CHE 3222 Unit Operations Laboratory I

Application of the Bernoulli Equation (i.e. Mechanical Energy Balance) to piping, fittings, valves, and meters

Prelab questions and the Job Safety Analysis form are due BEFORE you can begin your lab experiment! Note, much of this material is adapted from Incropera and DeWitt, chapter 5 Introduction Safety The national Chemical Safety Board has strongly emphasized increasing safety awareness and instruction across chemical engineering and chemistry degree programs throughout the country. In response to this we are reinforcing our longstanding safety policies with new activities designed to increase your awareness and conduct of safe practices during all Unit Operations laboratory activities. More details are presented elsewhere laboratory documentation, but a few rules for working in the Unit Operations laboratory are emphasized here:

Upon entering the laboratory, you are to put on safety glasses. They are to be worn throughout your participation in laboratory experiments.

You MUST wear long pants and closed-toed shoes (you can use a locker, providing your own lock). Locks will be removed (by cutting if necessary) at the end of the semester to allow the juniors access for the spring lab section.

Absolutely NO food or drink in the lab.

Fully answer each of these questions PRIOR TO THE LAB PERIOD. Use any fluids text and the endless variety of online resources.

1. Discuss the difference between laminar and turbulent flow. What characterizes it? How does temperature affect flow of incompressible fluids?

2. Present the Bernoulli equation and show its reduction of terms to accurately describe the measurement of pressure drop across a given fitting, valve or flow meter.

3. What is the Reynolds number? How is it derived and what physical meaning

does it have? Why is it dimensionless (hint:discuss the meaning of “dimensional analysis”)?

4. List three important dates in the history of plumbing systems and the significance

of those dates. (You may have to focus on something like water supply for cities).

5. What does pipe surface roughness have to do with determining pressure losses in piping systems? What different methods exist for calculating friction factors? What governing

6. What procedures/calculations are used to predict pressure drop in piping

systems for incompressible fluids under Newtonian flow? What simiplifications/idealizations may reasonably be assumed for the mechanical energy balance when working with water flowing in a piping system? (Be specific in your answers)

7. Does temperature significantly affect pressure drop of water flowing in a piping

system? (Discuss in detail).

8. How do Venturi and orifice meters work? What principles of flow allow the determination of flow rate by these devices?

9. What is Net Positive Suction Head? Why is it important in assessing pumping of

fluids?

10. What is brake horsepower?

11. How is a pump curve determined? Is one pump curve applicable to more than one size of pump? What limitations are there to using a pump curve?

12. Write out a stepwise procedure for running the fluid flow in piping system to

determine the pressure drops over various valves and fittings.

13. Create a table for recording all flow rates, and corresponding pressure drops for each fitting, valve, or pipe length. Table must be organized to clearly represent the data obtained.

Experimental Objectives The “big picture” for this experiment is to measure the pressure drop across a selected valve, fitting, length of pipe, or meter using the mercury-filled manometer on your experimental apparatus. You will measure this pressure drop at three different flow rates (for EACH of your different fittings, valves, etc.). Then, using the Bernoulli equation, reduced correctly for your specific valve, fitting, pipe section, etc. you will calculate a pressure drop predicted in this fitting based upon the frictional losses calculated for your flow conditions in the system. Lastly, you will plot the three calculated and three experimentally observed pressure drops in Excel (for each of the three different flow rates measured) to see how closely the actual experimental data correlates with the pressure drops predicted by the Bernoulli equation.

FLOW MEASUREMENT AND ANALYSIS

Fluid transport and flow is ubiquitous in the chemical process industries. Consequently, a chemical engineer must understand the importance of concepts like frictional losses in pipe flows, effects of fittings on pressure losses, performance of flow meters, etc. This study is focused on analyzing flow measurements to determine pressure drops across a variety of pipe sizes, fittings, valves and flow meters in a closed-loop system. Our experimental apparatus is shown at left. A supply tank (conical tank against the far wall) supplies water from the municipal system through a centrifugal pump (blue pump seen below tank) to a series of different sized and types of pipes, valves, fittings, and meters. Do Not adjust these valves (leave open)

Select flow circuit with these valves.

Theoretical background The mechanical energy balance, or Bernoulli Equation, was developed in the fluids class. The full equation has the form

2

2

Using the image below of a pump transferring water from a “Wet well” to a “discharge well”, we can identify the terms in the above equation. Let point “a” be the surface of the water in the wet well and point “b” be the discharge point in the discharge well. The

terms and describe the pressure at each of these two points. The terms and

describe the heights of points “a” and “b” above the pump “Datum” line. The

elevation terms are describing the potential energy on either side of the pump. The Kinetic energy of the system (at points “a” and “b”) are described by the velocity terms. The energy required by the pump to move the fluid through the system is described by

.

And, lastly, all of the frictional losses in the system due to the pipe roughness, the elbows, fittings, valves, meters, etc. are described by the term . To capture all of these frictional losses in this term, it can be expressed as

4 2 ∗

From your fluids course you should recall that the friction factor (f) or “Fanning Friction Factor” is found using the Reynolds and an appropriate chart plotted for various roughness factors (see an example at the end of this handout). It is important to note that the MOODY Friction factor chart shown at the end of this handout is different from the Fanning Friction factor by a factor of 4. You are expected to sort this out and use the proper friction factor with the proper equation! The equation above uses the Fanning Friction Factor. Of course, the Bernoulli Equation may be applied over ANY points “a” and “b” of your choosing. In fact, for this experiment, we are going to write the balance over just a single fitting (or set of fittings), valve, meter, length of pipe, etc. Pressure drop across a straight section of horizontal pipe To begin, let’s examine a situation where we are wanting to measure the energy losses over a horizontal straight length of pipe (as will be the situation for one of your measurements in this experiment) such as is illustrated in the diagram below. Writing the Bernoulli balance around this simple system. We get the following reduction in terms:

The velocity at the pipe inlet and exit is approximately equivalent (in our case, though not necessarily always). The pipe is horizontal, therefore the potential energy terms fall out. The pump is not between points “a” and “b” (it is “outside” the system as we are defining the straight pipe)—therefore that term vanishes. We are therefore left with the above expression. Moving the pressure terms to the left hand side we get the following:

42

We get a further reduction in terms because there are no fittings, valves, meters, etc. between points “a” and “b”—just a straight pipe section. Using the volumetric flow rate (from our meter reading) and the pipe inside diameter (using our calipers to measure), and the pipe length between the two manometer taps (points “a” and “b”), we can now calculate the frictional loss on the right hand side of the equation. Note, the pressure taps across the pipe length should be the ONLY ones open. All others must be closed to give an accurate reading of pressure drop across the pipe section. Getting all of the units in their correct form, we can express this frictional energy term as

though, by multiplying through by the water density, we could actually get units of

which are standard units of pressure. You will read the manometer in millimeters of

mercury (the scale applied to the manometer fluid). By converting this manometer

height you can likewise get it in pressure units of

. Thus the left hand side of the

equation above represents your actual experimental data and the right hand side of the equation represents your predicted pressure drop based upon the pipe characteristics. Pressure drop across four 45o or 90oells (i.e. elbows) Elsewhere in your piping network, you will find located four elbows (or “ells”)—one set of 45o and one set of 90o. By opening the pressure taps on either side of one of these sets (and making sure all others are closed) you can measure the pressure drop across these ells using the mercury manometer. Again, the Bernoulli equation is reduced and now has the form shown below

4 2

Notice that the summation term for fittings has been included. In brief, the “K” values may be found in a number of ways. One easy way is to use correlations provided by a number of sources. From the image below, we can see that the K value is plotted as a function of the pipe diameter (in inches). Using your nominal pipe diameter (meaning for a 1 inch Schedule 40 American standard pipe, you would use 1 inch on the x axis below—not the precise inside diameter measured by your calipers) you can read from the linear curve the K value to use in the equation above. IMPORTANT! Notice the summation sign. Since you will have FOUR 90o elbows in this arrangement, you must multiply that K value obtained from the plot by 4—“summing” up a K value for EACH of the four elbows.

You can then calculate the frictional loss on the right hand side of the equation just as you did for the straight pipe length. Again, you will graphically compare that calculated value with the measured experimental value (from the manometer) for EACH of the three different flow rates used in your experiment.

Use the figure at left for the 45o elbows just as you will for the 90o elbows.

Orifice plates and venture meters Despite what you might believe, the “engineering world” has not completely gone to digital instrumentation. Analog instruments (such as Orifice meters and Venturi meters) are still widely used in industry. The images below will help you get a better perspective on how they operate. Use your fluids text and the numerous online resources to follow the same process we used above for comparing observed pressure drop (from the manometer reading) to predicted pressure drop. These calculations will need to be included in your report.

Laboratory Preparation

1. Measure and record the diameter of each pipe in the system. A small section of each type of pipe is chained to the frame at the left hand side of the experiment (when viewing the experiment while standing in front). Note the types of fittings, valves and flow meters present . Note, calipers are available from the laboratory instructor for this purpose. Compare your measured inside diameters to those published for steel pipe (Schedule 40), and for copper tubes using the tables provided below. Note that copper tubing is not classified by schedule, but rather by application of use—(e.g. “Type L” in the table below).

2. Trace the flow route from the supply tank (seen against the far wall in the picture above) Note the large blue-handled ball valves used to open/close a given piping circuit.

Laboratory Procedures

1. Fill up the holding tank to 2/3 full with water. Check that the appropriate valves are open, and turn on the recirculation loop. Make sure that the bypass to the control valve is open.

2. Set the flow loop with an arbitrarily-chosen flowrate (by setting the blue-handled manual ball valve just downstream from the centrifugal pump).

3. At the chosen flow rate (read from the electronic meter in the blue/green housing just upstream from the manual control valve) take pressure drop readings on the mercury manometer from a sufficient combination of pressure taps for each pipe length, valve, fitting or meter.

a. Determine the effect of length on pressure drop. b. Determine the effect of pipe diameter on pressure drop. c. Determine the pressure drop across various flow meters and valves.

Discuss the degree of pressure drop across various valve types and why it varies.

d. Determine the effect of various piping configurations on pressure drop. 4. Repeat step 3 by adjusting the main valve to a new setting. Do this for a total of

three separate flow rates. 5. After turning the pump off and drain the holding tank.

Calculations

1. Using the appropriately reduced form of the Bernoulli mechanical energy balance, calculate the pressure drop estimated over your selected fittings, piping sections, valves, etc. (select at least five different items). Plot BOTH the actual, measured pressure drop AND the predicted pressure drop (from your calculations) versus the flow rate in properly labeled and formatted Excel spreadsheets. Include these in your final report.

2. Discuss the comparisons of experimental observations with theoretical calculations from the calculations in step 1. How close are your calculations to the measured pressure drops?

3. Present the equations for predicting pressure drop using the venturi meter coefficient and the orifice meter coefficient.

Other Information Venturi Meter: Inlet Diameter: 1.610 inches Throat Diameter: 1.116 inches Orifice Meter: Internal Diameter: 1.610 inches Orifice Diameter: 1.000 inches Magnetic Flowmeter: 0 – 100% of Full Scale; Full Scale is 100 gpm. Therefore the reading on the meter is in gallons per minute. References Any selected introductory fluids text should provide necessary material for conducting this experiment.