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Compressible Flow in a Convergent-Divergent Nozzle Introduction A Convergent- Divergent or Laval Nozzle is a device that, under different conditions of fluid flow is capable of generating the full range of Mach numbers from the subsonic, (M <1) through to the supersonic (M>1). Although air is a compressible fluid, the effects of change in density on the flow parameters only become significant at Mach numbers above approximately 0.6 Bernoulli's equation can be used to characterise incompressible flow but the effects of change in density at higher Mach numbers rule out its use in transonic and supersonic flow. The aim of this experiment is to demonstrate the relationships between the pressure, temperature, density and Mach number in flowing fluid as the Mach number approaches and potentially reaches unity. Experimental apparatus A convergent-divergent nozzle has been machined into a length of transparent bar (see figures & below). Tappings have been drilled into the nozzle to allow temperature and pressure sensors to be introduced into the flow before, at and after the throat of the nozzle. Air under pressure is supplied to the lower end of the nozzle from the building compressed air system and some control over its flow rate provided with valve upstream of the nozzle. Following its passage through the nozzle, the air is allowed to expand ina larger diameter tube, in which its velocity and temperature are recorded, before is discharged to atmosphere Da.Vo.Th Figures 1& 2. Schematic diagram and photograph of the convergent-divergent nozzle D, Some key dimensions: P2,T2 Location Diameter (mm) D1 15.83 P.T.T, D2 D2 4.31 Da 15.83 1 D4 80 The measurements: 1. Use the anemometer to measure the maximum possible air velocity at the exit of the discharge tube when the inlet valve is fully opened 2. Determine suitable flow velocities at which to take readings. The flow rate can be controlled by changing the opening of the inlet valve, 3. At each flow rate, measure the pressure and temperature at the inlet, throat and exit of the nozzle (stations 1, 2 & 3) and the temperature in the discharge tube (station 4). 4. Ensure you have recorded all the physical dimensions of the apparatus required to analyse the flow The ambient temperature and pressure should also be recorded Results and discussion: 1. Calculate the air mass flow rate through the system for each inlet valve setting. Care should be given to ensuring that the measurements recorded have the appropriate units and baseline. 2. From continuity equation, calculate the velocity at each section (inlet, throat and exit) of the nozzle 3. Calculate the speed of sound at each section (inlet, throat and exit) of the nozzle. 4. Calculate the Mach number at each section (inlet, throat and exit) of the nozzle. 5. Plot the pressure density and Mach number distributions in the axial direction for each flow rate 6. Discuss the results in detail In addition to considering the variation in the flow parameters given above, you should also consider whether the system is isentropic and the impact that this might have on the results achieved The experiment should be properly documented as formal lab report of approximately 1000 words in length. The report is to be correctly formatted and referenced in accordance with the Harvard referencing system Although the experiment will be conducted as a group activity, each student is to submit their own individual report via Turnitin which should be their work except where stated otherwise. If academic misconduct of any nature is suspected (e g plagiarism or collusion) it will be considered using the appropriate procedures. Group No Velocity T1 T2 T3 T4 P1 P2 P3 Units. Units Units. Units. Units. Units.. Units. Units. 1 2 3 4 Ambient Pressure: Ambient Temperature:

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A convergent-divergent (C-D) nozzle is used to produce supersonic flow from a reservoir of pressure and a particular geometry. This geometry consists of a section of decreasing area which reaches a minimum and then increases again. The purpose of this shape is creation of supersonic flow. The nozzle contracts the flow by decreasing area continually until the smallest portion of area called the throat....
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