# To calculate:
# - Ae
# - Thrust
# Solution:
energy_in = energy(T1, V1, m=m_rate)
# Applying the conservation of energy equation
def eqn_energy(Te):
energy_out = energy(Te, Ve, m=m_rate)
return energy_in + q - energy_out
Te = num.solve_nr(eqn_energy, init=T1)
rhoe = eos.rho(pe, Te)
# Applying conservation of mass equation
def eqn_mass(Ae):
return mass(rhoe, Ae, Ve) - m_rate
Ae = num.solve_nr(eqn_mass, init=1.0)
momentum_in = m_rate * V1
momentum_out = m_rate * Ve
pressure_thrust = (pe - p_amb) * Ae
# ------------------------------------
A1 = Ae = A = 1 # m^2, assumed = 1 as mass flow rate needs to be calculated per unit area
# To calculate:
# - heat added per unit mass
# - mass flow rate per unit area
# Solution:
molar_mass = 12 * 1 + 16 * 2
R = prop.R(molar_mass)
cp = prop.cp(R, gamma)
energy_in = energy(T1, V1, cp, m=1)
energy_out = energy(Te, Ve, cp, m=1)
# Conservation of energy equation
def eqn_energy(q):
return energy_in + q - energy_out
q = num.solve_nr(eqn_energy)
# Using the ideal gas equation of state at the inlet
rho1 = eos.rho(p1, T1, R)
m = mass(rho1, A1, V1)
print("The amount of heat being added to the carbon dioxide per unit mass of gas is %f J/kg." % q)
print("The mass flow rate through the duct per unit cross-sectional area of the duct is %f kg/s-m^2." % m)
# To calculate: mass flow rate
# Solution:
molar_mass = 2.016 # kg/kmol
R = prop.R(molar_mass)
cp = prop.cp(R, gamma)
Te = isen.T2(T1, pe / p1, gamma)
# Conservation of energy equation
def eqn_energy(Ve):
return energy(T0, 0, cp) - energy(Te, Ve, cp)
Ve = num.solve_nr(eqn_energy, init=100.0) # +ve initial guess
# Conservation of momentum
momentum_in = 0
pressure_thrust = (pe - p_amb) * Aexit
def eqn_momentum(me):
momentum_out = me * Ve
return thrust - momentum_out + momentum_in - pressure_thrust
me = num.solve_nr(eqn_momentum, init=0.0)
print(
"If the required thrust is %f MN, the required hydrogen mass flow rate is %f kg/s."
D3 = 9e-2 # m
# ------------------------------------
# To calculate: V3
# Solution:
rho1 = eos.rho(p1, T1)
rho2 = eos.rho(p2, T2)
rho3 = eos.rho(p3, T3)
A1 = area_circle(D1)
A2 = area_circle(D2)
A3 = area_circle(D3)
m1 = mass(rho1, A1, V1)
m2 = mass(rho2, A2, V2)
# mass conservation equation
def eqn(V3):
m3 = mass(rho3, A3, V3)
return m1 + m2 - m3
V3 = num.solve_nr(eqn, V1)
print("The velocity in the exit pipe is %f m/s." % V3)
plt.imshow(plt.imread("images/q06_im01.svg.png"))
plt.axis("off")
plt.show()
T2 = -50 + 273 # K
# ------------------------------------
# To calculate: T3
# Solution:
# assume m1 = m2 = 1
m1 = 1 # kg/s
m2 = m1
m3 = m1 + m2
# conservation of energy
e1 = energy(T1, V1, m=m1)
e2 = energy(T2, V2, m=m2)
# e1 + e2 - e3 = 0
def eqn(T3):
V3 = 0
return e1 + e2 - energy(T3, V3, m=m3)
T3 = num.solve_nr(eqn, init=T1)
print("The temperature of the air in the large chamber is %f K or %f deg. C." %
(T3, T3 - 273))
plt.imshow(plt.imread("images/q05_im01.svg.png"))
plt.axis("off")
plt.show()
Ve = 30 # m/s
Te = 80 + 273 # K
pe = 2.45e6 # Pa
# ------------------------------------
# To calculate:
# - Heat added/removed per kilogram of air
# - density of air at inlet of heat exchanger
# - density of air at exit of heat exchanger
# Solution:
energy_in = energy(T1, V1)
energy_out = energy(Te, Ve)
# Conservation of energy equation
def eqn_energy(q):
return energy_in + q - energy_out
q = num.solve_nr(eqn_energy) # sign of q indicates whether heat is added or removed
qdir = "heat added"
if q < 0: qdir = "heat removed"
rho1 = eos.rho(p1, T1)
rhoe = eos.rho(pe, Te)
print("The %s per kilogram of air flowing through the heat exchanger is %f J/kg." % (qdir, abs(q)))
print("The density of the air at the inlet of the heat exchanger is %f kg/m^3." % rho1)
print("The density of the air at the exit of the heat exchanger is %f kg/m^3." % rhoe)