Q3 - Converging-Diverging nozzle

Question 1

describe regime 1 converging-diverging nozzle

Answer 1

pb>pI, v<c, ve<c, pe=pb ; S=const

Question 2

describe regime 1.5 converging-diverging nozzle

Answer 2

pb=pI, v<c, vt=c, ve<c, pe=pb ; S=const

Question 3

describe regime 2 converging-diverging nozzle

Answer 3

pb€(pII,pI), v<c in C, vt=c, shockin D, ve<c, pe=pb ; S=/=const

Question 4

describe regime 2.5 converging-diverging nozzle

Answer 4

pb=pII, v<c in C, vt=c, shock at exit, ve<c, pe=pb ; S=/=const

Question 5

describe regime 3 converging-diverging nozzle

Answer 5

pb€(pIII,pII), v<c in C, vt=c, v>c in D, ve>c, pe=pb ; S=const; over expanded

Question 6

describe regime 3.5 converging-diverging nozzle

Answer 6

pb=pIII, v<c in C, vt=c, v>c in D, ve>c, pe=pb ; S=const; best performance

Question 7

describe regime 4 converging-diverging nozzle

Answer 7

pb<pIII, v<c in C, vt=c, v>c in D, ve>c, pe>pb ; S=const; under expanded

Question 8

when is the flow isentropic in the whole converging-diverging nozzle

Answer 8

when S is costant (1, 1.5, 3, 3.5, 4)

Question 9

for a converging-diverging nozzle, if the exit mach number is higher than 1, what regime could it be.

Answer 9

3, 3.5 or 4

Question 10

A converging-diverging nozzle is designed to operate isentropically with an exit Mach
number of 2. The nozzle is supplied from an air reservoir with the pressure 500 kPa and
temperature 400 K. The nozzle throat area At (Area throat) is 10 cm2.
(d) Find mass flow rate.

Answer 10

Given Me, P0 and T0 and At

Find Tc = T0/k2.
Find Pc = p0/(k2^(k/(k-1)))
Use state equation to find rho_c = (Pc1000)/(RgTc)(1000 to convert from Kpa to Pa)
Find cc = sqrt(RgkTc)
Find m_dot = Atrho_c*cc.

Question 11

A converging-diverging nozzle is designed to operate isentropically with an exit Mach
number of 2. The nozzle is supplied from an air reservoir with the pressure 500 kPa and
temperature 400 K. The nozzle throat area A* is 10 cm2.
(e) Find the exit temperature Te and pressure Pe.

Answer 11

Assuming for an isentropic flow. We can use the formulas
Te = T0/(1+k1Me^2)
and
Pe = P0/((1+k1Me^2)^(k/(k-1)))

Question 12

A converging-diverging nozzle is designed to operate isentropically with an exit Mach
number of 2. The nozzle is supplied from an air reservoir with the pressure 500 kPa and
temperature 400 K. The nozzle throat area A* is 10 cm2.
(f)Find the exit area Ae.

Answer 12

To find exit area Ae, is a very similar process to finding exit area for Converging nozzle.
Use state equation to find rho_e = (Pe1000)/(RgTe)

ce = sqrt(kRgTe)
ve = Me*ce

As we know flow is easy
m_dot_t = m_dot_e

Therefore
Ae = m_dot_t/(rho_e*ve). This will give an answer in m^2.