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MIDDLE EAST TECHNICAL UNIVERSITY

DEPARTMENT OF MECHANICAL ENGINEERING

ME 306 FLUID MECHANICS II (Section 3 – Dr. Sert)

EXPERIMENT 1

FRICTION IN PIPES AND FITTINGS

PREPARATION

In this course, you will conduct the experiments at the Fluid Mechanics Laboratory, by yourself, with little help or instruction from

the teaching assistants. You must read the lab sheet thoroughly and understand what you are expected to do (and why) for each

experiment, before coming to the lab. Data should be recorded into the “report” section at the end of this manual. After collecting

the data, 2-3 students will team up to complete the report section, which should be submitted to the assistant before leaving the lab.

For this you will have 1 hour.

1. OBJECTIVE

In this experiment, the friction factor of a pipe and the head loss coefficient of a pipe fitting will be determined for steady

incompressible air flow in a pipe.

2. THEORY

In a steady incompressible pipe flow, the irreversibilities are expressed in terms of a head loss, or a drop in hydraulic grade line.

Head loss is proportional to the velocity head, 𝑉2/(2𝑔). A head loss coefficient k can be defined for each pipe element in the flow.

In general, these losses, or irreversibilities, can be represented as:

ℎ𝑓 = 𝑘𝑉2

2𝑔=

Δ𝑝

𝜌𝑎𝑖𝑟𝑔

(1)

in the absence of elevation change, where Δ𝑝 is the static pressure drop through the element in Pa, 𝑉 is the average flow velocity

through the section in m/s, 𝑔 is the gravitational acceleration in m/s2 (𝑔 = 9.81 m/s2), ℎ𝑓 is the head loss in m, 𝑘 is the head loss

coefficient, 𝜌𝑎𝑖𝑟 is the density of air in kg/m3, which is the working fluid in this experiment.

The volumetric flow rate through a pipe system can be determined by using an orifice meter as

𝑄 = 𝐶0(Δℎ)1/2 (2)

where 𝑄 is the volumetric flow rate in m3/s, 𝐶0 is the calibration constant of the orifice meter in m5/2/s, Δℎ is the difference of the

deflection of the alcohol columns at the inlet and the outlet of the orifice plate, measuring the pressure drop across the orifice meter.

The average velocity through a section having a cross-sectional area of 𝐴 can be found as

𝑉 = 𝑄/𝐴 (3)

The static pressure drop in Pa across a conduit (a pipe section, a fitting, etc.) can be obtained by using an alcohol manometer

connected to the inlet and outlet of the conduit as

Δ𝑝 = 𝜌𝑎𝑙𝑐𝑜ℎ𝑜𝑙𝑔Δℎ (4)

where 𝜌𝑎𝑙𝑐𝑜ℎ𝑜𝑙 is the density of alcohol in kg/m3, Δℎ is the difference of the deflection of the alcohol columns between the inlet and

the outlet of the conduit.

Substituting Equation (4) into Equation (1), the head loss coefficient can be obtained as

2

𝑘 =2𝑔

𝑉2

𝜌𝑎𝑙𝑐𝑜ℎ𝑜𝑙Δℎ

𝜌𝑎𝑖𝑟

(5)

The value of 𝑘 is dependent on the Reynolds number. For pipes, the head loss coefficient, 𝑘, is dependent on the friction factor as:

𝑘 = 𝑓𝐿

𝐷

(6)

where 𝑓 is the Darcy’s friction factor, 𝐿 is the length of the pipe and 𝐷 is the diameter of the pipe. Substituting Equation (6) into

Equation (5), the friction factor for a pipe section can be obtained as

𝑓 = 𝑘𝐷

𝐿=

𝐷

𝐿

2𝑔

𝑉2

𝜌𝑎𝑙𝑐𝑜ℎ𝑜𝑙Δℎ

𝜌𝑎𝑖𝑟

(7)

3. EXPERIMENTAL SETUP

The schematic of the experimental set-up is presented in Figure 1. The various pipe elements and sections in the schematic are

presented in Table 1. The diameters of the pipes are constant; the pipe elements may have changing cross-sections (e.g. sudden

expansion/contraction). The photograph of the experimental set-up is presented in Figure 2.

Figure 1 Schematic drawing of the experimental set-up

Table 1 Pipe elements/sections in the piping system

Tap # Element/Section

1 inlet

2 outlet

2-3 long pipe section, 𝐿𝑝𝑖𝑝𝑒 = 2.50 m

Long pipe

Venturi meter Sudden expansion-contraction

Bend

Orifice meter

Blower

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4 11 10 23 22 21

2

20

19

18

17

16

15 14

13

12

1

5

6 9

7 8

3

3-4 U-turn, 𝐿𝑈−𝑡𝑢𝑟𝑛 = 0.31 m

5-9 Orifice meter (𝐷, 𝐷/2 tapping - to be used in this experiment)

6-9 Orifice meter (corner tapping - not used in this experiment)

7-8 Orifice meter (flange tapping - not used in this experiment)

10-11 Venturimeter

13-14 Bend

15-16 Valve

16-17 Bend

17-18-19 T-bend

19-20 Long radius elbow ( 𝑟/𝐷 = 6 )

21-22 Sudden expansion ( 𝐷1/𝐷2 = 1/1.625 )

22-23 Sudden contraction (𝐷1/𝐷2 = 1.625/1 )

1-12-13 T-bend

20-21 Bend plus pipe ( 𝐿𝑏𝑒𝑛𝑑 = 0.15 m, 𝐿𝑝𝑖𝑝𝑒 = 0.80 m )

4. PROCEDURE

(i) Record the ambient temperature (your lab supervisor will direct you to the wall thermometer). The ambient pressure is to be

taken as 101.3 kPa (standard atmospheric pressure).

(ii) Determine the density and kinematic viscosity of air from the table provided in the lab, based on the standard atmospheric

pressure and the ambient temperature (interpolate if necessary)

(iii) Open the flow rate adjuster valve (shown in Figure 2) fully. Also make sure that the inlet throttle of the blower is partially open

(so that air can be sucked in). Ask your lab supervisor to start the air blower.

(iv) Record the following manometer deflections (ℎ)

a) across the long pipe section (2 - 3),

b) across a hydraulic element (pipe element) indicated by your lab supervisor,

c) across the orifice meter (5 - 9).

Note that the manometer columns are labeled in accordance with the labeling of pipe sections.

(v) To change the flow rate, gradually close the flow rate adjuster valve to the desired position.

(vi) Repeat steps (iv) and (v) so that you have data at a total of five different flow rates. To obtain an “even” distribution of the five

flow rate values, close the valve (when changing the flow rate) until the manometer deflection across the orifice meter drops by an

amount approximately equal to the maximum deflection (the first data point for the fully open valve) divided by 4. That is, if the

first orifice reading is 𝛥ℎ1, then your next reading should be taken approximately when the deflection drops to 𝛥ℎ2 = 𝛥ℎ1 −

(𝛥ℎ1/4), the next at 𝛥ℎ3 = 𝛥ℎ2 − (𝛥ℎ1/4), and so on.

(vii) When you are finished, ask your lab supervisor to stop the blower.

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Figure 2 The experimental set-up at the Fluid Mechanics Laboratory

5. CALCULATIONS AND PLOTS

Use the provided report sheets attached at the back to prepare your lab report.

(i) Determine the air flow rate using the orifice meter pressure drop data for all five data points. Make sure that the manometer

reading is in millimeters in your calculations.

(ii) Determine the average velocity in the pipe at each flow rate. Use the provided pipe diameter (on the data sheet of the report). In

your calculations, the pipe diameter should be in meters.

(iii) Obtain the Reynolds numbers at each flow rate.

(iv) Determine the head loss coefficient and friction factor for the straight long pipe (section 2-3) for five different flow rates. Make

sure that the manometer reading is in millimeters and the velocity in m/s, in your calculations.

(v) Plot pipe friction factor versus Reynolds number on the provided graph paper. Draw each axis with a suitable scale. Don’t forget

to label these axes and specify the appropriate units. Mark your results on the graph paper and draw the “best” line/curve.

(vi) Determine the head loss coefficient of the chosen hydraulic element for five different flow rates. Make sure that the manometer

reading is in millimeters and the velocity in m/s, in your calculations.

(vii) Plot head loss coefficient for the hydraulic element versus Reynolds number on the provided graph paper. Draw each axis with

a suitable scale. Don’t forget to label these axes and specify the appropriate units. Mark your results on the graph paper and draw

the best line/curve.

6. DISCUSSION

At the end of your report, you will add a Discussion section on a separate sheet of paper, in which you will discuss your results.

Specifically you should answer the below questions.

(i) What is the flow regime in the experiment (if there is more than one, indicate which results correspond to which flow regime)?

(ii) Are the results in the graphs as expected? Discuss with respect to the type of element (the pipe section and the specific hydraulic

element) and the flow regime. Refer to the Moody Chart in your discussion.

manometers

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Names of the Students:

ID Numbers:

Lab. Group: Date:

Lab. Supervisor: Course Section:

ME 306 FLUID MECHANICS II

EXPERIMENT 1: FRICTION IN PIPES AND FITTINGS

EXPERIMENT REPORT

1. EXPERIMENTAL DATA

Air temperature (𝐶) Diameter of the pipe, 𝐷 (m) 0.0508

Air pressure (kPa) 101.3 Orifice meter constant, 𝐶𝑜 , m5/2/s 0.07

Density of air, 𝜌𝑎𝑖𝑟 (kg/m3) Length of the long pipe, 𝐿 (m) 2.50

Kinematic viscosity of air, 𝜈𝑎𝑖𝑟 (m2/s) Density of alcohol, 𝜌𝑎𝑙𝑐𝑜ℎ𝑜𝑙 (kg/m3) 804

1 2 3 4 5

Pressure drop through the orifice meter (5-9) h in m of

alcohol column (mm)

Pressure drop through the long pipe (2-3)

h in m of alcohol column (mm)

Pressure drop through the hydraulic element h in m of

alcohol column (mm)

Hydraulic element section: ____________

2. SAMPLE CALCULATIONS (For the maximum flow rate only)

2.1. Volumetric Flow Rate and Average Velocity

𝑄1 = m3 /s

𝑉1 = m/s

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2.2. Reynolds Number

(𝑅𝑒𝐷)1 = 𝑉1𝐷1 𝜈1 =⁄

2.3. Head Loss Coefficient for the Straight Long Pipe

2.4. Friction Factor for the Straight Long Pipe

(𝑓2−3)1 =

2.5. Head Loss Coefficient for the Hydraulic Element

𝑘1 =

3. RESULTS

1 2 3 4 5

Volumetric flow rate, 𝑄 (m3/s)

Average velocity, 𝑉 (m/s)

Reynolds number, 𝑅𝑒

Head loss coefficient for the long pipe, 𝑘2−3

Friction factor for the long pipe, 𝑓

Head loss coefficient for the hydraulic element , 𝑘 (hydraulic

element section:___________)

(𝑘2−3)1 =

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Figure 3.1 Pipe friction factor versus Reynolds number

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Figure 3.2 Head loss coefficient for the hydraulic element section ( __ ) versus Reynolds number