#Calculate the boundary layer thickness
#for the aeroplane
# variables
v=1.61*10**(-4) #ft**2/s
x=2. #ft
V=200. #miles/hr
# calculation
#1 mile = 5280 ft
#1 hr = 3600 sec
delta_aeroplane=5*(v*x/(V*5280/3600.0))**0.5
# result
print "The boundary layer thickness for the aeroplane is %f ft\n"%delta_aeroplane
#for the boat
v1=1.08*10**(-5) #ft**2/s
x1=2. #ft
V1=10. #miles/hr
#1 mile = 5280 ft
#1 hr = 3600 sec
delta_boat=5*(v1*x1/(V1*5280/3600.0))**0.5
print "The boundary layer thickness for the boat is %f ft"%delta_boat
#Calculate the force required to tow a square metal plate by a boat
# variables
rho_water=998.2 #Kg/m**3
V=15. #km/hr
v=1.004*10**(-6) #m**2/s
l=1. #m length of plate
#Calculations
#1 km = 1000 m
#1 hr = 3600 s
Rx=(V*1000/3600.)*l/v #dimentionless (reynold's number)
Cf=1.328/Rx**0.5 #dimentionless
F=Cf*rho_water*(V*1000/3600.0)**2 #N
#Result
print "The force required to tow the square plate is %f N"%F
#Calculate the distance between the wall and edge of the laminar sublayer and buffer layer
#Variables
V=10. #ft/s
l=0.25 #ft
v=1.08*10**(-5) #ft**2/s
f=0.0037 #dimentionless (fanning friction factor)
u01=5. #dimentionless
y01=5. #dimentionless
#Calculations
R=V*l/v #dimentionless (reynold's number)
u1=V*(f/2.0)**0.5 #ft/s
r1=y01*v/u1 #ft
#for buffer layer
u02=12. #dimentionless
y02=26. #dimentionless
r2=y02*v/u1 #ft
#Results
print "the distance between the wall and edge of the laminar sublayer is %f ft\n"%r1
print "the distance between the wall and edge of the buffer layer is %f ft"%r2
#Calculate the boundary layer thickness and the drag on the plate
# variables
V=50. #ft/s
l=20. #ft
b=1. #ft
v=1.08*10**(-5) #ft**2/s
# calculation and result
R=V*l/v #dimentionless (reynold's number)
delta=0.37*l/R**0.2 #ft
print "The boundary layer thichness at the end of the plate is %f ft\n"%delta
Cf=0.072/R**0.2 #dimentionless
rho_water=62.3 #lbm/ft**3
V=50. #ft/s
#let A be the area of contact
A=2*l*b #ft**2
#1 lbf.s**2 = 32.2 lbm.ft
F=(1/2.0)*Cf*rho_water*V**2*A/32.2 #lbf
print "The drag on the plate is %f lbf"%F