Chapter 1 : Fluid pressure and Its Measurement

Example 1.1 Page No : 9

In [1]:
# Variables
p = 343350. 			#pressure at any point in pa
w = 9810. 			    #gravitational consmath.tant
s1 = 1.
s2 = 13.6

# Calculations 
h1 = (p/w)
h2 = h1*s1/s2

# Results 
print "pressure in term of height of water(m)",h1
print "pressure in term of height of mercury(m)",round(h2,7)

pressure in term of height of water(m) 35.0
pressure in term of height of mercury(m) 2.5735294

Example 1.2 Page No : 10

In [4]:
# Variables
h1 = 0.75 			#atm pressure in term of mercury
w = 9810.
w1 = 13.6*w 			#specific weight of mercury
w2 = 15000.
h2 = 3. 		

# Calculations 
Patm = w1*h1
p = w2*h2 			# gauge pressure
Pabs = Patm+p

# Results 
print "gauge pressure(N/m2)",p
print "absolute pressure(N/m2)",Pabs

gauge pressure(N/m2) 45000.0
absolute pressure(N/m2) 145062.0

Example 1.3 Page No : 10

In [3]:
# Variables
h1 = 2.5
h2 = 1.5
s1 = 1
s2 = 0.8
w = 9810

# Calculations 
p2 = s2*w*h2 			#Pressure intensity at interface
p1 = s1*w*h1
p = p1+p2

# Results 
print  "pressure intensity at interface(N/m2)",p2
print  "pressure intensity at bottom(N/m2)",p

pressure intensity at interface(N/m2) 11772.0
pressure intensity at bottom(N/m2) 36297.0

Example 1.4 Page No : 11

In [4]:
# Variables
p = 71613. 			#gauge pressure
w = 9810

# Calculations 
phead = p/w
patm = 10.33
pabs = patm+phead

# Results 
print "absolute pressure in term of water height in meters",pabs

absolute pressure in term of water height in meters 17.63

Example 1.5 Page No : 11

In [5]:
# Variables
h1 = 0.05
h2 = 0.1
s1 = 0.8
s2 = 13.6
w = 9810

# Calculations 
p = s2*h2*w 			#pressure at balance line 
p1 = s1*h1*w 
pf = p-p1

# Results 
print  "pressure in pipe(N/m2)",pf

pressure in pipe(N/m2) 12949.2

Example 1.6 Page No : 12

In [6]:
# Variables
h1 = 0.2
h2 = 0.5
s1 = 0.9
s2 = 13.6

# Calculations 
h = -(h1*s1+h2*s2)
w = 9810
p = h*w

# Results 
print  "vacuum pressure (N/m2)",p

vacuum pressure (N/m2) -68473.8

Example 1.7 Page No : 13

In [7]:
# Variables
s1 = 0.8
s2 = 13.6
dh = 0.4

# Calculations 
h = dh*13.6-dh*0.8
w = 9810
pd = w*h

# Results 
print  "pressure difference in height of water()",h
print  "presuure difference in N/m2",pd

pressure difference in height of water() 5.12
presuure difference in N/m2 50227.2

Example 1.8 Page No : 14

In [8]:
# Variables
s1 = 0.8
s2 = 0.7
h1 = 1.5
h2 = 0.3
h3 = 0.7
s3 = 13.6

# Calculations 
hd = h2*s2+h3*s3-h1*s1
w = 9810
pd = hd*w

# Results 
print  "diffrence in pressure in term of height of water(m)",hd
print  "difference in pressure (N/m2)",pd

diffrence in pressure in term of height of water(m) 8.53
difference in pressure (N/m2) 83679.3

Example 1.9 Page No : 15

In [9]:
# Variables
s1 = 1.6
s2 = 0.8
s3 = 13.6
p1 = 98100.
p2 = 176580.
w = 9810.

# Calculations 
h1 = p1/w
h2 = p2/w
h = (h2-h1+1.6*s2-4.1*s1)/(s3-s2)

# Results 
print "difference in mercury level(cm)",h*100

difference in mercury level(cm) 21.25

Example 1.10 Page No : 16

In [10]:
# Variables
s1 = 1.2
s2 = 1
s3 = 0.7

# Calculations 
h = (s1-s2)*0.3/(s2-s3)

# Results 
print "difference in height(cm)",h*100

difference in height(cm) 20.0

Example 1.11 Page No : 17

In [11]:
# Variables
s1 = 0.8
s2 = 13.6
z = 0.02
w = 9810
h2 = 0.2
h1 = 0.1

# Calculations 
h = h2*s2-h1*s1+(z*h2*(s2-s1))
p = h*w

# Results 
print "pressure of the oil in N/m2",p

pressure of the oil in N/m2 26400.672

Example 1.12 Page No : 18

In [12]:
# Variables
l = 4
b = 2
h = 3
w = 9810
s = 0.8

# Calculations 
p1 = w*l*b*h*s
p2 = w*s*l*h*1.5
p3 = w*s*b*h*1.5

# Results 
print "total pressure on horizontal base",p1
print  "total pressure on larger vertical base",p2
print "total pressure on smaller vertical walls",p3

total pressure on horizontal base 188352.0
total pressure on larger vertical base 141264.0
total pressure on smaller vertical walls 70632.0

Example 1.13 Page No : 18

In [2]:
import math

# Variables
p = 490500.
w = 9810.

# Calculations 
h = p/w
D = 0.15
A = math.pi*D*D*0.25
pt = w*A*h
h1 = (D*D)/(16*h)

# Results 
print "total hydrostatic pressure in N",round(pt,2)
print "position of centre of pressure below the centre of pipe : %f"%h1

total hydrostatic pressure in N 8667.85
position of centre of pressure below the centre of pipe : 0.000028

Example 1.14 Page No : 19

In [4]:
import math

# Variables
w = 9810.
h = 4.
d = 2.

# Calculations 
a = d*d*0.25*math.pi
p = w*a*h
h1 = d*d/64
T = p*(h1) 

# Results 
print  "torque required to keep the disc in vertical position in N.m %.4f"%T

torque required to keep the disc in vertical position in N.m 7704.7560

Example 1.15 Page No : 20

In [6]:
# Variables
w = 9810.
h = 2.
l = 2.
b = 1.

# Calculations 
a = l*b
p = w*a*h
h1 = h+(b*l*l*l/(12*b*l*l))

# Results 
print "total pressure",p
print "location of its centre of pressure",round(h1,4)

total pressure 39240.0
location of its centre of pressure 2.1667

Example 1.16 Page No : 21

In [7]:
# Variables
h1 = 8
w = 9810
wd = 6

# Calculations 
p1 = 0.5*w*h1*h1*wd
h2 = 4
p2 = 0.5*h2*w*h2*wd
h11 = 0.66666*h1
h22 = 0.6666*h2
p = p1-p2
hf = (p1*(h1-h11)-p2*(h2-h22))/p

# Results 
print "resultant force",p
print "position of its line of action",round(hf,5)

resultant force 1412640.0
position of its line of action 3.11109

Example 1.17 Page No : 22

In [17]:
# Variables
z = 9810
w = 10
h = 2

# Calculations 
p = 0.5*h*h*w*z
h1 = h*0.6666

# Results 
print "total hydrostatic thrust",p
print "its point of application",h1

total hydrostatic thrust 196200.0
its point of application 1.3332

Example 1.18 Page No : 22

In [18]:
# Variables
a1 = 1.4*2.2*1.4
x1 = 1.6+0.7
x11 = (1.4*1.4/(12*2.3))+x1
x2 = 0.7
x22 = (1.4*1.4/(12*0.7))+x2
z = 9810

# Calculations 
p1 = z*a1*x1
p2 = z*a1*x2/1.4
p = p1-p2
h = (p1*(3-x11)+p2*(1.4-x22))/p
f = (p1*(3-x11)-p2*(1.4-x22))/1.4

# Results 
print "resultant force",p
print "force acting horizontally on the top of the gate",f

resultant force 76141.296
force acting horizontally on the top of the gate 36660.624

Example 1.19 Page No : 24

In [8]:
# Variables
s = 1.5
s1 = 0.9
w = 9810
h1 = 0.9
h2 = 0.6

# Calculations 
p1 = 0.5*w*s*s1*h1*h1 			#total pressure due to oil
p2 = w*h1*h2*s*s1 			# total pressure due to oil above water
p3 = w*h2*h2*0.5*s 			#total pressure due to water
p = p1+p2+p3
h = ((p1*0.6666*h1)+(p2*(h1+0.5*h2))+(p3*(0.6666*h2+h1)))/p

# Results 
print "resultant pressure on the wall in N/m2",p
print "position of centre of pressure from free surface",round(h,5)

resultant pressure on the wall in N/m2 15163.8075
position of centre of pressure from free surface 1.00521

Example 1.20 Page No : 26

In [20]:
# Variables
d = 2.4
h = 1.6
s = 1.2

# Calculations 
a = d*s
w = 9810
p = w*a*h*s
h1 = ((2*s*s*s*d)/(12*a*h))+h

# Results 
print "total pressure in N",p
print "its point of application",h1

total pressure in N 54245.376
its point of application 1.75

Example 1.21 Page No : 26

In [6]:
import math

# Variables
x = 30.
d = 1.2
h = 1.5
w = 9810.

# Calculations 
z = math.sin(x*math.pi/180)
h1 = (z*d*0.5)+h
a = 0.25*math.pi*d*d
p = a*w*h1
h11 = (d*d*z*z)/(16*h1)+h1

# Results 
print "total pressure",round(p,3)
print "position of centre of pressure",round(h11,4)

total pressure 19970.728
position of centre of pressure 1.8125

Example 1.22 Page No : 27

In [9]:
import math

# Variables
d = 2
z = 0.5

# Calculations 
h = z+0.5*d
w = 9810
a = math.pi*d*d*0.25
p = a*w*h
h11 = (1/(16*1.5))+1.5

# Results 
print "total pressure on the plate %.3f N"%p
print "position of centre of pressure",round(h11,5)

total pressure on the plate 46228.536 N
position of centre of pressure 1.54167

Example 1.23 Page No : 28

In [10]:
import math

# Variables
x = 30.
z = math.sin(x*math.pi/180)
h = 6-(z*0.5)
l = 1.
b = 4.
a = l*b
w = 9810.

# Calculations 
p = w*a*h
h11 = (z*z)/(12*h)+h
f = p*0.5072

# Results 
print "force normal to the gate at point B",round(f,2),"N"

force normal to the gate at point B 114439.54 N

Example 1.24 Page No : 29

In [11]:
import math

# Variables
x = 30.
z = math.sin(math.pi*x/180)
d = 1.4
h = 3.
b = 1.5

# Calculations 
h1 = z+d
a = 0.5*h*b
w = 9810
p = w*a*h1
h11 = ((z*z*h*h*h*b)/(36*a*h1))+h1

# Results 
print "total pressure on the plate",round(p,2),"N"
print "position of centre of pressure",round(h11,4),"m"

total pressure on the plate 41937.75 N
position of centre of pressure 1.9658 m

Example 1.25 Page No : 30

In [15]:
import math

# Variables
d = 1.8
h = 2.4
w = 9810
s = 0.8

# Calculations 
p1 = w*d*d*h*0.25*math.pi
h1 = ((d*d)/(16*h))+h
p = w*(s*1.5+2.4)
p2 = p*math.pi*d*d*0.25
p = p2-p1
ab = w*(s*1.5+1.5)
de = w*(s*1.5+3.3)
ce = de-ab
x = ((0.5*ce*d*0.3)/(0.5*(ab+de)*d))
h2 = x+h
h12 = h1-h2

# Results 
print  "change in total pressure",round(p,3)
print "position of centre of pressure",h2
print "change in position of centre of pressure",round(h12,6),"m"

change in total pressure 29956.091
position of centre of pressure 2.475
change in position of centre of pressure 0.009375 m

Example 1.26 Page No : 31

In [18]:
import math


# Variables
l = 5.
r = 3.
a = l*r
h = r*0.5
w = 9810.

# Calculations 
ph = w*a*h
pv = w*0.25*math.pi*r*r*l
p = math.sqrt((ph*ph)+(pv*pv))
z = ph/pv
theta = math.degrees(math.atan(z))

# Results 
print "resultant pressure on the gate",round(p,2),"N"
print "angle of resultant force with vertical",round(theta,7)

# note : rounding off error.

resultant pressure on the gate 411011.12 N
angle of resultant force with vertical 32.4816366

Example 1.27 Page No : 32

In [19]:
import math

# Variables
s = 5.
z = math.sin(math.radians(45.))
a = 2*s*z
h = s*z
w = 9810.

# Calculations 
ph = w*a*h
pv = w*((0.25*s*s*math.pi)-(0.5*a*h))

# Results 
print "horizontal pressure",ph,"N"
print "vertical pressure",round(pv,1),"N"

horizontal pressure 245250.0 N
vertical pressure 69993.9 N
In [ ]: