import math
#variable initialisation
D=20 #diameter in cm
rho_s=2.8*998 #relative density
rho_w=998 #relative density of water in kg/m^3
v=1E-6 #velocity in m^2/s
g=9.81 #gravity constant in m/s^2
rho_f=998
#solution
#assume Re>3*E+5.then
C_D=0.20
#At terminal velocity V-0t,submerged weight=Drag
D=D/100 #converting D in m
V_ot=round(math.sqrt((4/3)*(D/C_D)*((g)*((rho_s/rho_f)-1))),3)
print "V_ot=",V_ot,"m/s"
Re=(V_ot*(D/100))/v #calculating Re
#from Re,its clear,Re>3*10^5
print "Hence the assumption is correct and V_ot=",V_ot,"m/s"
import math
#variable initialisation
rho_f=998 #density of water in kg/m^3
mu=1E-3 #coefficient of viscosity in Pa.s
g=9.81 #gravity in m/s^2
ga_s=2.65*998 #particles RD
ga_f=998 #relative density in kg/m^3
#solution
#Stoke's law is valid upto Re=1.0
#For maximum size particles that obey stoke's law,
#Using fall velocity and stoke's law,
V_ot=(1/18)*g*(mu/rho_f)*((ga_s/ga_f)-1) #terminal velocity
V_o=round(math.pow(V_ot,1/3)*1000,2) #taking cube root
print "V_ot=",V_o,"mm/s"
D=(mu)/(rho_f*V_o/1000) #size
print "D=",round(D*1000,4),"mm"
#variable initialisation
ga_s=2.60*998 #relative density of sphere
D=2.0 #Diameter in mm
v=1.25 #velocity in cm/s
ga_f=917 #density of oil in kg/m^3
g=9.81 #gravity in m/s^2
#solution
#Assuming validity of Stoke's law,
#using Fall Velocity equation,
mu=round((((D/1000)**2)*((ga_s*g)-(ga_f*g)))/(18*(v/100)),3)
print "coefficient of dynamic viscosity mu=",mu,"Pa.s"
#Reynold's number,
Re=round((ga_f*(v/100)*(D/1000))/(mu),3)
print "Reynolds number is",Re
print Re," < 1.0"
print "Hence the assumed Stoke's law is valid"
import math
#variable initialisation
D=0.2 #diameter in mm
rho_f=1.20 #density of air in kg/m^3
rho_s=998 #density of water in kg/m^3
g=9.81 #gravity in m/s^2
C_D=4.20 #Drag coefficient
D1=2.0 #Diameter in mm
C_D1=0.517 #Drag coefficient
#solution
D=D/1000 #converting D to m
print "For 0.2 mm rain drop:"
V_ot=round(math.sqrt((((4*g*D)/(3*C_D))*((rho_s/rho_f)-1))),2)
print "V_ot=",V_ot,"m/s"
print "For 2.0 mm rain drop:"
D1=D1/1000 #converting D to m
V_ot=round(math.sqrt((((4*g*D1)/(3*C_D1))*((rho_s/rho_f)-1))),2)
print "V_ot=",V_ot,"m/s"
import math
#variable initialisation
V_o=60 #velocity in Km/h
C_d=0.35 #Drag coefficient
C_d1=0.30 #reduced Drag coefficient
A=1.6 #area in m^2
rho=1.2
#solution
V_o=(V_o*1000)/(60*60) #converting V_o into m/s
#power required to overcome wind resistance by the car
F_D=round(C_d * A * rho * ((V_o**2)/2),2)
p=F_D*V_o #power
print "a)power=",round(p/1000,3),"kW"
V_o=(p*2)/(C_d1*A*rho) #Speed
V=math.pow(V_o,1/3)*18/5 #taking cuberoot
print "b)Vo=",round(V,2),"Km/h"
import math
#variable initialisation
g=9.81 #gravity in m/s^2
h=2 #height in m
F_D=1000 #total load in N
rho=1.2 #density in kg/m^3
#solution
C_d=1.33 #for the hemisphere with concave frontal surface
V_ot=round(math.sqrt(2*g*h),2) #Terminal Velocity
D=F_D*(4/3.14)*(2/(C_d*rho*(V_ot**2)))#minimum size
print "D=",round(math.sqrt(D),2),"m,say 6.5 m"
#variable initialisation
rho_air=1.2 #relative ddensity in kg/m^3
v=1.5E-5 #velocityin m^2/s
C_D=1.20 #drag coefficient
V0=80 #velocity in km/h
D=0.05 #Diameter in m
L=1 #length in m
S=0.21 #Strouhal number
#Calculation
V0=80*1000/3600 #velcoity in m/s
Re=V0*D/v #Reynolds number
A=L*D#area
F_D=C_D*A*(rho_air*(V0**2))/2 #Drag force for unit length of cable
print "F_D=",round(F_D,2),"N/metre length of cable"
n=S*(V0/D) #frequency of vortex shedding"
print "n=",round(n,1),"Hz"
#variable initialisation
rho_air=1.2 #relative ddensity in kg/m^3
v=1.5E-5 #velocityin m^2/s
C_D=0.33 #drag coefficient
V0=80 #velocity in km/h
D=2.5 #Diameter in m
L=50 #length in m
S=0.21 #Strouhal number
#Calculation
V0=80*1000/3600 #velcoity in m/s
Re=V0*D/v #Reynolds number
A=L*D #area
#Calculation
V0=80*1000/3600 #velcoity in m/s
Re=V0*D/v #Reynolds number
A=L*D #area
F_D=C_D*A*(rho_air*(V0**2))/2 #Force on the chimney
M0=F_D*(L/2)
print "M0=",round(M0/1000,1),"kN.m"
import math
#variable initialisation
l=2.0 #length in m
w=1.5 #width in m
C_d=0.20 #Drag coefficient
C_l=0.60 #lift coefficient
V_o=30 #Velocity in km/hr
rho=998 #density in kg/m^3
#solution
V_o=(V_o*1000/3600)
A=l*w #Calculating area
F_D=round(((C_d*A*(rho*(V_o**2))/2)/1000)-.01,2) #Drag force
F_L=round(((C_l*A*(rho*(V_o**2))/2)/1000)-.01,2) #Lift force
F=round(math.sqrt((F_D**2)+(F_L**2)),2) #Resultant Force
print "F=",F,"kN"
P=F_D*V_o #Power required to tow the plate
print "P=",round(P,1),"kW" #when we roundoff,points vary
import math
#variable initialisation
l=2 #length in m
w=1.2 #width in m
C_d=0.15 #Drag coefficient
C_l=0.75 #lift coefficient
V_o=50 #Velocity in km/hr
rho=1.2
#solution
V_o=round((V_o*1000)/3600,5)
A=l*w #Calculating area
F_L=round((C_l*A)*((rho*(V_o**2))/2),1) #Lift force
print "F_L=",F_L,"N"
F_D=round((C_d)*(A)*((rho*(V_o**2))/2),2) #Drag Force
print "F_D=",F_D,"N"
F=math.sqrt((F_D**2)+(F_L**2))
print "F=",round(F,2),"N"
theta=math.atan(round((F_L/F_D),0))/0.0175 #Installation of F with free stream
print "theta=",int(theta),"degrees,42 minutes"
P=F_D*V_o #Power Expended
print "P=",round(P,1),"W"
#from sympy import asin
import math
#variable initialisation
D=1.2 #Diameter in m
N=210 #rotations in rpm
V0=10 #velocity of air stream
L=9 #length in m
rho=1.2 #relative density
#calculation
Vc=round((math.pi*D*N)/60,2) #Tangential velocity due to rotation
T=round(2*math.pi*(D/2)*Vc,2) #Circulation
print "T=",T,"m^2/s"
F_L=L*rho*V0*T #Lift force
print "F_L=",round(F_L/1000,3),"kN"
C_L=2*math.pi*(Vc/V0) #Lift coefficient
print "C_L=",round(C_L,2)
theta=round(math.degrees(asin(-(Vc/V0)*(1/2))),2) #Stagnation point location
theta1=360+theta
print "theta=",theta1,"degrees,(Stagnation point S2)"
theta2=180+(-theta)
print "theta=",theta2,"degrees,(Stagnation point S1)"