CHEMICAL ENGINEERING LABORATORYengr.uconn.edu/~ewanders/CHEG237W/DRAINtime_fall01.pdf · CHEMICAL...

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C:\Documents and Settings\suzy.ENGR_STUDENT\My Documents\courses\cheg237W\DRAINtime fall01.DOC 09/05/03 Fenton/Coughlin/Fall’01 CHEMICAL ENGINEERING LABORATORY CHEG 237 Draining Time for a Tank with an Outlet Pipe Objective: The purpose of this exercise is to observe the effect of system variables on the drain time of a tank and develop a mathematical model that describes the depth of fluid in the tank as a function of time, pipe dimensions, and fluid properties. Model-generated results should be compared to observed experimental results. Theory: An overall mass balance can be combined with the mechanical energy balance to give a differential expression describing the change in fluid height with respect to time. In order to create a useful model, velocity in the outlet pipe must be expressed as a function of the liquid depth in the tank. Models of varying complexity can be generated depending on the mechanical energy balance terms retained in the derivation. For instance, if pressure and frictional effects are neglected, an energy balance between the top surface of the fluid and the drain pipe outlet will yield the following expression U b 2 = 2g(h + L) (1) where h is the liquid depth, L is the pipe length, U b is the velocity of the fluid exiting the pipe, and g is acceleration due to gravity. Such simplifying assumptions, however, may result in a model that does not represent the physical system and consequently cannot accurately predict system behavior. In general, friction cannot be neglected and lost-work term(s) must be included in the general energy equation. The lost work due to friction with pipe walls is h f L D U g f b c = 4 2 2 (2) For laminar flow Re / 16 = f (3) For turbulent flow in a smooth pipe, a popular approximation (Blasius) is 4 / 1 Re / 079 . 0 = f (4) where h f is lost work due to friction with pipe walls, f is the Fanning friction factor, D is pipe diameter, g c is the gravitational conversion factor, Re = ρUD/µ , µ is the fluid viscosity, and ρ is the fluid density. Check the references [McCabe et al. (2001), Perry (1997) or Geankoplis (1993)] for other empirical expressions for friction loss, including loses due to entrance and exit effects. 1

Transcript of CHEMICAL ENGINEERING LABORATORYengr.uconn.edu/~ewanders/CHEG237W/DRAINtime_fall01.pdf · CHEMICAL...

Page 1: CHEMICAL ENGINEERING LABORATORYengr.uconn.edu/~ewanders/CHEG237W/DRAINtime_fall01.pdf · CHEMICAL ENGINEERING LABORATORY ... fluid properties. ... Re = ρUD/µ , µ is the fluid viscosity,

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Fenton/Coughlin/Fall’01

CHEMICAL ENGINEERING LABORATORY CHEG 237

Draining Time for a Tank with an Outlet Pipe

Objective: The purpose of this exercise is to observe the effect of system variables on

the drain time of a tank and develop a mathematical model that describes the depth of fluid in the tank as a function of time, pipe dimensions, and fluid properties. Model-generated results should be compared to observed experimental results.

Theory: An overall mass balance can be combined with the mechanical energy balance to give a differential expression describing the change in fluid height with respect to time. In order to create a useful model, velocity in the outlet pipe must be expressed as a function of the liquid depth in the tank. Models of varying complexity can be generated depending on the mechanical energy balance terms retained in the derivation. For instance, if pressure and frictional effects are neglected, an energy balance between the top surface of the fluid and the drain pipe outlet will yield the following expression

Ub2 = 2g(h + L) (1)

where h is the liquid depth, L is the pipe length, Ub is the velocity of the fluid exiting the pipe, and g is acceleration due to gravity. Such simplifying assumptions, however, may result in a model that does not represent the physical system and consequently cannot accurately predict system behavior. In general, friction cannot be neglected and lost-work term(s) must be included in the general energy equation. The lost work due to friction with pipe walls is

h f LD

Ugfb

c

= 42

2

(2)

For laminar flow Re/16=f (3) For turbulent flow in a smooth pipe, a popular approximation (Blasius) is

4/1Re/079.0=f (4)

where hf is lost work due to friction with pipe walls, f is the Fanning friction factor, D is pipe diameter, gc is the gravitational conversion factor, Re = ρUD/µ , µ is the fluid viscosity, and ρ is the fluid density. Check the references [McCabe et al. (2001), Perry (1997) or Geankoplis (1993)] for other empirical expressions for friction loss, including loses due to entrance and exit effects.

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Preliminary Preparations: ♦ Before class, derive the equations for each of the flow cases (laminar, turbulent,

and non-Newtonian if applicable) ♦ Bring your personal safety equipment, lab book, textbook, calculator, etc. ♦ Be prepared at all times to answer the following questions:

1. How important are entrance loss and kinetic energy terms in the general energy equation?

2. What times do your equations predict for very long and very short exit pipes? Are these reasonable?

3. For which pipe lengths do you expect the greatest deviations between observed and calculated results? Why?

4. What is meant by the term “entrance length”? What is its value?

5. How does roughness affect drain time? Equipment: Metal and plastic tanks and a selection of pipes and fluids are available.

Sample dimensions of the exit pipes for the metal tank are:

DIAMETER (in) : 0.302 0.148 0.182 0.182 0.182 LENGTH (in): 24 24 12 3 orifice

Procedure: Determine the tank diameter by a suitable means (e.g., by filling with

weighed amounts of water). Be sure the pipes are clean.

Fill the tank and allow it to drain through each of the outlet pipes. Record the depth as a function of time. Do this for all the fluids supplied (normally a 50% glycerin solution and water are the fluids tested). Be sure to save all the glycerin solution. Measure lengths, temperatures, and other properties that are needed for your model. Determine the reproducibility of your experimental runs and the precision of your experimental measurements.

Analysis: Estimate experimental error in individual measurements and the error

between repeat runs. Determine the observed effect of controlled variables (pipe length, pipe diameter, and fluid viscosity) on the drain time. Solve your model(s) for the fluid height vs. time and compare with the experimental data. The models can be solved in a variety of ways depending on the complexity of the model.

Report: Describe the design of your experiments and the results obtained, including

an error analysis. Provide thoughtful and quantitative discussion of observed results, explain trends using physical principles and relate your experimental observations to results predicted by your model. Express any discrepancies between observed and predicted results in terms of quantified experimental uncertainties or model limitations.

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TIPS FOR PLANNING EXPERIMENTS AND ANALYZING DATA FROM DRAINING TANK Generally, you will want to test your data with respect to the mechanical energy balance (MEB). You will also want to use another equation that give the relationship between the velocity in the tank and the velocity in the tube through which the liquid drains. What is the name of the latter equation? The data you measure for each experimental configuration consists of height of the liquid level vs. time. Although the MEB contains height, it is written as a steady-state equation involving velocity. Thus you might try two types of approaches: (1) differentiate your data to obtain velocity as a function of height and (2) integrate the MEB equation to obtain height as a function of time. Be sure to plot your data in a way that tests the MEB. Which of these two approaches is preferred. Why? What are the advantages and disadvantages of each approach? Is it valid or justifiable to apply the MEB (derived for steady flow) to your experiments, which are not conducted under steady state conditions? Examine the MEB to determine how to plot the data in order to obtain a straight line. What is the significance of the values of the slopes and intercepts of the straight-line graphs? How well do your data conform to straight lines? Use regression analysis to test the goodness of fit. If you do not obtain straight lines, explain why you do not. Repeat experiments several times. Are the results reproducible? For an experiment done several times under identical conditions, how closely do values of slope and intercept agree? Analyze the reproducibility of the experiments by testing the values of slopes and intercept. How are the values of slopes and intercepts related to energy losses due to friction, expansion and contraction? Plan experiments that will test changes in these types of energy loss. Do changes in the slopes and intercepts that you deduce from the experimental data conform to the changes expected in energy loss? This is an opportunity to use your experimental data (and parameters calculated from your data) to test theoretical predictions regarding energy losses. References: McCabe, W. L., Smith, J. C. and Harriott, P., Unit Operations of Chemical Engineering,

6th Ed., McGraw-Hill, New York, NY, (2001). Perry, J. H., editor, Chemical Engineer’s Handbook, 7th Ed., McGraw-Hill, New York,

NY (1997). Geankoplis, C.J., Transport Processes and Unit Operations, 3rd Ed., Prentice Hall, New

Jersey (1993).

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