Figure 5 shows the variation of the mass

flow rate against back pressure through the orifice. The mass flow rate remains

constant until the point of 320 back pressure where it then begins to drop. The

drop is quite sharp and as it reaches the back pressure, the mass flow rate

eventually decreases to zero. The theoretical maximum flow rate, max, is 0.008 kg s-1 which is when the probe is fully inserted

into the nozzle. The maximum value based on the results is 0.0056 kg s-1.

The reason for this difference is due to the theoretical equation not accounting

for the frictional losses occurring in the pipe of turbulence created from the

orifice.

The analysis of figure 5 shows that the

mass flow rate for was exactly the same for the values of back pressure from 0

to 150 kPa with a negligible drop until 280 kPa where the flow of the fluid is

initially subsonic, sonic at the throat, supersonic at the exit of the throat

until it experiences a shock and settles down to subsonic speeds. The mass flow

rate then sharply declines from back pressure 320 to 370 kPa. Here the flow of

the liquid is as before except that when it leaves the throat, it exits at

subsonic speeds without a shock. Finally, at the 390 kPa back pressure, the

mass flow rate is quite low hence the fluid is flowing at subsonic speeds

throughout. Pipe

Figures 6 and 7 show the variation of streamwise

pressure within the nozzle for various back pressures at supply pressures of

250 kPa and 350 kPa respectively. For the back pressure values of 200 kPa in

figure 6, the system flows at subsonic speeds throughout. This is because the trend

line maintains a relatively steady gradient and never reaches a sharp turning

point. For the back pressure values of 150 kPa in figure 6 and 250 kPa in

figure 7, the adverse pressure gradient changes at the sonic throat which means

they reach Mach 1 and then slow down to subsonic speeds. This checks out as

both have a turning point from a region of the sonic throat at approximately

100 to 120 mm. Note that a lower supply pressure shows a lower pressure

gradient (p/p0).

For all other back pressure

values, they initially pass through the regime of subsonic speed followed by sonic

speed at the throat. After passing the throat, they briefly go through

supersonic speed before experiencing shock and returning to subsonic speeds.

The shock wave accompanied by flow deceleration is when the outlet pressure is

above the design value. This can be seen on the graph as the remaining trendlines

start with a fairly constant gradient before slowing decreasing in pressure and

as the value of the back pressure gets closer to the supply pressure, there is a

sharp decrease on gradient to zero and subsequently levelling off.

Conclusion

From these

experiments, it is concluded that the method of accelerating a gas from rest to

supersonic speeds is by accelerating the fluid subsonically through a

convergent-divergent nozzle is successful. It confirms the theory that the mass

flow rate remains constant when pressure at the nozzle exit is reduced. Furthermore,

the speed of the flow cannot exceed Mach 1 at the throat as the mass flow rate

is negligible and fluid cannot flow at supersonic speeds at the throat. The

Mach number is the ratio between the fluid velocity and the velocity of sound.