Fluid Flow Analysis Penn State Chemical Engineering

Revised Spring 2015

1

Table of Contents

LEARNING OBJECTIVES............................................................................................................ 1

EXPERIMENTAL OBJECTIVES AND OVERVIEW ................................................................. 1

PRE-LAB STUDY...................................................................................................................... 2

EXPERIMENTS IN THE LAB .................................................................................................. 2

THEORY ........................................................................................................................................ 3

BACKGROUND ........................................................................................................................ 3

ADDITIONAL THEORY TOPICS: (These are important learning points for prelab, prelab

quiz, conducting the experiment and for writing the report. Please download the electronic

reserve materials for this lab and review. Also make sure to watch the video.) ........................ 4

PRE-LAB QUESTIONS (to be completed before coming to lab) ................................................. 5

DATA PROCESSING PREPARATION (Excel spreadsheet to be used for data processing in the

lab must be prepared before coming to the lab for the experiment) ............................................... 9

DATA PROCESSING .................................................................................................................. 11

KEY POINTS FOR REPORT ...................................................................................................... 13

EXPERIMENTAL SETUP ........................................................................................................... 15

EXPERIMENTAL PROCEDURE ............................................................................................... 17

REFERENCES ............................................................................................................................. 19

Appendix A: Fanning Friction Factor Chart ................................................................................ 20

LEARNING OBJECTIVES

1. Understand the engineering Bernoulli equation and use it to calculate the pressure drop

(Ptubing) in a pipe due to the skin friction loss in the pipe.

2. Learn correlation between fluid flow rate (Q) and tube diameter (D) at a given Ptubing.

3. Assess the effect of tube coiling on fluid flow rate and pressure drop.

4. Utilize the student’s t-test and understand the statistical significance.

EXPERIMENTAL OBJECTIVES AND OVERVIEW

In this experiment, you will use both a straight pipe model and a coiled pipe model to estimate

the pressure drop given the flow rate and also to estimate the flow rate given the pressure drop.

2

You will then determine which model better represents the piping system in the lab. The piping

system consists of a flow meter, a pressure gauge, and a series of elbows, valves, and 50 ft

lengths (=L) of ½ in, ¼ in, and 4 mm internal diameter smooth plastic tubing. The tubing is

coiled around an 8 inch diameter spool and experiences approximately 5 feet of elevation drop.

The end of the tubing is open to the atmosphere and drains to the floor drain. We want to find the

relationship Q = f(D) at a fixed ΔPtubing. But, ΔPtubing cannot be read directly from the gauge

because the elbows and valves are between the gauge and the start of the tubing. So, we must

find Q iteratively until ΔPtubing reaches the set value for each tube with different diameter.

PRE-LAB STUDY:

1) Calculate the pressure drop through the tubing (Ptubing) at Q = 4.5 gpm for a tube with D

= 0.5” and L = 50 ft using a straight pipe model. This will be the tubing pressure drop set

point, 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

, for the remainder of the experiment.

2) Predict 𝑄𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 for tubes with D = 0.25” and 4mm at the same 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

using the

straight pipe model and the same 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

.

3) Re-process the data using a coiled tube model.

a. Using a coiled model and the predicted 𝑄𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 values, calculate 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑐𝑜𝑖𝑙𝑒𝑑 .

b. Recalculate the flow rate for a coiled pipe model (𝑄𝑐𝑜𝑖𝑙𝑒𝑑) using 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

.

4) Q is proportional to Dx when ΔPtubing and elevation change are held constant. Derive an

equation describing how Q varies with D, Q = f(D), for the straight tube. It should have a

form 𝑄 = 𝑎 × 𝐷𝑥 where a and x are constants.

EXPERIMENTS IN THE LAB:

5) Measure 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑒𝑥𝑝

when you set the flow rate to the predicted 𝑄𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 value in the pre-

lab calculation. Check if your initial guess for Q gives the target 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

value.

6) Adjust 𝑄𝑒𝑥𝑝 until 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑒𝑥𝑝

becomes equal to the 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

value. Note that 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑒𝑥𝑝

is

not read directly, so 𝑄𝑒𝑥𝑝 must be adjusted iteratively until (Pgauge – ΔPconduit) =

𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

. Note that ΔPconduit is also a function of 𝑄𝑒𝑥𝑝.

CALCULATIONS IN THE LAB:

3

7) Process the experimental data and compare them with straight tube model and coiled tube

model calculations.

8) Calculate exponential values (x) for 𝑄 = 𝑎 × 𝐷𝑥 from the plot of Q vs. D at a given

pressure drop (𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑒𝑥𝑝 = 𝑃𝑡𝑢𝑏𝑖𝑛𝑔

𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡) and compare the experimental results with the

straight and coiled pipe models while considering statistical significances.

THEORY

BACKGROUND

There are two basic problems that are encountered in the industry dealing with fluid flow

mechanics -- determining the pressure drop at a given flow rate and determining the flow rate at

a given pressure drop. In the first case, when the flow rate is given, the Reynolds number may

be directly determined to classify the flow regime so that the appropriate relations between the

Fanning friction factor, f, and Reynolds number, Re, can be used. In the second case, the

velocity is unknown, and the Reynolds number and flow regime cannot be immediately

determined. In this case, it is necessary to assume the flow regime, apply the necessary

calculations, and verify the Re afterwards to determine if the equations used are applicable.

Symbols used for the variables are shown in the following table:

Variables associated with flow in closed conduits

Variable Symbol Dimension

pressure drop ΔP mass/(length*time2)

Fluid velocity v length/time

Volumetric flow rate Q length3/time

conduit diameter D length

conduit length L length

conduit roughness length

Fluid viscosity mass/(length*time)

Fluid density mass/length3

4

ADDITIONAL THEORY TOPICS: (These are important learning points for prelab, prelab quiz,

conducting the experiment and for writing the report. Please download the electronic reserve

materials for this lab and review. Also make sure to watch the video.)

Reynold number, Re (laminar vs turbulent flows)

Fanning friction factor

(1) Bernoulli equation without friction and then with skin friction (hfs) [neglect the kinetic

energy correction factors – these are minor]

(2) relationship between skin friction parameters in a straight pipe Fanning friction factor

as a function of pressure difference, pipe diameter & length, fluid velocity (length/time)

and density

(3) the Bernoulli equation with the skin friction term substituted in and no velocity change

D

LfVPhg

22

(4) The Bernoulli equation when gravity is neglected (no or negligible elevation change) and

no velocity change.

Friction factor parameter in a straight pipe from Hagen-Poiseuille equation in the laminar flow

regime (friction factor equation as a function of Reynold’s number)

Effects of roughness on the friction parameter in the turbulent flow regime

Friction factor chart

Empirical equation for the friction factor for a smooth pipe in the turbulent flow regime as a

function of Reynold’s number – use a simpler single-term equation – there are many

correlations. McCabe, Smith, and Harriott has one, Perry’s handbook has another called the

Blasius Equation.

Pressure drop across fitting and valves

Dean effect and critical Reynolds number for the coiled tubing

Effect of tube coiling on friction factor (Perry’s handbook section 6-18)

Student’s t-test (you can find and learn this subject from internet and examples on ANGEL)

They can be found in:

5

1. McCabe, Smith, & Harriott, Unit Operations of Chemical Engineering (end of chapter 4 and

champter 5)

In 7th

Edition: pp 86-126 (TP155.7.M3 2005)

In 6th

Edition: pp. 95-113 (TP155.7.M3 2001)

In 5th

Edition: pp 70-110 (TP155.7.M393 1993)

In 4th

Edition: pp 61-97 (TP155.7.M393 1985)

2. Perry’s Handbook, 7th

edition

3. S. Ali, Fluid Dynamics Research 28, 295–310 (2001) [on ANGEL]

PRE-LAB QUESTIONS (to be completed before coming to lab)

Note: The theoretical calculations involved in determining the flow rates for the three tubing

sizes are based on the assumption that water behaves as a nearly incompressible Newtonian

fluid, in which the physical properties may be estimated as ρ = 1 gm/cm3 and μ = 0.01 poise for

the observed water temperature range of 32°F - 60°F. All of the theoretically calculated results

correspond to the pressure drop across the 50 ft lengths of “tubing only”. However, preceding

elbows and valves introduce a ΔP in addition to the 50 ft of tubing. Therefore, when setting up

the pressure gauge for the flow measurement, you must account for the pressure drop through the

elbows and valves for the corresponding flow rates. The pressure drops through the valves and

elbows for given flow rates can be found in Appendix B. This is an extremely important detail

to keep in mind. A flow rate of 4.5 gal/min is assumed for the ½ in tubing. The following

questions help you to understand the governing principles and how to set up the experiment and

handle data.

1. For flow through a horizontal pipe or tube (no elevation change) with constant diameter D

and length L,

a) What is the pressure drop, ΔP, if the friction factor, f, is zero (no friction loss)?

ΔP<0 , ΔP=0, or ΔP>0

b) What is the pressure drop if f > 0? Justify your answer.

6

2. For the same length and diameter of tube , with the same flow rate, would the friction factor

be larger for a straight tube or a coiled tube? Why?

3.

ΔPh is the pressure change due to elevation change, ΔPconduit is the pressure drop due to valves

and elbows and fittings, and ΔPfriction is the pressure loss due to friction in the tube (which is

denoted as ps in McCabe, Smith, & Harriott book). In the figure, the thick line is the tube

part of interest.

a) If ΔPfriction = 20 psi and ΔPh = 4 psi, what is the pressure at point Ptubing? Write the

balance equation for ΔPfriction, ΔPh and ΔPtubing [Ptubing is the applied pressure through

the tube, which you will be using in the following theoretical calculations.]

b) If ΔPconduit= 12 psi, what is the pressure gauge value (Pgauge) that you should read to

get ΔPfriction = 20 psi. Write the balance equation for Pgauge, ΔPconduit, ΔPh and ΔPfriction.

The overall procedure of this experiment is described in the video lecture (on Angel). Briefly,

you will perform the following 2 experiments.

1) Set Q to predicted value and measure Ptubing

You will set Q to the value determined from the straight pipe model (for each tubing size) and

record the resulting Pgauge. You will then calculate the corresponding Ptubing and compare it to the

predicted straight model and coiled model Ptubing.

2) Set Ptubing and measure Q.

You will do the reverse experiment. You will set Ptubing to the straight model predicted value.

ΔPconduit

= 12 psi

Pgauge

ΔPfriction = 20 psi

ΔPh =

4 psi

Flow meter

Pexit=0 psig

Ptubing

Do not copy

The right-side (boxed with dashed line) is

the system you should consider in

theoretical calculation:

Pfriction = pressure due to frictional loss in

the 50ft tube.

Ptubing = head pressure applied to the tube.

Ph = pressure due to the elevation change

between the entrance and exit of the tube.

Pgauge = pressure you need to

know or will measure during

the experiment.

Dcoil = 8”

7

You will then read the flow rate that gives you this Ptubing. However, you cannot read Ptubing

directly; instead, you can set Q and measure Pgauge. Ptubing is then calculated using ΔPconduit at the

set flow rate (from the chart in the Appendix B). Thus, you need to know a rough estimate of the

flow rate that will give the target Ptubing value. You will then iterate through different flow rates

until you obtain a Ptubing that matches the target straight model predicted Ptubing. Note that

ΔPconduit is dependent on flow rate. The following pre-lab questions guide you through the

necessary calculations.

4. Write an equation for the skin friction loss in pipes that relates ΔPfriction, friction factor (f),

velocity (V), pipe length (L), pipe diameter (D), and density (ρ).

5. The friction factor (f) can often be estimated using empirical equations. Find friction factor

estimation equations for laminar flow and turbulent straight pipe flow. Note: pick an

equation that has a single term (i.e. no addition or subtraction).

6. How does the skin friction factor (f) vary with the fluid velocity (V) or Reynolds number

(Re)? Sketch a plot of log(f) vs log (V) or log(f) vs log (Re). Mark the different fluid flow

regimes and the (approximate) slopes of the lines.

7. Use Excel (using the “Solver” function), Mathematica (“FindRoot” command), or any other

program (you can use Matlab or Mathcad) to simultaneously solve three equations. Note that

debugging help is most easily available for Excel format work.

(1) the Bernoulli equation applicable to the 50 ft tube (thick line part in figure for #3) [It

should include the pressure drop (Ptubing), elevation change (h), and skin friction factor

(f)].

(2) the friction factor (f) equation for turbulent flow.

(3) the Reynold number (Re) equation.

Note that lbm (pound mass) and lbf (pound force) are different quantities.

Set up these calculations so that you can easily repeat them a number of times.

You need these calculations to answer #8 and #9. The calculation results of questions 8 and 9

should be summarized in Table 1. Refer to the diagram in question #3 for a schematic of the

system (the pressure values in this diagram should not be used) and Appendix B for the pressure

loss due to valves and elbows (conduit). Bring your program to the lab.

8

8. For the ½ inch tube:

Determine whether the flow rate is laminar or turbulent for a flow rate of 4.5 gpm.

Determine the theoretical pressure drop through the tubing, 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

(in psi), for a flow

rate of 4.5 gpm and h = 5 ft.

9. Now, we are repeating the experiment with ¼ inch and 4mm tubing, instead of ½ inch tube.

Calculate the velocity and flow rate using the same 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

at the entrance of the tube

as calculated for the ½ inch tubing.

Determine whether the flow rate is laminar or turbulent for the flow rates found above.

Adjust your previous calculation if the Reynold’s number is not in the regime you

assumed.

Table 1. Theoretically calculated pressures and flow rates in the experimental setup for a

specific 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

utililizing a straight pipe model

10. The fluid flow (Q) through a pipe depends on the tubing diameter (D) if Ptubing, elevation

change, and tube length are held constant. Derive the relationship Q = f(D) for the straight

pipe model (L = 50 ft, no valves or fittings). It should take the form 𝑄 = 𝑎 × 𝐷𝑥 where a

and x are constant. Determine the theoretical x value for turbulent flow. (you do not need to

find a value for a)

11. Explain the Dean Effect observed in coiled tube flow.

12. The friction factor (f) can often be estimated using empirical equations. Find friction factor

estimation equations for laminar and turbulent coiled pipe flow (Dcoil= 8 inches). Use

D

Predicted

Qstraight

(gpm)

Re

Friction factor

f

straight tube

Theoretical

Pfriction

(psi)

𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

(psi)

Estimated

Pconduit

(psi)

Predicted

Pgauge

(psi)

0.5 inch 4.5

0.25 inch Same as

above

Same as

above

4mm

(using turbulent flow

equation)

Same as

above

Same as

above

(using laminar flow

equation)

Same as

above

Same as

above

9

Perry’s Handbook Section 6-18 and associated text and/or the on-line video (all found on

ANGEL).

13. What is the critical Reynold’s number (definition)? What is the critical Reynold’s number

for straight pipe flow and for coiled pipe flow?

14. What are the objectives for this experiment?

15. Explain what data you will collect, how you will collect it, and what you will use it for.

DATA PROCESSING PREPARATION (Excel spreadsheet to be used for data processing

in the lab must be prepared before coming to the lab for the experiment)

1. Prepare a data processing excel spreadsheet to be used for the data processing in the lab. All

calculations will be done in excel.

a) Prepare a header section with your names and group ID.

b) Prepare a units section where you show unit conversions. Make it so that you can

reference the appropriate cell when a certain conversion is needed in later calculations.

Refer to the pre-lab calculations for the unit conversions used.

c) Show all needed formulas from the pre-lab calculations clearly explained in text boxes

d) When using your spreadsheet in the lab, make sure that you use cell references when

using previously calculated values or constants (instead of copying them); this will

update the entire spreadsheet if/when a mistake is found early in the spreadsheet. (no

work required for 1.d)

2. Using the calculated flow rates for each diameter tubing for the straight pipe model, calculate

the tubing pressure drop for coiled pipe flow, and fill out table 2. Make sure to check the

flow regime and adjust the model if necessary. Note that the only difference with the straight

pipe model calculations is in the friction factor.

Table 2. Theoretically calculated pressures for set flow rates in the experimental setup

utililizing a coiled pipe model. The set flow rates match the calculated flow rates for the

straight pipe model with a specified straight pipe 𝑃𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

.

10

3. Repeat the coiled tube calculations, but this time hold 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑐𝑜𝑖𝑙𝑒𝑑 constant to the same value

used in the straight tube model calculations. Again, check the flow regime and adjust models

if necessary. Fill out Table 3.

Table 3. Theoretically calculated pressures and flow rates in the experimental setup for a

specific 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑐𝑜𝑖𝑙𝑒𝑑 utililizing a coiled pipe model

4. Set up tables for data collection.

a. Part 1: you will set Q and measure Pgauge. You will need to calculate Pconduit from

Q and appendix data (use an equation in your spreadsheet so you can repeat the

D

Predicted

Qstraight

(gpm)

Re Crictical

Re

Friction factor

f

coiled tube

Pfriction

(psi)

𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑐𝑜𝑖𝑙𝑒𝑑

(psi)

Estimated

Pconduit

(psi)

Predicted

Pgauge

(psi)

0.5 inch 4.5

0.25 inch From Table

1

4mm From Table

1

(using turbulent flow

equation)

(using laminar flow

equation, if necessary)

D

Predicted

Qcoiled

(gpm)

Re Critical

Re

Friction factor

f

straight tube

Theoretical

Pfriction

(psi)

𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑐𝑜𝑖𝑙𝑒𝑑

(psi)

Estimated

Pconduit

(psi)

Predicted

Pgauge

(psi)

0.5 inch

From

Table 1

0.25 inch

Same as

above

Same as

above

4mm

(using turbulent flow

equation)

Same as

above

Same as

above

(using laminar flow

equation)

Same as

above

Same as

above

11

calculation easily), then calculate Ptubing. Test your spreadsheet by using Q = 5

gal/min and Pgauge = 19 psi.

b. Part 2: you will set Pgauge and measure Q. You will need to calculate Ptubing as in

part 1. You will adjust Pgauge until P tubing matches the theoretical. You will

record every iteration.

DATA PROCESSING

Overview

Part 1. Let’s check if the flow rate that you calculated using the straight tube model works well.

Adjust Pgauge until the actual flow rate is the same as the predicted Qstraight in Table 1. Record

the experimental Pgauge value. Repeat this step for D = 0.5 inch, 0.25 inch, and 4 mm.

Part 2. You may see discrepancy between the theoretical prediction and the experimental data.

Could that be due to the tube coiling? Adjust Q until the (PgaugePconduit) value becomes

equal to 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑒𝑡 . Record Qexp for D = 0.5 inch, 0.25 inch, and 4 mm. Note that Pconduit

changes each time the flow rate changes.

Calculations

1. Find Pconduit from the chart given in the Appendix and calculate the actual 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑎𝑐𝑡𝑢𝑎𝑙 . Fill

out Table 4. (you will have 3 data points for each condition)

Table 4. Calculating 𝐏𝐭𝐮𝐛𝐢𝐧𝐠𝐚𝐜𝐭𝐮𝐚𝐥 when Q is set to the predicted Qstraight.

Tube

diameter Qstraight

(from pre-lab)

Experimental

Pgauge

Experimental

Pconduit 𝑃𝑡𝑢𝑏𝑖𝑛𝑔

𝑎𝑐𝑡𝑢𝑎𝑙

0.5 inch 4.5 gpm

0.25inch

4 mm

12

2. Calculate the average 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑎𝑐𝑡𝑢𝑎𝑙 and the standard deviation for each tubing size.

3. Fill out Table 5 and make a graph of 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

, 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑐𝑜𝑖𝑙𝑒𝑑 , and 𝑃𝑡𝑢𝑏𝑖𝑛𝑔

𝑎𝑐𝑡𝑢𝑎𝑙 versus tube

diameter (D) showing all 3 cases.

Table 5. Comparison of predicted Ptubingstraight

and Ptubingcoiled to 𝑃𝑡𝑢𝑏𝑖𝑛𝑔

𝑎𝑐𝑡𝑢𝑎𝑙 when Q is set to the

predicted value for the straight pipe.

Tube

diameter

Predicted

Qstraight (from pre-lab)

𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

(from pre-lab)

𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑐𝑜𝑖𝑙𝑒𝑑

(from lab-prep)

𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑎𝑐𝑡𝑢𝑎𝑙

𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑎𝑐𝑡𝑢𝑎𝑙

Standard

Deviation

0.5 inch

0.25inch

4 mm

4. Now let’s look at the data where you set the flow rate to match a certain pressure drop.

You adjusted the flow rate, Qexp, until you got 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑒𝑥𝑝

= 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

in the lab.

a. Calculate the average Q and standard deviation for each diameter studied.

b. Make a table comparing the actual Q values with the predicted Q values for

straight and coiled tubing. Fill out Table 6.

Table 6. Comparing flow rate and Reynolds numbers

Tube

diameter

𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑒𝑥𝑝

= 𝑃𝑡𝑢𝑏𝑖𝑛𝑔𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡

= (write your theoretical value) Experimental

Straight tube model Coiled tube model

Qstraight Restraight Qcoiled Recoil Recritical QExp S.D.

QExp ReExp

1.5 inch

0.25inch

4 mm

13

5. Using the data from Table 6, calculate the exponent x of the model

𝑄 = 𝑎 × 𝐷𝑥

for the experimentally measured data as well as for the theoretical values predicted for

the straight and coiled tubing. Make sure to calculate the error on x. The error can be

calculated in Excel. To do so, you can linearize the data by taking logarithm: i.e. plotting

lnQ versus lnD. Then, you can perform statistical analysis on the linearized data and

obtain the error of the slope. Determine the statistical significance of the difference

between the two models and of each model with the experimental data by performing a t-

test. Information on statistical analysis can be found on the class ANGEL site.

KEY POINTS FOR REPORT

If report requires a theory section, do further research on subjects included in “relevant theory”

section on page 3.

1. Include some industrial examples for which the material studied in this experiment is

applicable.

2. Include the process diagram or schematics of the fluid flow experimental system (identify

essential parts and connect them in a simple and easy-to-follow way). Place this in the

appendix or experimental section of the report, as appropriate.

3. [from part 1] Consider the plot of experimental Ptubing and theoretical Ptubing calculated

with the straight and coil tube models for the ½”, ¼”, and 4mm diameter tubing. Discuss

any trends or differences that you observe.

4. [from part 2] Consider the plot of the experimental Q values and Qtheoretical (calculated for

both straight and coiled tubes) vs. the tube diameter at constant Ptubing. Discuss why the

deviation between the straight and coiled models is larger at higher tube diameters.

Which model, straight or coiled, would you recommend for the experimental set-up?

Why?

5. Compare the experimental Reynolds number with the theoretical values calculated for

both straight and coiled tubing as well as the critical Reynolds number for the transition

in the coiled tubing. (all comparisons based on the same ΔPtubing)

14

6. Discuss how the exponent x of the experimental data compares with the theoretical

values. Discuss the statistical significance of the differences from the theoretical models.

Based on the x values, which model would you recommend? If your recommendation of

models is different here from Q#3, reconcile the difference.

15

EXPERIMENTAL SETUP

The following figure is a picture of the fluid mechanics apparatus. The system consists of a

pressure gauge to measure the total pressure of the system, three valves to route the flow through

a specific tube, a rotameter to measure the flow rate in the system, and three sizes (1/2 in, ¼ in,

and 4mm) of 50 ft tubing, which are arranged in an 8 in diameter coil.

Figure 1: Fluid Mechanics System

Pressure Gauge

Rotameter

Tubing coil

½ in valve

¼ in valve

4mm valve

Do not copy

Elevation

change of

tubing

air valve

16

Using this setup, the pressure drop for a flow rate of 4.5 gal/min through the ½ inch tubing is

measured. Compare this experimental value to the theoretical pressure drop through the 50 ft of

tubing. Make sure to account for the pressure drop in the elbows and valves. Then measure the

flow rate achieved in the smaller tubing with the same theoretical pressure drop over the tubing,

again making sure to account for the pressure drop in the elbows and valves, and compare the

flow rates to the theoretically calculated values.

Warnings:

After adjusting the rotameter, it takes a minute or two for the float to settle into

position. Therefore, after making flow adjustments, wait for the float to attain its

position before taking flow and pressure readings.

Rotameter readings are generally taken at the top of the widest part of the float.

The rotameter is a flow measuring/regulating device and should not be used to stop

flow completely. To stop flow completely, use the ball valve upstream. Also note

that the lowest flow rate on the rotameter is not zero.

All of the valves associated with the tubing system must be completely opened. If

the valves are only partially opened this will introduce a restriction in your system

and produce a larger pressure drop than expected, resulting in poor experimental

data.

17

EXPERIMENTAL PROCEDURE

1.) Observe the piping system on the blue mounting board. Close the three yellow ball

valves to the off position. Also, make sure that the three tee valve knobs have the

pointed end downward so that the flow is directed to the tubing coil.

2.) Open the main water valve on the back wall by turning it a ¼ turn and ensure that it is

fully opened.

3.) Open the yellow ball valve for the ½ in tubing system.

4.) Twist the rotameter dial to the left to allow the water to flow through the 0.5 inch tubing.

Make sure that the end of the tubing is in the drain.

5.) [part 1 of data processing.] Set the flowrate at 4.5 gpm for 0.5 inch tubing and record

Pgauge. The experimental value might be different from the theoretically calculated Pgauge

in Table 1. Reduce the flow rate and again bring it back up to 4.5 gpm in order to obtain

a total of 3 data points at 4.5 gpm.

6.) Repeat step 5.) for the 0.25 inch and 4 mm tubing using the predicted Qstraight from Table

1.

Note that the rotameter cannot read flow rates below 0.5 gpm. A graduated cylinder and

stopwatch must be used to determine the flow rate for 4 mm tubing.

7.) [part 2 of data processing] Adjust the flow on the rotameter until Pgauge matches your

theoretical Pgauge from Table 1 and record the flow rate (Q). Calculate Pconduit from this

Q and then Ptubing. Ptubing (=Pgauge - Pconduit) Adjust the flow on the rotameter until

Ptubing becomes equal to your theoretical Ptubing in Table 1. Record the experimental Q

value that gives the theoretical Ptubing. Note that Pconduit varies with the flow rate and

your flowrate may not be the same as Qtheoretical in Table 1. It is likely that ΔPconduit will

also vary from the ΔPconduit in Table 1. You will need to use trial and error for several

iterations from the theoretical starting point.

8.) Reduce the flow rate and redo step 7.) in order to obtain 3 data points.

9.) Reduce flow to less than 0.5 gpm using the rotameter. Open the yellow ball valve for

the next tubing size to be studied before closing the yellow ball valve for the ½ in tubing.

18

10.) Repeat steps 7.) - 9.) for both 0.25 inch and 4 mm tubing using the predicted Ptubing from

Table 1

Note than the rotameter is incapable of reading low flow rate. A graduated cylinder and

stopwatch must be used to determine the flow rate for 4 mm tubing.

11.) Reduce the flow rate to <0.5 gpm using the rotameter, and close the main water line.

19

REFERENCES

1Welty, Wicks, Wilson, and Rorrer. Fundamentals of Momentum, Heat, and Mass Transfer. 4

th

ed. John Wiley & Sons, Inc. New York, 2001.

2Perry. Perry’s Chemical Engineering Handbook. 7

th ed. McGraw-Hill, New York, 1997.

3Bird, Stewart, and Lightfoot. Transport Phenomena. 2

nd ed. John Wiley& Sons Inc. New

York, 2002.

4McCabe, Smith, and Harriott. Unit Operations of Chemical Engineering. 7

th ed. McGraw-Hill,

New York, 2005.

20

Ap

pen

dix

A:

Fan

nin

g F

rict

ion

Fact

or

Ch

art

21

APPENDIX B: Pressure drops through elbows and valves (all combined in experimental set-up)

1/2 inch ID tube 1/4 inch ID tube 4 mm ID tube

Q (gpm) ΔP (psig) Q (gpm) ΔP (psig) Q (gpm) ΔP (psig)

0.50 0.0 0.50 0.0 0.50 6.0

1.00 0.0 1.00 1.0 1.00 20.0

1.50 0.0 1.50 4.0 1.50 55.0

2.00 1.0 2.00 7.0 2.00 NA

2.50 2.0 2.50 11.0 2.50 NA

3.00 3.0 3.00 15.0 3.00 NA

3.50 4.0 3.50 20.0 3.50 NA

4.00 6.0 4.00 28.0 4.00 NA

4.50 7.0 4.50 34.0 4.50 NA

5.00 8.0 4.70 37.0 5.00 NA

The equations given in the graphs are the best fit. You can use these equations to calculate the

pressure drop at the flow rate that you measured in the lab.

y = 1.3333x3 - 18x2 + 82.667x - 122

R² = 1

3

4

5

6

7

8

9

3 3.5 4 4.5 5 5.5

pre

ssu

re d

rop

(p

sig)

flow rate (gpm)

1/2" ID tube

y = 4.0x2 - 4.0x + 1.0 R² = 1.0

0

1

2

3

4

5

0 0.5 1 1.5 2

pre

ssu

re d

rop

(p

sig)

flow rate (gpm)

1/4" ID tube

y = 17.333x3 - 10x2 + 12.667x - 3E-12

R² = 1

0

10

20

30

40

50

60

0 0.5 1 1.5

pre

ssu

re d

rop

(p

sig)

flow rate (gpm)

4mm ID tube