter the pressure at which output voltage is to be calculated=:')
R3=R1*(1+b*p2);
dR=R3-R2;
r=1;
Eo=(r*dR*Ei)/((1+r)**2*R2)
print' The output bridge voltage is d volt\n',round(Eo,4)
#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : McLeod Gage
# Example 7 # Page 362
print("Vb=150*10**-6")
print("d=1.5*10**-3")
print("a=pi*d**2/4;")
from math import pi,sqrt
Vb=150*10**-6 #('enter the volume of the Mc Leod gage=:')
d=1.5*10**-3 #('enter the diameter of capillary=:')
a=pi*d**2./4.;
p=40*10**-6 #('enter the pressure for which the gage reading is to be noted=:')
#y=(-p*area_cap+sqrt((p*area_cap)**2-4*p*area_cap*Vb))/(2*area_cap);
l=p*a;
y=(sqrt(l**2+(4*l*Vb))-l)/(2*a)
print'The gage reading comes out to be d mof Hg\n',round(y,3)
#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : Knudsen Gage
# Example 8 # Page 363
Td=40. #('enter the temperature difference=:')
Tv=300. #('enter the gas temperature at which the force has to be calculated=:')
p=2*10**-6 #('enter the pressure(in m of Hg)=:')
pa=p*13600*9.81;
k=4*10**-4; # knudsen constant
F=(pa*Td)/(k*Tv);
print'So the required force is N',F
#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : Sound Measurement
# Example 9# Page 369
from math import sqrt
print("Lp=104")
Lp=104 #('enter the sound pressure level in decibles=:')
print("pa=20*10**-6;")
print("p=sqrt(10**(Lp/10)*pa**2);")
pa=20*10**-6; # rms pressure threshold of hearing
p=sqrt(10**(Lp/10)*pa**2);
print'root mean square sound pressure is Pa\n',p
#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : Sound Measurement
# Example 10# Page 370
Lp1=75 #('enter the sound level first machine=:')
Lp2=77 #('enter the sound level second machine=:')
Lp3=79 #('enter the sound level third machine=:')
from math import log10
print("Since the noise levels are incoherent,the total sound pressure is the sum of the mean square value of the individual sound pressures")
Lp_total=10*log10(10**(Lp1/10)+10**(Lp2/10)+10**(Lp3/10));
print'The total sound pressure is dB',round(Lp_total,2)
#decibles are normally rounded off to the nearest integers
#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : Knudsen Gage
# Example 11 # Page 371
Td=20. #('enter the temperature difference=:')
Tv=500. #('enter the gas temperature at which the force has to be calculated=:')
p=6*10**-6 #('enter the pressure(in m of Hg)=:')
pa=p*13600*9.81;
k=4*10**-4; # knudsen constant
F=(pa*Td)/(k*Tv);
print'So the required force is N',round(F)
#CHAPTER 6 _ PRESSURE AND SOUND MEASUREMENT
#Caption : McLeod Gage
# Example 12 # Page 373
from math import pi,sqrt
Vb=110*10**-6 #('enter the volume of the Mc Leod gage=:')
d=1.72*10**-3 #('enter the diameter of capillary=:')
a=pi*d**2./4.;
p=80*10**-6 #('enter the pressure for which the gage reading is to be noted=:')
#y=(-p*area_cap+sqrt((p*area_cap)**2-4*p*area_cap*Vb))/(2*area_cap);
l=p*a;
y=(sqrt(l**2+(4*l*Vb))-l)/(2*a)
print'The gage reading comes out to be d mof Hg\n',round(y,4)