Chapter 2 : Floatation and Buoyancy

Example 2.1 Page No : 43

In [1]:
import math 
		
#initialisation of variables
l = 60. 		#ft
w = 10. 		#ft
h = 5.   		#ft
t = 3./16 		#in
sp  = 7.75
H = 4. 	    	#ft
w1 = 62.4 		#lb/ft**3
y = 4. 		    #ft
		
#CALCULATIONS
V = (l*w+2*w*h+2*l*h)*t/12
W = V*w1*sp
x = W/(w1*l*w)
W1 = H*l*w*w1
dW = (W1-W)/2238
		
#RESULTS
print  'weight of water print laced = %.1f tons'%(dW)

weight of water print laced = 62.5 tons

Example 2.3 Page No : 50

In [2]:
import math 
		
#initialisation of variables
D = 64. 		#lb/ft**3
d = 6.   		#ft
l = 10. 		#ft
W = 2. 	    	#tons
		
#CALCULATIONS
V = W*2240/D
h = V/(math.pi*d**2/4)
BM = d**2/(16*h)
P = -(math.sqrt(64*BM*2*10*math.pi*(22400-math.pi*d**4))-W*22400)/10
		
#RESULTS
print  'Minimum pull required = %.f lbs '%(P+3) 

Minimum pull required = 3665 lbs

Example 2.4 Page No : 52

In [3]:
import math 
		
#initialisation of variables
sg = 7.
sg1 = 5.
d = 8. 		#in
t = 1. 		#in
		
#CALCULATIONS
x = (sg+sg1)+math.sqrt(d*(sg*(sg1+t)+1))
		
#RESULTS
print  'maximum length of cylinder = %.2f in '%(x) 

maximum length of cylinder = 30.55 in

Example 2.7 Page No : 56

In [4]:
import math 
		
#initialisation of variables
W = 2000. 		#tons
m = 15. 		#/tons
dx = 24. 		#ft
l = 3. 	    	#in
dx1 = 5. 		#ft
		
#CALCULATIONS
GM = m*dx/(W*(l/(dx1*12)))
		
#RESULTSS
print  'metacentric height = %.1f ft '%(GM) 

metacentric height = 3.6 ft

Example 2.8 Page No : 56

In [5]:
		
#initialisation of variables
M = 350. 		#tons
l = 50. 		#ft
w = 20. 		#ft
W = 100. 		#tons
h = 6.   		#ft
M1 = 250. 		#tons
		
#CALCULATIONS
V = M*2240/64
d = V/(l*w)
BM = l*w**3/(12*w*l*d)
y = (((BM+(d/2))*(M/10))-(M1*h/10))/(W/10)
		
#RESULTS
print  'Highest position of centre of gravity = %.2f ft '%(y)

Highest position of centre of gravity = 15.96 ft

Example 2.9 Page No : 58

In [2]:
import math 
		
#initialisation of variables
W = 2000. 		#tons
l = 250. 		#ft
w = 30. 		#ft
a = 1./15
W1 = 50. 		#tons
h = 10. 		#ft
		
#CALCULATIONS
BG = (l*w**3*64/(W*2240*12))-(W1*h/(a*W))
		
#RESULTS
print  'distance of the centre of gravity = %.2f ft '%(BG) 

# note : rounding off error

distance of the centre of gravity = 4.29 ft

Example 2.10 Page No : 58

In [4]:
import math 
		
#initialisation of variables
l = 91. 		#ft
w = 30. 		#ft
h = 6. 	    	#ft
W = 40. 		#tons
a = 3. 		    #degrees
cg = 3. 		#ft
d = 4.  		#ft
W1 = 60. 		#tons
cg1 = 1. 		#ft
		
#CALCULATIONS
W2 = (l*w*d*64/2240)-W1
y = (W2*(h/2)+W1*(cg+d))/(l*w*d*64/2240)
BG = y-(d/2)
BM = l*w**3/(12*l*w*d)
GM = BM-BG
dx = GM*l*w*d*64*math.tan(math.radians(a))/(60*2240)
		
#RESULTS
print  'maximum distance through which the load can be shifted = %.1f ft '%(dx)

maximum distance through which the load can be shifted = 4.6 ft

Example 2.11 Page No : 60

In [8]:
import math 
		
#initialisation of variables
W = 5000. 		#tons
I = 1.4*10**6 		#ft**4
k = 12.2 		#ft
BG = 6.5 		#ft
		
#CALCULATIONS
BM = I*64/(W*2240)
GM = BM-BG
T = 2*math.pi*math.sqrt(k**2/(GM*32.2))
		
#RESULTS
print  'period of oscialltion = %.2f sec '%(T) 

period of oscialltion = 11.03 sec