Friction Loss

FRICTION LOSS ALONG A PIPE OBJECTIVE:

To observe the head loss that occurs in a pipe due to frictional resistance, hydraulic gradient, and the relationship between head loss and the Reynold’s number.

PROCEDURE:

See attached experimental procedure handout.

RESULTS:

Show trial-by-trial data for both the mercury and water friction loss experiments in two different tables. Include the flow rate, velocity, hydraulic gradient, Reynold’s number, friction factor, and dynamic viscosity for each of the trials in these tables. Also in a final table, compare the Reynold’s number, R, friction factor, f, average absolute viscosity (average µ’s in the laminar region), µavg, Laminar slope, and Turbulent slope. The theoretical absolute viscosity, µavg, can be found by using an average temperature from the laminar region and interpolating from the given chart.

CALCULATIONS: Show one sample calculation for each step, as outlined in the attached calculations section. GRAPHS:

Plot the velocity versus hydraulic gradient on 3-cycle log-log paper or in a spreadsheet (change both axes to be logarithmic). Indicate the transition point between the laminar and the turbulent flow regions.

DISCUSSION:

1.

Compare your critical Reynold’s number with the theoretical value at which the transition from laminar to turbulent flow occurs. What are the most significant reasons for the differences between the two?

2.

Why is it necessary to multiply the differential heads recorded from the mercury-manometer meter by 12.6?

3.

What are the two types of energy losses typically associated with pipe flow? What determines which one will predominate as the most significant loss of head incurred by a fluid flowing along a pipe?

4.

What is the hydraulic gradient and how is it related to the energy gradient?

1

EXPERIMENTAL PROCEDURE

1.

Level the apparatus on the bench so the manometer stand is vertical. (Assume it is level when we start the lab.)

2.

Check to see what manometer is turned on (mercury or water?). The water or mercury manometer is introduced into the circuit by directing the lever on the tap towards the relevant connecting pipe. Select the water manometer on first.

3.

Turn on the flow rate in your tub. There is a small knob on the apparatus used to adjust the flow rate. Open this supply valve to allow water to enter the apparatus.

4.

Turn the supply valve off. The levels in the two limbs of the inverted U-tube should settle on the same value. If not, check that the flow from the tub has not stopped, or that there are no air bubbles in the system. If this does not work, open the bleed valves slightly to release pressure (please see your TA before you do this).

5.

Fully open the needle valve to obtain the maximum differential head (approximately 400 mm).

6.

Find the flow rate using the volume-time method by timing the collection of a suitable amount of water in a graduated cylinder.

7.

Record the temperature of the water filling up the graduated cylinder.

8.

Record the pressure heads.

9.

Repeat steps 5, 6, and 8 while decreasing the difference in manometer readings by 50 mm down to 300 mm, then by 40 mm down to 180 mm, then by 20 mm down to 100 mm, and then by 10 mm down to 0 mm.

10.

Switch to the mercury manometer. Increase the flow until a pressure difference of 10 mm is obtained. Again, measure flow rate and temperature.

11.

Repeat step 10 (except only measure temperature for the first trial) increasing the difference by 10 mm up to 60 mm, then by 20 mm up to 200 mm, and then 30 mm up to the maximum difference possible.

2

CALCULATIONS

GIVEN: • • • • •

1 m3 = 1*106 ml Pipe is made of brass Length of pipe between piezometer tappings, dl = 524 mm Nominal Diameter of the pipe, D = 0.003 m Cross-sectional area of the pipe, A = 7.07 ™ 10-6 m2

Water Manometer:

dh = h1-h2 Q

dl = .524 m

1.

Calculate the Hydraulic Gradient, iH2O, for the water manometer The hydraulic gradient is equal to the change in hydraulic head per unit length, and is usually a negative number as hydraulic head decreases in the direction of the flow. The hydraulic head is the sum of elevation and pressure that is measured by the manometer tube, or in other words, the driving force of the fluid flow. The hydraulic gradient can be written as: iH 2O =

dh h1 − h2 = dl 0.524m

3

Mercury:

dh

Q dl = .524m

2.

Calculate the Hydraulic Gradient, iHg, for the mercury manometer Mercury’s density is 13.6 times that of water, which must be taken into account when finding the hydraulic gradient. iHg =

3.

dh  ∆h × (13.6 − 1)  =  dl  0.524m 

Solve for the flowrate, Q, found by using the volume-time method Q=

V T

where: V = Volume of water filled in the graduated cylinder, and T = The time it takes to fill the graduated cylinder to the volume 4.

Using the continuity equation, calculate the velocity of the water through the apparatus. Q =V × A

Therefore:

V=

Q A

(Note that the inside diameter of the pipe is 0.003 m.) 5.

Plot the hydraulic gradient, i, (y-axis) versus the velocity (x-axis) on 3-cycle loglog paper or in a spreadsheet (change both axes to be logarithmic). Indicate the transition point between the laminar and the turbulent flow regions. This can be determined by finding the point on the graph where there is an abrupt change in the slope. At the transition point, the Reynold’s number should be equal to 2000 theoretically, and somewhat close to this value experimentally.

4

LAMINAR FLOW CALCULATIONS: In laminar flow, the fluid particles move in straight lines. A.

Calculate the coefficient of absolute viscosity, µ, from Poiseuille’s equation, using each value of i in the laminar region as indicated in your graph.

µ=

i × ρ × g × D2 32 × V

where: i = hydraulic gradient ρ = density (dependent on temperature so use the tables in the back of the book to find this) g = gravity = 9.81 m/s2 D = inside diameter = 0.003 m V = velocity (from step 4) B.

Average the absolute viscosity values for the laminar region, µavg

C.

Calculate a Reynold’s number for each flow rate in the laminar region.

R=

ρ ×V × D µ avg

Make sure that all Reynold’s numbers calculated are less than 2000 as this is the definition for laminar flow. If some of your flow rates are greater than 2000, then they are turbulent and your transition point is incorrectly place. Move your transition point, move the points that were greater than 2000 to your turbulent calculations, and recalculate µavg and R for your laminar flow points that are remaining. D.

Knowing that the flow is laminar under pressure in a circular pipe, the friction factor can be solved for using the following equation: f =

E.

64 R

The slope of the laminar line on the plot can also be determined using the following equation: Laminar Slope =

5

log i1 − log i2 log V1 − log V2

TURBULENT FLOW CALCULATIONS: In turbulent flow, the fluid particles follow random paths. A.

Determine the absolute viscosity, µ, of the turbulent flow region by interpolation using the values from Table 1.

Table 1: Absolute Viscosity Chart Temp. (deg C) 0 10 20 30 40

B.

µ *10-4 (Ns/m2) 17.90 13.10 10.10 8.00 6.56

Calculate a Reynold’s number for each flow rate in the turbulent region. R=

ρ ×V × D µ chart

Make sure that all Reynold’s numbers calculated are greater than 2000, as this is the definition for turbulent flow. If some of your Reynold’s numbers are less than 2000, then they are laminar and your transition point is incorrectly placed. Move your transition point, and move the points that had R < 2000 to your laminar calculations. C.

Use Darcy’s equation to calculate the friction factor at each flow rate in the turbulent flow region. f =

D.

i × D × 2× g V2

The slope of the turbulent line on the plot can also be determined using the following equation: Turbulent Slope =

6

log i1 − log i2 log V1 − log V2

COMPARE AND CONTRAST: 6.

Compare and contrast experimental with theoretical values. A.

Theoretical and experimental slopes Theoretical Laminar = 1.0 Theoretical Turbulent = 1.85

B.

Reynold’s Number, R, at the transition point Experimental versus 2000

C.

Friction factor, f, at the transition point Experimental versus Moody Diagram at R = 2000

D.

Absolute viscosity, µ Experimental versus lab handout interpolation

EXAMPLE TABLES: Table 1: Water Friction Loss Data Sheet h2 Volume Time Temp. h1 (mL) (s) (deg. C) (m) (m) 200 200 150 150 150 100 100 100 40 30

21.13 24.46 22.62 24.97 28.09 21.86 26.44 35.68 23.65 25.37

24 24 24 24 24 24 24 24 24 24

0.508 0.425 0.390 0.378 0.368 0.350 0.345 0.333 0.320 0.315

0.050 0.045 0.190 0.205 0.220 0.233 0.250 0.263 0.278 0.285

dh (m)

Q 3 (m /s)

V (m/s)

I

0.458 0.380 0.200 0.173 0.148 0.117 0.095 0.070 0.042 0.030

9.47E-06 8.18E-06 6.63E-06 6.01E-06 5.34E-06 4.57E-06 3.78E-06 2.80E-06 1.69E-06 1.18E-06

1.339 1.157 0.938 0.850 0.755 0.647 0.535 0.396 0.239 0.167

0.874 0.725 0.382 0.330 0.282 0.223 0.181 0.134 0.080 0.057

7

R

f

4424.65 0.014 3822.28 0.017 3099.90 0.021 2808.16 0.023 2496.25 0.026 2071.29 0.031 1712.49 0.037 1269.01 0.050 765.81 0.084 535.42 0.120 Uavg of Laminar Flow 2 (Ns/m )

u 2 (Ns/m ) 9.05E-04 9.05E-04 9.05E-04 9.05E-04 9.05E-04 9.49E-04 9.32E-04 9.27E-04 9.22E-04 9.42E-04 9.34E-04

Table 2: Mercury Friction Loss Data Sheet Volume Time Temp. h1 h2 (mL) (s) (deg. C) (m) (m) 110 170 220 240 300 350 400 450 500 500 550 600

22.83 22.07 22.43 21.36 23.08 24.83 23.99 23.55 23.99 22.13 22.40 23.02

24 24 24 24 24 24 24 24 24 24 24 24

0.192 0.199 0.210 0.220 0.230 0.240 0.262 0.280 0.300 0.325 0.343 0.358

0.183 0.178 0.170 0.160 0.150 0.142 0.123 0.108 0.092 0.070 0.052 0.040

dh

Q (m3/s)

V (m/s)

I

R

f

u (Ns/m2)

0.113 0.265 0.504 0.756 1.008 1.235 1.751 2.167 2.621 3.213 3.667 4.007

4.82E-06 7.70E-06 9.81E-06 1.12E-05 1.30E-05 1.41E-05 1.67E-05 1.91E-05 2.08E-05 2.26E-05 2.46E-05 2.61E-05

0.682 1.089 1.387 1.589 1.839 1.994 2.358 2.703 2.948 3.196 3.473 3.687

0.216 0.505 0.962 1.443 1.924 2.356 3.342 4.136 5.002 6.132 6.997 7.647

2252.35 3600.77 4585.03 5252.41 6076.23 6589.31 7794.32 8932.44 9742.90 10561.78 11477.92 12184.13

0.028 0.018 0.014 0.012 0.011 0.010 0.008 0.007 0.007 0.006 0.006 0.005

9.05E-04 9.05E-04 9.05E-04 9.05E-04 9.05E-04 9.05E-04 9.05E-04 9.05E-04 9.05E-04 9.05E-04 9.05E-04 9.05E-04

Table 3: Final Results Table Property Experimental R 2071.29 f 0.031 uavg 9.34E-04 Laminar Slope 1.007 Tubulent Slope 2.11

Theoritical 2000 0.030 9.05E-04 1 1.85

EXAMPLE GRAPH:

8

% Difference 3.56 3.33 3.20 0.70 14.05

Table 2: Mercury Friction Loss Data Sheet Volume (ml)

Average Volume (ml)

Temperature =

Time (s)

Average Time (s)

h1 (mm)

h2 (mm)

12.6 x (h 1-h 2) (mm)

°C

Table 3: Water Friction Loss Data Sheet Volume (ml)

Average Volume (ml)

Temperature =

Time (s)

Average Time (s)

°C

9

h1 (mm)

h2 (mm)

(h 1-h 2) (mm)