def c5p22():
# Given Functions
def force_grav(rho_object, v, g=9.8):
return rho_object * v * g
def force_buoy(rho_medium, v_displaced, g=9.8):
return rho_medium * v_displaced * g
def vol_sphere(rad):
return 4.0 / 3 * np.pi * rad**3
def vol_dry(rad, h):
return (np.pi * h**2 / 3) * (3 * rad - h)
def vol_disp(rad, h):
return vol_sphere(rad) - vol_dry(rad, h)
# Constants
rho_object, rho_medium, rad = 200., 1000., 1.
# args for solutions
f = lambda h: force_grav(rho_object, vol_sphere(rad)) - force_buoy(
rho_medium, vol_disp(rad, h))
a, b = 0., 2.
return {
'bisection': num.bisection(f, a, b),
'false_position': eng_form(num.false_position(f, a, b))
}
def c5p7():
f, a, b, *kwargs = [
lambda x: np.log(x**2) - 0.7, 0.5, 2.0, {
'maxSteps': 3
}
]
return {
'bisection': num.bisection(f, a, b, **kwargs[0]),
'false_position': num.false_position(f, a, b, **kwargs[0])
}
def c5p16():
# Given functions:
def rho(q, n, mu):
return 1.0 / ( q * n * mu )
def n( N, ni ):
return 0.5 * ( N + np.sqrt( N**2 + 4 * ni**2 ) )
def mu( T, T0, mu0 ):
return mu0 * ( T / T0 )**(-2.42)
# Constants
T0, T, mu0, q, ni, rho_desired = 300., 1000., 1360., 1.7 * 10**(-19), 6.21 * 10**9, 6.5 * 10**6
# args for solutions
f = lambda N: rho( q, n(N,ni), mu(T,T0,mu0) ) - rho_desired
a,b = 0., 2.5 * 10**10
return {'bisection': eng_form( num.bisection( f,a,b ) ),'false_position':eng_form( num.false_position(f,a,b) ) }
def c5p16():
# Given functions:
def rho(q, n, mu):
return 1.0 / (q * n * mu)
def n(N, ni):
return 0.5 * (N + np.sqrt(N**2 + 4 * ni**2))
def mu(T, T0, mu0):
return mu0 * (T / T0)**(-2.42)
# Constants
T0, T, mu0, q, ni, rho_desired = 300., 1000., 1360., 1.7 * 10**(
-19), 6.21 * 10**9, 6.5 * 10**6
# args for solutions
f = lambda N: rho(q, n(N, ni), mu(T, T0, mu0)) - rho_desired
a, b = 0., 2.5 * 10**10
return {
'bisection': eng_form(num.bisection(f, a, b)),
'false_position': eng_form(num.false_position(f, a, b))
}
def c5p22():
# Given Functions
def force_grav( rho_object, v, g=9.8 ):
return rho_object * v * g
def force_buoy( rho_medium, v_displaced, g=9.8 ):
return rho_medium * v_displaced * g
def vol_sphere( rad ):
return 4.0/3 * np.pi * rad**3
def vol_dry( rad, h ):
return (np.pi * h**2 / 3) * (3 * rad - h)
def vol_disp( rad, h ):
return vol_sphere(rad) - vol_dry( rad, h )
# Constants
rho_object, rho_medium, rad = 200., 1000., 1.
# args for solutions
f = lambda h: force_grav( rho_object, vol_sphere( rad )) - force_buoy( rho_medium, vol_disp( rad,h ))
a,b = 0.,2.
return {'bisection': num.bisection( f,a,b ) ,'false_position':eng_form( num.false_position(f,a,b) ) }
def c5p7():
f,a,b,*kwargs = [lambda x: np.log( x**2 ) - 0.7, 0.5, 2.0, {'maxSteps':3}]
return {'bisection':num.bisection( f,a,b,**kwargs[0] ), 'false_position':num.false_position( f,a,b,**kwargs[0] )}
