Chapter 1 : Hydrostatics

Example 1.1 Page no : 9

In [1]:
#initialisation of variables
h1 = 2 			#in
h2 = 2 			#in
wn = 13.6 			#g/cc
w = 1 			#g/cc
W = 62.4 			#lbs/ft**3

#CALCULATIONS
ha = ((h2*wn/w)-h1)/12
pa = ha*W/144

#RESULTS
print  'Pressure of water = %.2f lb/sq in '%(pa)

Pressure of water = 0.91 lb/sq in

Example 1.2 page no : 11

In [1]:
#initialisation of variables
a = 6 			#ft
h = 2 			#ft
sm = 13.6
sw = 1
sl =0.8

#CALCULATIONS
dh = h*(sm-sw)+a
h1 = (dh-a)/(sl-1)

#RESULTS
print  'pressure difference in ft of water = %.1f ft of water '%(dh)
print  'reading of mercury = %.f ft of liquid '%(h1)

pressure difference in ft of water = 31.2 ft of water 
reading of mercury = -126 ft of liquid

Example 1.3 page no : 11

In [12]:
#initialisation of variables
sm = 13.6
so = 0.9
sw =1
hb = 8 			#ft
hc = 7.5 			#ft
hd = 1.75 			#ft

#CALCULATIONS
pa = (sm-so)*sw
pc = pa - hb*so
pd = pa+so*2-sm*2.5-hc
pb = hb+hd+pd

#RESULTS
print  'pressure at A = %.2f ft of water '%(pa)
print  'pressure at B = %.2f ft of water '%(pb)
print  'pressure at C = %.2f ft of water '%(pc)
print  'pressure at D = %.2f ft of water '%(pd)

pressure at A = 12.70 ft of water 
pressure at B = -17.25 ft of water 
pressure at C = 5.50 ft of water 
pressure at D = -27.00 ft of water

Example 1.4 page no : 12

In [20]:
#initialisation of variables
lm = 2 			#ft
lw = 5 			#ft
lo = 8 			#ft
so = 0.75
p = 40 			#lb/in**2
w = 62.4 			#lbs/ft**3
sm = 13.6
#CALCULATIONS
h = p*144/w
Pd = (h-lm*sm)
Pc = Pd-lw
Pb = Pc-lo*so
Pg = Pb*w/144
#RESULTS
print  'Reading of the pressure guage at the top of tank  = %.1f lb/in**2 '%(Pg)

Reading of the pressure guage at the top of tank  = 23.4 lb/in**2

Example 1.5 page no : 13

In [22]:
#initialisation of variables
h = 42 			#in
w = 62.4 			#lbs/ft**3
#RESULTS
D = h*w/(144*12)
#CALCULATIONS
print  'Depth of point  = %.1f lb/in**2 '%(D)

Depth of point  = 1.5 lb/in**2

Example 1.6 pageno : 14

In [23]:
#initialisation of variables
h = 200 			#ft
w = 62.4 			#lbs/ft**3
#RESULTS
D = h*w/(144)
#CALCULATIONS
print  'Depth of point  = %.1f lb/in**2 '%(D)

Depth of point  = 86.7 lb/in**2

Example 1.7 pageno :15

In [24]:
#initialisation of variables
w = 62.4 			#lbs/ft**3
l = 2 			#ft
b = 3 			#ft
h = 10 			#ft
#CALCULATIONS
P = w*l*b*h
#RESULTS
print  'Total pressure  = %.f lb '%(P)

Total pressure  = 3744 lb

Example 1.8 page no : 15

In [5]:
import math 

#initialisation of variables
l = 2. 			#ft
b = 3. 			#ft
a = 60. 			#degrees
h = 8. 			#ft
w = 62.4 			#lbs/ft**3
#CALCULATIONS
x = h+(b/l)*math.cos(math.radians(a))
P = w*l*b*x
#RESULTS
print  'total pressure  = %.f lb '%(P)


# Note : Answer is different in book please calculate manually using calculator.

total pressure  = 3276 lb

Example 1.9 page no : 15

In [6]:
#initialisation of variables
l = 2. 			#ft
b = 3. 			#ft
h = 8. 			#ft
w = 62.4 			#lbs/ft**3
#CALCULATIONS
P = w*l*b*(h+(b/2))
#RESULTS
print  'total pressure  = %.f lb '%(P)

# Note : Answer is different in book please calculate manually using calculator.

total pressure  = 3557 lb

Example 1.10 pageno : 17

In [7]:
#initialisation of variables
l = 6. 			#ft
b = 4. 			#ft
w = 62.4 			#lbs/ft**3
h = 10. 			#ft

#CALCULATIONS
P = w*l*b*(b/2)
hn = (b/2)+(l*b**3/(12*l*b*(b/2)))
P1 = w*(h+(b/2))*l*b
h1 = (h+(b/2))+(l*b**3/(12*l*b*(h+(b/2))))

#RESULTS
print "Total pressure  = %d lb"%(P1)
print "Depth  = %.2f ft"%(hn)
print 'pressure in ft in case 2 = %.3f ft '%(h1)

Total pressure  = 17971 lb
Depth  = 2.67 ft
pressure in ft in case 2 = 12.111 ft

Example 1.11 page no : 18

In [8]:
import math 

#initialisation of variables
sp = 0.87
d = 12. 			#ft
W = 62.4 			#lb/ft**3
Wa = 30. 			#lb/in**2

#CALCULATIONS
A = math.pi*d**2/4
w = W*sp
x = Wa*144/(w)
P = round(w*A*x,-3)
h = x+(A*d**2/16/(A*x))

#RESULTS
print  'force exerted by the oil upon the gate  = %.f lb '%(P)
print  ' position of centre of pressure  = %.3f ft '%(h)

# Note : Answer may vary because of rounding error.

force exerted by the oil upon the gate  = 489000 lb 
 position of centre of pressure  = 79.689 ft

Example 1.12 page no : 18

In [11]:
#initialisation of variables
import math 
w = 62.4 			#lb/ft**3
a = 60. 			#degrees
l = 18. 			#ft
b =  4. 			#ft
W = 8000. 			#lb

#CALCULATIONS
P = w*b/(math.sin(math.radians(a))*2)
h = ((b/(12*(math.sin(math.radians(a)))**3))*(math.sin(math.radians(a)))**2/(b/(math.sin(math.radians(a))*2)))+0.5
h1 = (1-h)/math.sin(math.radians(a))
x = ((l*W)/(h1*P))**(1./3)

#RESULTS
print  'Level of water  = %.2f ft '%(x)

Level of water  = 13.74 ft

Example 1.13 page no : 19

In [31]:
import math 

#initialisation of variables
w = 62.4 			#lb/ft**3
l = 12 			#ft
b = 6 			#ft
h = 5.196 			#ft
a = 60 			#degrees
a1 = 45 			#degrees

#CALCULATIONS
P = w*l*b*h/2
h1 = ((l*b**3*(math.sin(math.radians(a)))**2/12)/(l*b*(h/2)))+(h/2)
R = round(P*(b-(h1/math.cos(math.radians(a/2))))/((b*math.sin(math.radians(a1)))/2),-2)

#RESULTS
print  'Total comression in the promp CD  = %.f lb '%(R)

Total comression in the promp CD  = 11000 lb

Example 1.14 page no : 22

In [10]:
import math 

#initialisation of variables
w = 62.4 			#lb/ft**3
h = 4. 			#ft
b = 6. 			#ft
sg = 1.45
h1 = 5. 			#ft
a = 90. 			#degrees

#CALCULATIONS
P1 = w*sg*h*b*(h1+(h/2))
P2 = w*h*b*(h/2)
Pr = P1-P2
hup = ((b*h**3/12)*(math.sin(math.radians(a)))**2/(h*b*(h1+(h/2))))+(h1+(h/2))
x1 = h+h1-hup
hd = h*2/3
x2 = h-hd
x = (P1*x1-P2*x2)/Pr
d = h1+h-x
F = Pr*x/4

#RESULTS
print  'P resultant  = %.f lb '%(Pr)
print  'depth of centre of pressure  = %.3f ft '%(d)
print  'force F required to act horizontally at the top of gate  = %.f lb '%(F)


# Note : The answer given in texxtbook is wrong. Please check using a calculator.

P resultant  = 12205 lb 
depth of centre of pressure  = 7.074 ft 
force F required to act horizontally at the top of gate  = 5878 lb

Example 1.15 page no : 23

In [1]:
import math 

#initialisation of variables
w = 15. 			#ft
D = 15. 			#ft
W = 62.4 			#lb/ft**3
a = 120. 			#degrees
h1 = 15. 			#ft
h2 = 4. 			#/ft
h3 = 18. 			#ft

#CALCULATIONS
Pu = round(w*D*W*w/2,-3)
hu = ((w*D**3/12)/(w**2*D/2))+w/2
Pd = W*h2*w*h2/2-8
hd = ((w*h2**3/12)/(h2*h1*(h2/2)))+(h2/2)
P = Pu-Pd
h = (Pu*(h1-hu)-Pd*(h2-hd))/P
F = P/(2*math.sin(math.radians(a/4)))
RT = round(F*(h3-(h1/10)-h)/(h3-(h1/5)),-3)
RB =F-RT


#RESULTS
print 'Resultant water pressure on each gate : %d lb'%P
print 'Height of c.p from bottom %.2f ft'%h
print  'RB  = %.f lb '%(RB)

Resultant water pressure on each gate : 97520 lb
Height of c.p from bottom 5.28 ft
RB  = 24520 lb

Example 1.16 page no : 25

In [86]:
#initialisation of variables
import math 
h = 42. 			#ft
w = 25. 			#ft
d = 8. 			#ft
W = 150. 			#lb/ft**3
w1 = 62.4 			#lb/ft**3

#CALCULATIONS
W1 = W*(h*d+(h*(w-d)/2))
P = round(w1*h*(h/2),-3)
R = round(math.sqrt(W1**2+P**2)-100,-2)
o = math.tan(math.radians(P/W1))
AE = round((d*h*(d/2)+(w-d)*h*(d+(w-d)/3)/2)/(d*h+h*(w-d)/2),2)
EF = round(14*P/W1,2)
AF = EF+AE
AH = w/2
e = round(AF-AH,1)
BS = round(W1*e*AH/(w**3/12),-1)
DS = W1/w-3
Smax = BS+DS
Smin = DS-BS
u = w1 * h
#RESULTS
print "Resultant thrust R = %d lb"%R
print  'S max  = %.f lb/sq ft '%(Smax)
print  ' S min  = %.f lb/sq ft '%(Smin)
print 'Normal stress on vertical plane at the base due to water pressure and is uniform = %d lb/sq ft'%u

Resultant thrust R = 117500 lb
S max  = 8045 lb/sq ft 
 S min  = 265 lb/sq ft 
Normal stress on vertical plane at the base due to water pressure and is uniform = 2620 lb/sq ft

Example 1.17 page no : 27

In [14]:
#initialisation of variables
W = 145. 			#lb/cu ft
M = 500. 			#lb
W1 = 64. 			#lb/cu ft

#CALCULATIONS
dW = W-W1
V = M/dW

#RESULTS
print  'Volume of concrete  = %.1f cu ft '%(V)

Volume of concrete  = 6.2 cu ft

Example 1.18 page no : 28

In [87]:
#initialisation of variables
W = 10000. 			#tons
A = 15000. 			#ft**2
d = 15. 			#ft
Dsw = 64. 			#lb/ft**3
Dw = 62.4 			#lb/ft**3

#CALCULATIONS
Vsw = 2240./Dsw
Vw = 2240./Dw
dV = Vw-Vsw
V1 = W*dV
h = W/A
h1 = d+h

#RESULTS
print  'Depth necessary to just float the ship in river  = %.2f ft '%(h1)

Depth necessary to just float the ship in river  = 15.67 ft

Example 1.19 page no : 31

In [2]:
# find Rightening moment

import math 

#initialisation of variables
W = 5000. 			#tons
w = 10. 			#tons
d = 30. 			#ft
x = 5.5 			#in
l = 10. 			#ft
a = 15. 			#degrees

#CALCULATIONS
GM = round((w*d)*l/(W*(x/12)),1)
M = round(GM*math.sin(math.radians(a))*W,-1)

#RESULTS
print 'Metacentric Height = %.1f ft'%GM
print  'Rightening moment  = %.f lb '%(M)

Metacentric Height = 1.3 ft
Rightening moment  = 1680 lb

Example 1.20 page no : 31

In [7]:
import math 
import numpy

#initialisation of variables
l = 5. 			#ft
h = 20. 			#in
n = 1./15
AG = 50. 			#in
x = 30. 			#in
w = 62.4 			#lb/ft**3
#CALCULATIONS
AG1 = round(AG/(1+n),1)
G1G2 = round(n*x/(1+n),2)
W = l**2*w*(l/2)
h1 = 32. 			#in
BK = h1/2
GK = 10. 			#in
G1K = (AG+GK)-AG1
BG1 = BK-G1K
BM = (l**4./12)*2.*12/(l**3*BK*n)
G1M = BM+BG1
o  = G1G2/G1M

#RESULTS
print 'AG1 = %.1f in.'%AG1
print 'G1G2 = %.2f in.'%G1G2
print  'angle through which the cube will tilt  = %.3f in '%(o)

AG1 = 46.9 in.
G1G2 = 1.88 in.
angle through which the cube will tilt  = 0.153 in
In [ ]: