2 nozzle pressure distribution

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EPS Chemical Engineering Laboratory Notes

Version Jan 2016 of 4

Air from the main laboratory compressor is supplied through a regulator and passed through the INLETVALVE. There is a temperature sensor that can be used to record the temperature of the gas as it entersthe nozzle. The nozzle is a small metallic section that has a number of tapping points, each tapping pointallows the pressure along the nozzle to be measured by gauges 1 to 8. There are at most 3 nozzles to test

– Nozzle A,B and C. Dimensions of these nozzles are given later. There are to larger gauges that measurethe pressure across the nozzle – PI is the inlet pressure gauge and Po is the outlet pressure gauge. Thereis a control valve on the outlet line which regulates the outlet pressure (or sometimes called the backpressure). This means the rotameter can be used to record the mass flowrate of air as it leaves the unit – since the pressure of this air will be atmospheric.

4. Basic Theory In the conditions at which the air is being used in this experiment, it can be assumed that it is behaving likean ideal gas.

therefore

Pv =RT

In the case where the flow is adiabatic, the relationship between pressure and volume is given by:

=

cP

cv

Pv

= const

is the adiabatic index (for air =1.4) or more usually =

cP

cv

It can be shown that the velocity through the nozzle at a point, x , along the length of the nozzle, can beexpressed as

u R T P

P x i

x

i

2

1

2

11

..

where Px is the pressure at the position x.

The mass flowrate through a nozzle can be found by looking at the pressure upstream P 1 and the pressureat the point where the cross sectional area is a minimum P2, by the expression:

G =Cd

2 A

2P1

1

ln P

1

P2

æ

è ç

ö

ø÷

where

A is the cross sectional area of the nozzle Cd is the discharge coefficient

Subscript 1 refers to the upstream condition, 2 refers to the condition at the nozzle throat.

The maximum mass flowrate through the nozzle can then be given as:

G A P

R T t

i

i

. . ..

2

1

2

1

1

1 2

1

2

and the critical pressure ratio is





P

P

x

i

2

1

1

where = ratio of specific heats at const. pressure and volume.= 1.4 for air under the conditions used in this expt.

R = Universal Gas Constant

P = absolute pressure (Pi - inlet pressure)Ti = inlet temperatureG = mass flowrate of air

A nozzle is said to be ‘choked’ when the back pressure is low enough for the critical pressure to bereached at the throat.

Further details of flow through a restriction can be found in any good text book (ref 2), and generaldiscussions are found in the Chemical Engineering Handbook (ref 3).

5. Method

This is a straightforward experiment to do and should not take too long to collect all the data necessary.

However, the processing of the data will take some time.

Before any experimental work can be done the gauges must be calibrated against the inlet air pressuregauge which has been factory checked against a master. Each pressure gauge has a specificcharacteristic which means that given the same pressure, they will all ready slightly different. This is aresult of intrinsic differences in the construction of each gauge. Details of the calibration procedure aregiven below

Once the calibration procedure has been done, make sure that the correct nozzle for testing has beenfitted and each tapping point is connected to the correct pressure gauge. Open the outlet valve and slowlyopen in the inlet valve. Allow air to flow through the system. Adjust the inlet and outlet valve so that thedesired pressures appear on the appropriate gauges. Record the pressures from all gauges and the massflowrate using the rotameter. The rotameter is calibrated to give the mass flowrate of air through the

nozzle.

Use each of the nozzles, and cover a range of inlet/outlet pressures. Using the pressure data:1. Plot out the appropriate pressure curves along each nozzle – see the diagrams in Coulson &

Richardson (ref 1). Compare these with what the text suggests should happen. Note that you mayhave to plot the pressure ratio using the inlet pressure gauge as the reference.

2. Determine if any of the nozzles exhibit choked flow. Use the theory and calculate the criticalpressure ratio and hence pressure value that gives choked flow. Compare what you find.

3. Determine the velocity of the air as it flows through the nozzle and show this by any suitablemeans.

6. Operational Notes

1. The air to the apparatus is supplied by the main compressor via a reducer. This has been set andrequires no further adjusting. Air is switched on / off by the valve on the wall.

2. To change nozzles, gently loosen the knurled unions holding the nozzle in the line. Carefully loosen anddisconnect each tapping point in turn while rotating the nozzle to get access. Exchange the nozzle withthe one required from the box provided. Ensure ‘O’ rings are in place. Reconnect the tapping pointsstarting with no.1. Tighten all knurled unions. NO Tools are required, hand tight is sufficient providedthe connections are fitted correctly. For the purposes of BHOS students, assume that this was donecorrectly.





3. Remember that the rotameter has been calibrated at standard conditions (i.e. atmospheric pressure -101.3 kN/m2 and 20oC giving an air density of 1.2 kg/m3 ). Therefore use the correction factor graphsavailable on the apparatus if conditions are different from above. BHOS students should note that nofurther modification is needed

4. According to theory, when a gas undergoes a reduction in pressure, the temperature may drop.However with this particular system, the heat transfer is negligible and can be considered isothermal.

The two thermometer points on the equipment will demonstrate this feature.

5. All pressure gauges are standard 0 to 500 kPa gauges with 10 major divisions at 50, 100. 150 etc.There are 5 subdivisions between each major division.

Note: before starting any experimental work the gauges must be calibrated against the inlet air pressuregauge which has been factory set against a master. NO tools are required to tighten/release knurledunions, hand tight if sufficient provided the connections are fitted correctly.

The results should be plotted in the most appropriate way to compare with published trends and toillustrate the ‘choking’ of the different nozzles.

6.1 Calibration Procedure

To make sure we can correct the values for each gauge, we must first CALIBRATE each of the pressuregauges. This is done by:1. Closing the outlet valve and opening the inlet valve. Allow the rig to pressurise up.2. Close the inlet valve and make sure there are no pressure losses that might indicate a leak from

the rig.3. Record all pressure values4. Open the outlet valve a fraction and let the pressure drop by a small valve. Close the valve and

repeat step 3.5. Continue to repeat steps 3-4 until the pressure in the system reduces to atmospheric.6. Construct appropriate graphs and find the trend line equations that will allow you to determine the

correct pressure value from each pressure gauge. Use the INLET gauge as a reference (meaning – assume the inlet pressure gauge is the correct value).

6.2 Nozzle DimensionsDimensions of each nozzle (diameter and distance to each tapping point can be found in the scans below.Note that nozzle C is a converging nozzle only, nozzles A and B are converging/diverging.

7. SAFETY NOTE

There are no particular safety issues except:1. You are dealing with a gas at high pressure. Make sure the connection point between the main air

feed and the regulator is secure and that the regulator is operating normally.2. Do not open valves quickly. Turn all valves slowly so that changes are gradual.

8. References

1. Coulson & Richardson, Chemical Engineering, vol. 1, (chapter on compressible flow)2. Douglas, Gasiorek, Swaffield, “Fluid Mechanics”. 3. Perry’s Chemical Engineers Handbook

2 nozzle pressure distribution

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