Q2 - Converging nozzle

Question 1

describe regime 1

Answer 1

pb>p* : v<c, ve<c, pe=pb > p*, m_dot < m_dot max

Question 2

describe regime 1.5

Answer 2

pb=p* : v<c, ve=c, pe=pb = p*, m_dot = m_dot max

Question 3

describe regime 2

Answer 3

pb<p* : v<c, ve=c, pe=p* > pb , m_dot = m_dot max

Question 4

explain why the flow in the nozzle becomes insensitive to the parameters of the background gas if the background pressure, pb, drops below the critical pressure, p*, for the flow

Answer 4

When the flow becomes sonic, the information of the pressure variation cannot propagate upstream, and the upstream part of the flow becomes insensitive to that which occurs downstream.

Question 5

A big reservoir of air is attached to a converging nozzle with exit area 5 cm2 as it is shown in the figure below. The air temperature in the reservoir is 20 Degrees C. The maximal mass flow rate in the nozzle is measured to be 0.3 kg/s.
(e)Find the exit air temperature of the gas in the case pb <p*.

Answer 5

Find Tc by using Tc = T0/k2.

Question 6

A big reservoir of air is attached to a converging nozzle with exit area 5 cm2 as it is shown in the figure below. The air temperature in the reservoir is 20oC. The maximal mass flow rate in the nozzle is measured to be 0.3 kg/s.
(f) Find the exit and stagnation air pressure in the same case.

Answer 6

Find cc, using cc = sqrt(kRgTc).
As we are provided m_dot_max which is equivalent to m_dot_c (due to pb being smaller than pc, therefore regime 2).
We can use the mass flow rate equation and rearrange to find rho_c = m_dot_c/(Aecc), then use state equation to find pc = Rgrhoc*Tc, this will give an answer in Pa.(DON’T FORGET TO CONVERT TO KPA).

Use P0/Pc = k2^(k/(k-1)) to find Pc.