sp15 uo lab manual

1 | Unit Operations Lab Manual

UNIT OPERATIONS LAB MANUAL

Version Date: May 10, 2014

Chemical Engineering Department

University of Massachusetts Lowell

2 UNIT OPERATIONS LAB MANUAL | Unit Operations Lab Manual

TABLE OF CONTENTS

UNIT OPERATIONS LAB MANUAL ........................................................................................................................................ 1

TABLE OF FIGURES .................................................................................................................................................................... 3

TABLE OF TABLES ..................................................................................................................................................................... 3

CALIBRATION OF THE ROTAMETER FLOW STAND ....................................................................................................... 4

INTRODUCTION.......................................................................................................................................................................................... 4 PROCEDURE ................................................................................................................................................................................................. 4 DATA REQUIRED ........................................................................................................................................................................................ 5 EVALUATION ............................................................................................................................................................................................... 6

THE STUDY OF LAMINAR AND TURBULENT FLOW ....................................................................................................... 8

INTRODUCTION.......................................................................................................................................................................................... 8 THEORY .......................................................................................................................................................................................................... 9 PROCEDURE ............................................................................................................................................................................................... 10

PART 1. DETERMINATION OF FLOW TYPE IN RELATION TO REYNOLDS NUMBER............................................... 10 PART 2. VELOCITY DISTILLATIONS ............................................................................................................................................. 11

DATA REQUIRED ...................................................................................................................................................................................... 11 EVALUATION ............................................................................................................................................................................................. 11

FRICTION LOSSES IN PIPE FITTINGS ............................................................................................................................... 13

INTRODUCTION........................................................................................................................................................................................ 13 THEORY ........................................................................................................................................................................................................ 14 DATA REQUIRED ...................................................................................................................................................................................... 15 EVALUATION ............................................................................................................................................................................................. 15

THE ORIFICE METER.............................................................................................................................................................. 16

THEORY ........................................................................................................................................................................................................ 16 DATA REQUIRED ...................................................................................................................................................................................... 20 EVALUATION ............................................................................................................................................................................................. 21

FLUID FRICTION LOSSES ...................................................................................................................................................... 22

THEORY ........................................................................................................................................................................................................ 22 DATA REQUIRED ...................................................................................................................................................................................... 23 EVALUATION AND DISCUSSION........................................................................................................................................................ 24

EFFLUX TIME FOR TANK AND PIPE .................................................................................................................................. 25

INTRODUCTION........................................................................................................................................................................................ 25 THEORY ........................................................................................................................................................................................................ 25 DATA REQUIRED ...................................................................................................................................................................................... 29 EVALUATION ............................................................................................................................................................................................. 29

3 Table of Figures | Unit Operations Lab Manual

TABLE OF FIGURES

FIGURE 1. ROTAMETER APPARATUS ........................................................................................................................................ 7 FIGURE 2. THE REYNOLDS FLOW STUDY APPARATUS .................................................................................................................. 8 FIGURE 3. TWO SECTIONS OF PIPE JOINED BY A COUPLING ......................................................................................................... 14 FIGURE 4. DIAGRAM OF ORIFICE METER ................................................................................................................................. 17 FIGURE 5. DIAGRAM OF ORIFICE METER AT TAP 2 .................................................................................................................... 19 FIGURE 6. A DIAGRAM OF THE TANK OF WATER AND AN EFFLUX PIPE ........................................................................................... 25

TABLE OF TABLES

TABLE 1. APPARATUS MEASUREMENT ERRORS ......................................................................................................................... 5 TABLE 2. RAW DATA TABLE ................................................................................................................................................... 6 TABLE 3. REYNOLDS VALUE REGIONS ................................................................................................................................... 12 TABLE 4. FLOW CONDITIONS ......................................................................................................................................... 27

4 CALIBRATION OF THE ROTAMETER FLOW STAND | Unit Operations Lab Manual

CALIBRATION OF THE ROTAMETER FLOW STAND

INTRODUCTION

In the unit Operations laboratory exists two rotameter stands with 4 different rotameters attached to each. These rotameters measure the flow of water through them as a percentage of a maximum flow rate that is unique to each rotameter. For this reason, each individual rotameter must be calibrated for use in future labs. It is important to note that rotameters should be selected based on the amount of water that is desired to flow through them. If large amount of water are to be used, rotameter 4 would most likely be chosen, however if a low capacity of water is required, then rotameters 1-3 should be used. It is best to start with rotameter 2 and 3 first to get a general understanding of calibrating.

In order to complete this task it is assumed that the rotameters measure the flow rate linearly (increase in flow rate is proportional to increase in setting) and consistently. The rotameter must be calibrated by adjusting the rotameter valves to a certain flow percentage. A bucket, a stopwatch, and a weighing scale will be used to physically measure the flow rate (kg/s) at the specific setting.

Several data points will be taken along range of measurement for each rotameter (15%-85% flow). Each data point is to be taken 3 times for consistency and precision. Groups should take readings at flow percentages of 20%, 30%, 45%, 60%, 75%, and 85%.

When conducting the experiment, groups should do a few trial runs to ensure a constant recording time. As the flow rate is increased the volume of water in the bucket will increase, so the longer the time, less error will be associated with the results involving mass of the water and time.

PROCEDURE

The procedure listed below is for the use of rotameter 3. The same concept can be applied to any other rotameter.

Start-up Procedure

1. Open outlet globe valve (G3)

2. Open the ball valves for rotameter three (B5 and B6)

3. Open secondary inlet globe valve (G2)

4. Open main feed valve (F)

5. Slowly open inlet globe valve (G1) until marker on rotameter 3 reaches desired flow

percentage

6. Weight empty bucket


Operating Procedure

1. Adjust inlet globe valve (G1) until rotameter three at desired flow percentage

2. Place empty bucket near outlet hose

3. Start timer and place hose inside bucket simultaneously

4. Fill bucket roughly halfway for flow percentages equal to or below 60; fill to top for the rest

5. Pull hose away from bucket and stop timer simultaneously (jot down time)

6. Turn inlet globe valve (G1) off

7. Weight bucket (jot down weight)

8. Reset stop watch, drain bucket

9. Return to step 1

Shut-down Procedure

1. Close inlet globe valve (G1)

2. Close main feed valve (F)

3. Close secondary inlet globe valve (G2)

4. Close ball valves for rotameter three (B5 and B6)

5. Close outlet globe valve (G3)

TABLE 1. APPARATUS MEASUREMENT ERRORS

Measurement Device Error Scale 0.01 kg or 0.05 lbs Rotameters 0.5% flow Stopwatch 0.005 seconds (Reading error: 0.5 seconds)

DATA REQUIRED

1) Obtain time(seconds) 2) Obtain mass of bucket(lb.) 3) Obtain mass of water(lb.)


An example of how the results should be recorded is represented in the table below.

TABLE 2. RAW DATA TABLE

Flow [%] ( 1)

Time [s] ( 0.5)

Weight [lb] ( 0.05)

Bucket Weight [lb]

Final Weight [lb]

Observations

85

20

45

30

75

65

20

85

30

45

75

Note: It is important to make sure that the flow percentages are randomized. This is a common practice in data collection.

EVALUATION

1) Plot the data and create regression fits.

2) Compare plots of identical rotameter regression fits

3) Determine best fit line for each rotameter

Note: When performing a linear regression analysis for raw and correct, students should use excel

and IBM SPSS statistics.


FIGURE 1. ROTAMETER APPARATUS

8 THE STUDY OF LAMINAR AND TURBULENT FLOW | Unit Operations Lab Manual

THE STUDY OF LAMINAR AND TURBULENT FLOW

INTRODUCTION

Osborn Reynolds in 1883 was the first to study the transition in a flowing fluid from laminar flow to turbulent flow. He used an apparatus similar to the following:

FIGURE 2. THE REYNOLDS FLOW STUDY APPARATUS

A fine filament of dye was injected into the center of the streams of fluid as it flows out of the storage tank. Reynolds found out that for a low or laminar flow condition the filament of dye remained unchanged as it flowed through the tube. However, as the flow rate was increased the dye filament began to show a wavy pattern and if the flow rate increased into the turbulent region the dye filament tended to break up and the dye was dispersed into the flowing fluid. The point at which the dye begins to disperse into the fluid is sometimes referred to as the critical velocity. Prior to this velocity being reached, the viscous forces in the fluid will dampen out any type of disturbances in the flow. However, above the critical velocity the forces of inertia are increased and disturbances in the flow will not be dampened out and will cause the dispersion of the dye filament. Thus, the Reynolds number is a dimensionless parameter which is the ratio of the inertia forces to the dampening forces (forces of viscosity). The Reynolds number is expressed as:

=

=

=

Where:


D=diameter of pipe (ft.)

=average linear velocity of fluid (ft./sec)

=fluid density(/3)

=fluid viscosity of fluid (/ )

=kinematic viscosity of fluid (2/sec )

G=mass velocity of fluid (/2 )

In circular pipes, laminar flow will always be encountered at Reynolds numbers less than 2,000. Given that turbulent flow exists at Reynolds numbers greater than 4,000, in between these values exists the transition region. In this region, the flow may be either laminar or turbulent depending on the conditions under which the fluid entered the pipe, and the point at which the dye was injected into the pipe.

THEORY

This laboratory experiment will be divided into two sections. The first of which will be to use an apparatus similar to that of Reynolds to determine the ranges of laminar and turbulent flow as well as the transition region between them.

The second part of the experiment will concern the velocity profiles that exist in the pipe at the various types of flow patterns. Although there are many shapes of velocity distribution possible, only the linear cases will be discussed here.

Linear Velocity Equation:

=

Where a and b are constants.

Boundary Conditions:

B.C. # 1:

r=0 , =

B.C. #2:

r=R , =

From B.C #1:

a=

From B.C. #2:

=


=

Volume Flow Rate:

2

0 0

Volume:

(

)

2

0 0

2

2

2

0

3

3 |

0

2

2

( )2

3 |

0

2

= 2

2

3( )

2

Special Cases of Linear Flow:

1) Plus Flow: =

2

2

3( )

2

= 2

2) No Flow Along Pipe Wall: = 0

2

2

3( 0)

2

volume =1

3vmaxR

2

PROCEDURE

PART 1. DETERMINATION OF FLOW TYPE IN RELATION TO REYNOLDS NUMBER

In order for the students to see the basic differences between laminar and turbulent flow the first step is to set a very slow water flow rate of water through the glass tube. Open the valve that controls the flow of the dye solution (a very dilute solution of potassium permanganate in water) until a fine filament is noticeable in the fluid flow. The water flow rate should be checked to make certain that is well into the laminar region.


From now on, this type of flow will be designated as level 0 flow. The next step is to greatly increase the water flow and dye flow proportionally until the flow rate is well into the turbulent region. This type of flow will be designated as equal to level 1 flow. From now on it will be up to the student to record the flow type of laminar as 0, turbulent as 1, the types of flow between these two levels will be given fractional values between 0 and 1.

PART 2. VELOCITY DISTILLATIONS

The dye injector is located along the center line of the tube thus if the velocity of the dye flow is recorded as it passes down the center line of the tube the value of can be estimated. The wall velocity can be estimated by allowing a large concentration of dye to flow out of the injector. Since the specific gravity of the dye is greater than that of the water flowing in the pipe it will tend to fall toward the bottom surface of the pipe. Thus by measuring the velocity of the dye on the bottom surface of the tube, the value of the can be estimated.

For a large number of flow rates(going from lowest to highest) the student should measure the volumetric flow rate, centerline, wall fluid velocities and a characteristic level of the type of flow(0 or 1) along with any values that may fall between.

DATA REQUIRED

For the water flow:

a) Volumetric flow rate b) c) d) Level of flow type

For the glass pipe:

a) Inside Diameter(D)

EVALUATION

1) Calculate the Reynolds number from the Reynolds equation on page 5 for each flow rate used and plot this result versus the type of flow found (from level 0 to 1). The boundaries of the transition region should be marked off and compared with published levels of of 2,000 and 4,000.

2) From the experimental velocity data calculate the estimated volume flow rates of the water.

Compare these estimated values to the actual measured volume flow rate, and comment on which formula gives the closest to actual rates for the following regions of Reynolds numbers:


TABLE 3. REYNOLDS VALUE REGIONS

0 750

750 1500

1500 2100

2100 4000

4000 6000

6000 And above

13 FRICTION LOSSES IN PIPE FITTINGS | Unit Operations Lab Manual

FRICTION LOSSES IN PIPE FITTINGS

INTRODUCTION

When a fluid flows through a straight length of pipe, the pressure drop due to friction can be calculated by the Bernoulli Equation:

P1

+g

gcZ1 +

v121

2gc=

P2

+g

gcZ2 +

v222

2gc+Hf

Where represents the losses due to friction in the pipe, these friction losses can be calculated for

laminar flow by the use of Hagen-Poiseville Relation for circular tubes. This relation can be written as follows:

=32

2

The subscript s is used to indicate that this equation only calculates friction losses, where the fluid comes in contact with the pipe walls. As can be seen from this relationship it only takes into consideration the Length (L) and diameter (D) of the pipe. However, in most real cases there will be fittings such as couplings or unions and valves. Thus it will be the purpose of this laboratory experiment to examine the effect of fittings and valves on the pressure drop across a section of pipe.


THEORY

Although there are several means of calculating or expressing the pressure drop across fittings or valves, this laboratory will consider only the equivalent resistance in pipe diameters (). It has been found that if the equivalent length is expressed as a length of pipe in feet divided by the internal diameter of the pipe also in feet, it is almost independent of the size of the pipe or fitting in the laminar flow regions.

Let us consider two sections of pipe (A&B) joined by a coupling, ( C ).

FIGURE 3. TWO SECTIONS OF PIPE JOINED BY A COUPLING

The pressure drop ( ) could be calculated by use of the Bernoulli Equation and the Hagen-Poiseville Relation if the length was known. But since there is a coupling in the pipe, the length may not be equal to the physical length of the system ( + ). Thus, if the friction drop across the coupling could be specified as a length of pipe then the equation for the friction drop for the

system could be used and the equivalent length of the system would then be specified as:

= + +

The easiest means to determine the value of is by experimentation. First, determine for a long

length of pipe (L) the pressure drop () in inches of water. Then measure the pressure drop across the pipe fitting (P) in inches. Assume that the fitting of interest will fit the same diagram that was presented for the coupling. The value measure includes a length of pipe before and after the fitting. Thus it will be required to find the pressure drop for just the fitting (). This ca be calculated by:

= + ( + )


Rearranging and solving for :

= ( + )

Where:

= Pressure drop for just the fitting (inches of water)

= Pressure drop for fitting and connecting pipes (A&B) in (inches of water)

= Length of connecting pipe A (ft.)

= Length of connecting pipe B (ft.,)

= Pressure drop for long length of pipe of the same diameter and material as that of the connecting pipes, measured at the same flow conditions as .

L=Length of long pipe over which was measured.

The value calculated is of little use in this particular form, thus it must be changed to a more useful form. As was mentioned earlier the equivalent resistance in pipe diameters is the form that will be used for this laboratory. Thus the equivalent resistance in pipe diameters () can be calculated as follows:

= (

) (

1

)

Where:

=Actual internal diameter of the pipe (ft.)

In actual use, find the particular value for for each type of fitting in a system and the number of each type of fitting. Then the equivalent length of pipe for all the fitting equals the sum of the number of each type of fitting times its factor times the actual internal diameter (ft.) of the pipe.

DATA REQUIRED

1) Determine,,, for each type of fitting. 2) For the reference pipe, determine L, , .

EVALUATION

1) Determine for each type of fitting and mounting. 2) Compare values determined experimentally with those published. 3) Compare values for the threaded and sweat fitted pipe fitting.

16 THE ORIFICE METER | Unit Operations Lab Manual

THE ORIFICE METER

The orifice meter consists of a flat smooth plate with a round hole in the center. The hole can be of two styles, the first is a sharp-edged orifice which has the downstream edges cut at a 45 angle to the surface of the plate. The second type, square-edged, the hole through the plate has its edges perpendicular to the plate.

As the fluid passes through the constricting orifice the velocity increases which in turn increases the kinetic energy. But from the Bernoulli Theorem there must be a proportional decrease in pressure. Thus, by knowing the pressure drop across the orifice it is possible to determine the rate of fluid flow.

The pressure drop measurements are usually measured by one of the following pairs of pressure taps:

a) Corner taps- the openings into the pipe are as close to the upstream and downstream sides of the orifice plate.

b) Radius taps the taps are located a pipe diameter upstream and pipe diameter downstream from the orifice plate.

c) Pipe taps- the taps are located 2 pipe diameters upstream and 8 pipe diameters downstream from the orifice plate.

d) Flange taps- the taps are both located 1 inch upstream and 1 inch downstream from the orifice plate.

e) Vena constracta taps- the upstream tap is to 2 pipe diameters from the orifice plate while the downstream tap is located at the point of minimum pressure.

From a practical standpoint, radius taps are the best because the upper tap is located far enough upstream so that it is not affected by distortion in the flow pattern yet still has a reasonable size in the orifice unit. The corner taps and flange taps are convenient to use since they can be added to any piping system without the problem of drilling into any of the existing pip. The vena constracta taps give the maximum pressure differential, even with slow flow rates, but are good only with on size orifice. Thus it becomes a difficult proposition to change from one size orifice to another size. Of the various types of taps discussed, the pipe taps offer the lowest differential pressure with a given flow rate.

THEORY

A diagram of an orifice meter is given as follows:


FIGURE 4. DIAGRAM OF ORIFICE METER

Mass Balance:

1 = 2 =

=

Where:

W=mass flow rate

=density

=bulk velocity

A=cross sectional area

Mechanical Energy Balance (Bernoulli Equation):

=2

2

22

12

21+

2 1

+1

22 + + 2

Where:

= bulk velocity

P=pressure of fluid

=friction loss factor

=density

= work done by fluid on the system

g=gravity factor

H= height above a datum plane for inlet and outlet

The original equation that was developed for the mechanical energy balance contained the term:


3

The coefficient is used to correct for the assumption that:

2 =3

If there is no work done by the fluid on the system and the pressure taps are on the same level, then

=2

2

22

12

21+

2 1

+1

22 + + 2

Reduces to:

=2

2

22

12

21+

2 1

+1

22

Combining equations (1) and (3) and collecting terms:

=2

2(

1

2

1

1+ ) +

2 1

Solving for and converting it into the equation for mass flow rate by:

=

Yields

= 2 (

2 1 )

12

1

1+

In order to simplify this equation there will be three assumptions made.

1) The fluid fraction effect is negligible and thus =0. 2) The velocity profile at tap 1 is flat, thus has the value of unity(1=1). 3) The velocity profile at tap 2 has the following configuration


FIGURE 5. DIAGRAM OF ORIFICE METER AT TAP 2

Where:

= cross- sectional area of orifice hole

=cross-sectional area of pipe

The velocity outside the plug flow is assumed to be equal to zero.

=+

=

=

From the definition of :

1

2=

3

3

Combining equations:

1

2=

[3 (

)

3

] + [3 (

)3

]

3

This reduces to:

1

2=

2

2

From the assumptions made equation X becomes:


= 2 (

2 1 )

2

2 1

To account for the errors made in the assumptions, an orifice coefficient ( C ) is used, and to correct for the discrepancy between the pound-force units of pressure and the pound-mass units of density the gravitational factor is added. Thus the equation in final form is written as:

=

2

2

2 1

Where:

W=mass flow rate (lb./sec)

C=orifice coefficient

A=area of pipe (2)

=density (lb./3)

P = pressure drop (lb/2)

=area of orifice (2)

As can be seen, C is a function of the location of taps, roughness of pipe, flow rate, etc. Thus it is necessary to determine the actual value of C for each orifice instillation experimentally. The overall orifice coefficient () is just the combination of all of the fixed valves in the denominator of the final equation and the coefficient C.

It is given as:

= 2

=

2

2 1

And is dimensionless.

DATA REQUIRED

1) Calibration of orifice meter: actual mass flow rate and meter reading. 2) Determine the overall orifice coefficient (), orifice, P, W, Temperature.


EVALUATION

1) Calibration curve for orifice meter in gal/min flow. 2) Evaluate, .

Note:

=

= 2

Or

Log W = log N + 0.5 log P

Graph on a log-log plot, flow rate(W) vs. pressure drop(P) and compare the slope value to 0.5 and

the intercept valve to 2 . Use the average of for this calculation.

,

22 FLUID FRICTION LOSSES | Unit Operations Lab Manual

FLUID FRICTION LOSSES

Fluid flow in all practical engineering problems involves friction loses of various types. These friction losses, involve the conversion of energy from one form to another, such as kinetic energy to internal energy. In all cases fluid friction losses appear in the form of a rise in temperature in the fluid system.

There are generally two types of friction encountered in engineering practice, these are skin friction and form friction. Skin friction results as the fluid moves along in contact with the solid boundary. Form friction results when the boundary separation occurs thus producing a wake made of vortices. This type of friction results in a large friction loss. This later type of friction occurs when a system encounters a sudden contraction or expansion causing the main stream to separate momentarily from the solid boundary.

Our experiment will concern itself with the calculation of skin friction losses and the losses due to contraction of the main stream.

THEORY

For our experiment we will consider friction losses in syphon tubes of various diameters and lengths. We will begin our analysis of our system by applying the law of conservation of energy to the flow of an incompressible fluid in a circular tube. The law results in the Bernoulli Equation. For our case we will use the equation in the form corrected for the fluid friction.

1

+

1 +

2121

=2

+

2 +

2222

+

Where:

P = absolute pressure (lb. /2)

V=average linear velocity ft. /sec

=density of fluid lb. /3

=Newtons law conversion factor 32.174

2

g=acceleration of gravity ft/2

=friction losses in the system .

Z= height above a datum plane (ft.)

=kinetic energy factor

We can simplify the above equation as for our system 1=0 and 1=2. Thus we are left with:

(1 2) =

2222

+


Rearranging and solving for

=

(1 2)

2222

is composed of various friction losses i.e., contraction losses , losses in the bend and loss due to the friction in the tube .

= + +

=

22

2

=42

2

L= length of tube

D= inside diameter of tube

F= fanning friction factor

=resistance due to 180 return bend. Assume this loss to be equivalent to the loss in a straight tube equal to 50 tube diameters in length.

We can now rewrite the equation:

= 222

+4( + 50)

2 22

Now equating the equations, we obtain:

(1 2)

2222

=222

( +4( + 50)

)

We will let L+50D=1

Thus + =4122

2= 1

From equation 5 we can calculate the friction loss in a straight tube ( + 50)1 ft. long.

For Laminar flow f=16

=Reynolds number

f=0.00140 + 0.1250.32

DATA REQUIRED


1. Viscosity of the fluid. 2. Lengths and diameter of the tubes. 3. Density of the fluid. 4. Average velocity of flow through a pipe. 5. Height between datum planes.

EVALUATION AND DISCUSSION

For tubes of various length and diameter make various runs using different heads so that you obtain in both the laminar and turbulent range.

1. Calculate 2. Calculate 3. Calculate 1 by subtracting the results in 2 from 1.

4. Solve for f in + =4122

2= 1 for all runs using results from 3.

5. Make a plot of friction factor vs. Reynolds number for all runs. 6. What is the transition range of for each plot in 5? Does that diameter of the tubing have

any effect on this transition range? 7. Do the plots in 5 agree within experimental accuracy with the plots found in the literature

and texts? If not, why?

25 EFFLUX TIME FOR TANK AND PIPE | Unit Operations Lab Manual

EFFLUX TIME FOR TANK AND PIPE

INTRODUCTION

This experiment is designed to give the student an introduction to the principles of a mass balance analysis using the Bernoulli equation. The system used for this analysis will be the drainage of a tank of water through various diameters and length of efflux pipes. For the student, the most benefit can be derived if enough time is spent to completely understand the assumptions made in the derivation of the equations used in the analysis of the problem.

THEORY

A diagram of the system for analysis is given as follows:

FIGURE 6. A DIAGRAM OF THE TANK OF WATER AND AN EFFLUX PIPE

The Bernoulli equation for non-compressible flow is given as follows:

+

+2

2=

+

+2

2+

Where:


P=pressure of fluid (lb. /2)

=density of fluid (lb. /3)

g=acceleration of gravity (ft. /2)

= Newtons conversion factor(32.174

)

Z=height above datum plane

v= linear velocity (ft. /sec)

=velocity coefficient

=friction losses in the tank and pipe and contraction losses from tank to pipe

The reference points A and B are chosen at the interface of the fluid and air. These points are chosen such that the following simplifying statements can be made:

= 0

=

Thus the kinetic energy term at A can be neglected in comparison to the energy term at B. Thus the simplified Bernoulli equation can be written as:

=2

2+

The term is the friction losses and is composed of the following terms:

Constriction losses =

2

2

Friction losses in a pipe = 42

2

Friction losses in the tank are to be assumed to be negligible.

Where:

= contraction coefficient

f =friction factor

D=internal diameter of pipe (ft.)

Thus, with the addition of the terms and rearranging of the g and factors,

=2

2+


Becomes:

=2

2+

2

2+

422

Collecting common terms:

=22

[1

+ +

4

]

As the tank is allowed to drain the fluid head (h) decreases as a result, the velocity and the Reynolds number in the pipe decreases accordingly; thus, the general flow regions can be expressed as:

TABLE 4. FLOW CONDITIONS

Laminar Turbulent

=1.05 to 1.1 =0.40 to 0.55

=0.5 =0.88 to 0.97

=2

2(3 +

4

) where B = 3 =

2

2(1.6 +

4

) where B = 1.6

Since it is assumed a non-compressible flow system, then a velocity balance on the system leaders to:

= (

)

Where:

, equal the cross sectional areas of the pipe and tank respectively in 2

A general expression for equation =22

[1

+ +

4

] can be written as:

+ =22

( +4

)

Substituting in for the velocity term:

+ = (

)2

(1

2) ( +

4

) (

)

2

The problem that now arises is that the friction factor (f) is a function of the Reynolds number. If the Reynolds does not change greatly from h + L to L then it may be considered to be a constant and not as a function of dh. For the turbulent flow situation, the chart in McCabe and Smith, Unit Operations for chemical engineers indicates that this is the case for f as a function of . However, for the laminar flow situation, if the change in the Reynolds Number is small then the


approximation that f=16/ can be made. Considering just the turbulent flow case, the equation () can be rearranged and written as:

=

+4

0

1

2

+

2

1

For the turbulent flow case, this integrates to:

=

+4

1

2[1 + 2 + ]

For the laminar flow case relation:

=16

=

16

Can be substituted into + = (

)2

(1

2) ( +

4

) (

)

2 to give:

+ = (

)2

(1

2) ( +

64

2) (

)

2

The value of B for laminar flow is 3.0, for most all situations that will be encountered in this

experiment the term 64

2 will be quite large in comparison to B. Thus it can be justified to drop the

B term from the equation. Therefore + = (

)2

(1

2) ( +

64

2) (

)

2, after substituting for

, can be written as:

+ = (

) (1

2) (

64

2) (

)

In integral form this can be written as:

0

= (

) (1

2) (

64

2)

+

2

1

For the laminar flow case, this integrates to:

= 322

(1 +

2 + )


The average Reynolds number for any test run can be calculated by:

=2(1 2)

Where:

d= diameter of tank (ft.)

D= diameter of pipe (ft.)

T=time (sec)

DATA REQUIRED

1) Obtain L and D for the tube. 2) Obtain 1, 2 and for the tank. 3) Obtain and at the test temperature. 4) Obtain time (sec). 5) Obtain at least two runs for each different sized pipe used to verify reproducibility.

EVALUATION

1) For the turbulent systems: a) Compare the average f value determined experimentally by

=

+4

1

2[1 + 2 + ] with the published value determined at the average

Reynolds Number.

b) Comment on the assumptions made in the derivation of

=

+4

1

2[1 + 2 + ].

2) For laminar systems:

a) Compare the efflux time calculated by = 322

(1+

2+) with the

experimental value.

b) Comment on the assumption = 16

and other assumptions made in the

derivation equation of = 32

2 (

1+

2+).

3) How do the diameter and length interact with each other as factors that affect the efflux time? Are they additive or non-additive?

4) Whats the effect of pipe length on efflux time? Can you theoretically justify this? 5) Whats the effect of pipe diameter on efflux time? Can you theoretically justify this?

sp15 uo lab manual

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