1 / 14

Lab 4 Tank Discharge Experiment

Lab 4 Tank Discharge Experiment. Objective.

evan-jimenez
Download Presentation

Lab 4 Tank Discharge Experiment

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lab 4Tank Discharge Experiment

  2. Objective Your TA wants to measure the mass flow rate of a gas discharging from a large industrial tank through a small orifice. He plans to use various diameters of the orifice depending on the desired flow rate. Your task is to develop a procedure for making this measurement. It has been suggested that the process can be modeled as either an isothermal process or an isentropic process, but as of yet, this is unproven. The TA wants to know which process most resembles the actual case. The tank in the lab is a smaller version of the actual tank. You may use the experimental results to develop your procedure and to compare the isentropic versus isothermal cases.

  3. Introduction to Compressible Flow • Compressible flow is the study of fluids with their densities changing with time and space, usually for gases flowing at a speed comparable to the local speed of sound. • Fluid density is not constant, it changes with pressure, temperature. • Two important and distinctive effects for compressible flow is: (1) choked flow – flow is limited by the sonic condition, (2) shock wave – highly irreversible flow that fluid properties experience discontinuities. • Usually, there are four dependable variables to be determined: pressure, temperature, density, velocity. Need four equations to solve them (mass, momentum, energy, and state equation). • Mach number is the most important parameter.

  4. Flow through an orifice Due to high head loss due to the uncontrolled expansion downstream from the orifice, the actual flow rate will be smaller than theoretical value. The orifice discharge coefficient will be used to account for this discrepancy. Only empirical correlation can be used to find this coefficient. The detail is shown in Fig. 8.19, and the Equation (8.59) in Fox and McDonald. It is Fig. 8-56 and Equation (8-72) in Cengel and Cimbala. For our experiment, due to fact that the orifice diameter is very small, the coefficient of 0.6 can be used for theoretical development, that is, CD=0.6.

  5. How to model the process? • The whole process can be viewed as two parts: • the air in the tank, • air discharging through the orifice. • How to model the air remaining in the tank as air discharges from the tank is the objective of this experiment. In the experiment, you will measure the pressure, temperature in the tank as a function of time during the discharging process. The adiabatic assumption would be expected to be a good model for very rapid discharging process in which case there would be little time for significant heat transfer between the tank walls and the gas. On the other hand, the isothermal assumption is expected to be appropriate for slow tank discharge processes whereby there is sufficient time for heat transfer to maintain the temperature of the gas in the tank constant.

  6. Theoretical development of the models For the discharging process through the orifice, the flow is assumed to be isentropic. To make theoretical development simple, we want the choked flow through the orifice. The requirement for the choked flow is that the pressure in the tank is about twice the atmospheric pressure (see previous derivation). For the choked flow in the orifice, we have theoretical mass flow rate: Take into account the coefficient of discharge where CD is the coefficient of discharge, about 0.6 for the orifices we use in this lab.

  7. Now, let us model the air in the tank. Since: (1) If isothermal, T0 = constant, Also, (2) By equating (1) and (2) and solve for P0:

  8. If isentropic, we still have: If isentropic, then, (1) (2) By equating (1) and (2) and solve for P0:

  9. Lab 4 Tank Discharge Experiment Apparatus: (1) Test vessel (125 liters). (2) Compressor, used to pressurize the test vessel. (3) Orifices (D = 1/8", 3/32", 1/16") (4) One pressure transducer and one thermocouple for pressure and temperature measurement. (5) Valves to control the air flow. (6) Computerized data acquisition system. • Necessary Constants for the Lab: • Tank volume: 0.125 m3 • Nozzle discharge coefficient: Cd = 0.6.

  10. Experimental Requirements • Each group needs a disk to save your experimental data. • (1) Experimentally measure the pressure change with time for three different nozzle diameters. Set the initial pressure to 50 psig. • (2) From your experimental data, you should record the initial pressure, initial temperature, and the time period of the process for your subsequent analysis.

  11. Lab Report Requirements • Write a letter to your TA discussing the experiment. The letter should follow the formats shown in the documents “Letter format and FAQ” and “properly formatted business letter” found on the course website. In your letter, be sure to discuss how the isentropic and isothermal models compare with the experimental data. No uncertainty analysis is required. • On page 2 (or more pages, if necessary), show the theoretical derivation of pressure relationship with time for the isothermal case. Include a sample pressure calculation. • On page 3 (or more pages, if necessary), show the theoretical derivation of pressure relationship with time for the isentropic case. Include a sample pressure calculation. In your result, be sure to leave k (or γ) as a variable.

  12. Lab Report Requirements, cont. • On Page 4, show a plot of experimental pressure vs. time. On the same graph, plot the pressure obtained using the isentropic model, and plot the pressure using the isothermal model. There will be three plots, one for each plate. • On Page 5, show a plot of experimental temperature vs. time. On the same graph, plot the temperature obtained using the isentropic model, and plot the temperature using the isothermal model. There will be three plots, one for each plate.

  13. Lab Report Requirements, cont. • On Page 6, determine a polytropic constant for the pressure plot at 1/8 diameter orifice that allows your theoretical model to better match the experimental data. This is determined by adjusting the constant in your model so that the isentropic curve better matches your experimental curve. This will provide a mathematical model that accurately predicts this process. Plot your results, explain your results, and provide detail on how you determined this.

  14. Lab Report Requirements, cont. 7. On Page 7, plot the mass flow rate as a function of time for the 1/8 inch diameter orifice. You should have three curves; one for mass flow rate using the measured pressure, one for the mass flow rate using the predicted pressure from the isothermal model, and one for the mass flow rate using the predicted pressure from the isentropic model and the k values determined from the plot on Page 6.

More Related