# Chapter11-Hydrostatics¶

## Ex1-pg141¶

In [1]:
##Solutions to Problems In applied mechanics
##A N Gobby
import math
##initialisation of variables
w=62.5##lbf
a=4.*6.##ft
x=4.##ft
l=(6.*6**3)/3.-(6.*2**3)/3.##ft^3
q=24.*x##ft^3
##CALCULATIONS
T=w*a*x##lbf
P=l/q##ft
##RESULTS
print'%s %.2f %s'%('the depth of centre of pressure= ',P,' ft')

the depth of centre of pressure=  4.33  ft


## Ex2-pg142¶

In [11]:
##Solutions to Problems In applied mechanics
##A N Gobby
import math
##initialisation of variables
a=60.##degre
w=2.5##ft
x=3.##ft
p=6.*3.##ft^2
h=62.4##ft
p1=(3.*6**3)/12.##ft^4
##CALCULATIONS
D=w+x*(math.sin(a))##ft
T=h*p*D##lbf
P=(p1*math.sin(a)**2)/p*D+D+3##ft
##RESULTS
print'%s %.2f %s'%('the depth of centre of pressure= ',P,' ft')

the depth of centre of pressure=  5.03  ft


## Ex3-pg143¶

In [10]:
##Solutions to Problems In applied mechanics
##A N Gobby
import math
##initialisation of variables
t=62.5*4.*1.##lbf
a=2./3.*2.##ft
m=62.5*4*(4/3)##lbf
f=500.*2.##lbf ft
T=((62.5*2.*2.)/2.)*1./3.*2.##lbf
H=(62.5*2.*1.)##ft
##CALCULATIONS
H1=f/(H+T)*2./2.9##/ft
##RESULTS
print'%s %.2f %s'%('the trap door width= ',H1,' ft')

the trap door width=  3.31  ft


## Ex4-pg146¶

In [12]:
##Solutions to Problems In applied mechanics
##A N Gobby
import math
##initialisation of variables
g=6.##ft
g1=50.##ft
d=10.##ft
w1=10.##ft
w2=20.##ft
w3=62.5##ft
t=w3*60.*5.##lbf
t2=8.37##tonf
t1=g1+t##lbf
H=26.4##ft
##CALCULATIONS
M=t*d/3##lbf ft
D=w3*w2*g*d##lbf
M1=D*(w2/3.)##lbf ft
f=D-t##lbf
R=(M1-M)/f##ft
##RESULTS
print'%s %.2f %s'%('the moment of resultant force about gate base= ',R,' ft')

the moment of resultant force about gate base=  7.78  ft


## Ex6-pg148¶

In [16]:
##Solutions to Problems In applied mechanics
##A N Gobby
import math
##initialisation of variables
w=62.5##lbf/ft
w1=1.5##ft
d=4.##ft
w2=3.##ft
g=0.8##in
p1=2./3.*w1##ft
q=2./3.*p1##ft
##CALCULATIONS
t1=w1*w*w1/2.##lbf
p=(g*w*p1*p1)/2.##lbf
A=g*w*p1*1./2.##lbf
T=(w*0.5*0.5/2.)##lbf
P=t1-p-A-T##lbf
h=2.9*P/(t1*1.-p*2.)/3.-p*(1.*0.25)-(T*1.33)##ft
F=P*A/w+3##lbf

H=F/2.##lbf
##RESULTS
print'%s %.2f %s'%('depth of forces= ',F,' lbf')
print'%s %.2f %s'%('the moment of force on hinge= ',H,' lbf')

#ans is slightly different due to round off error

depth of forces=  8.00  lbf
the moment of force on hinge=  4.00  lbf