AIR FLOW IN PIPES LABORATOYOBJECTIVEThe objective of this experiment is to To find the velocity distribution equation and mean velocity of flow for turbulent flow of air in a pipe. To compare the mass flow rate of air obtained from the velocity from the velocity distribution using analytic from a parabolic nozzle. To determine the darcy friction factor for the pipe and compared it with that obtained from the smooth pipe laws of blasius and of Stanton and panel.

The result of the experiment are tabulated in table 1 below Data for calculating the tableThe measure result from the experiment areDynamic pressure head =total pressure head(PH)-static pressure headPipe diameter at traverse plane = 78.78mmBarometric pressure = 774.25mm of mercuryAmbient temperature = 23.3Manometer offset (zero error) = 3.6cm

Tapping pointDistance from flange (m)Static pressure head (cm H2O) (direct manometer reading)Corrected static pressure head (cm H2O) i.e. direct reading minus zero error

1 (blanked off)0.025-

2.000.054-21.90-18.30

3.000.084-22.10-18.50

4.000.140-18.80-15.20

5.000.279-11.90-8.30

6.000.508-11.40-7.80

7.000.737-11.40-7.80

8.000.965-12.00-8.40

9.001.880-13.20-9.60

10.002.794-14.10-10.50

11.003.708-14.90-11.30

12.004.623-15.60-12.00

13.005.537-16.40-12.80

14.006.106-17.10-13.50

Distance from lower wall y(mm)Total pressure head (cm H2O)Corrected total pressure head (cm H20)velocity from micro manometer (m/s)Average corrected total pressure Head (cm H20) Average velocity from micro Manometer (m/s)Air velocity across the pipe from (m/s) ( equation(3)Log of velocity across the pipe (m/s)Log of velocity from micro manometer(m/s)y/RLog of distance from lower wall(mm)Velocity head(H) (m/s)

1.00-14.30-10.7020.20-10.7020.2021.291.331.310.02-1.602.80

2.00-14.05-10.4521.70-10.4521.7022.221.351.340.05-1.293.05

3.00-13.90-10.3022.70-10.3022.7022.771.361.360.08-1.123.20

4.00-13.70-10.1023.40-10.1023.4023.471.371.370.10-0.993.40

5.00-13.50-9.9023.90-9.9023.9024.1461.381.380.13-0.903.60

6.00-13.30-9.7024.50-9.7024.5024.811.391.390.15-0.823.80

8.00-13.00-9.4025.30-9.4025.3025.771.4111.400.20-0.694.10

10.00-12.80-9.2026.00-9.2026.0026.391.421.410.25-0.604.30

12.50-12.60-9.0026.70-9.0026.7027.001.431.430.32-0.504.50

15.00-12.40-8.8027.40-8.8027.4027.591.441.440.38-0.424.70

17.50-12.2-8.6027.90-8.6027.9028.171.451.450.44-0.354.90

20.00-12.00-8.4028.40-8.4028.4028.731.461.450.51-0.295.10

25.00-11.80-8.2029.20-8.2029.2029.301.471.470.63-0.205.30

30.00-11.60-80.0029.80-8.0029.8029.851.471.470.76-0.125.50

35.00-11.40-7.8030.30-7.8030.3030.381.481.480.89-0.055.70

39.39-11.30-7.7030.50-7.7030.5030.651.491.4810.005.80

Table 1

Figure 1 Graph of v against y and graph of log v against log

Figure2 graph of static pressure head against distance

V=velocity at a distance y from the wall of the pipeR= radius pipe = 39.4mm=0.00394mmaximum velocityn=constant dependent on the Reynolds number flow

Y=0.107x+1.486

Intercept, Natural log 0f

(2a) from equation 2a To calculate volumetric flow rate, Q

(2b) Mean velocity,

(2c) Mass flow rate at transverse, 13600=101973pa But From equation (4) Where

= 0.131

equation (5)Darcy friction from factor using Where f=darcy friction factorL = length of the pipe diameter of pipemean velocity

From steam table, viscosity of air at temperature 294.3k=1.81kg/ms=

Blasius

Stanton and panel

From graph 0f log against log v calculation

Mass flow rate at transverse, =0.126=0.152kg/s

Mass flow rate at transverse, =0.126=0.152kg/s

= 0.131

Darcy friction factor using equation 5

Reynolds number

Blasius

Stanton and panel

The result of the experiment is tabulated in table 1 above, the experimental result of the distance from lower wall, total pressure head, velocity from the manometer taken increases respectively. And the average of them taken also increases. The result from table the were used to plot a graph of velocity (V) against the distance (y), log velocity (v) against log (Y/R) and static pressure head against distance along the pipe. From the log (v) against log(Y/R) increase in Reynoids number decreases the slope of the curve but to the law of logarithmic by prandtl and von karman suggested that by theoretical studies and observation that velocity across a pipe tends to increase as the logOf the distance from the wall from the graph. The law apply from a point that is closer that to the wall to the one very close to the centre of the pipe.(. A.C Walshaw and D.A.Jobson, mechanics of fluids third editon).y and the velocity depends on Reynolds number.

The value of n for the velocity distribution equation is not with the agreement with expected value as the calculated value ranges from of n ranges from 9.35-8.70 .increase in increases the flow rate as were in equation 4 when comparing the flow rate between the two graph in figure 1

From the graph of graph of v against y in figure 1 shows that the velocity is in agreement with the reading because the mean velocity of from the graph of v against y that was calculated is almost the same with the same with that calculated from the graph of log v against log with just a difference of with just a difference of 0.31mls. the difference in the velocity result from the experimental error due to calculation or approximation.

The mass flow rate that were calculated using equation 2c and 4 are not in agreement because the value of the mass flow rate obtained from 2c is slightly higher than the value obtained from equation 4. This is due to the fact that mass flow rate depends on the area, the higher the surface area higher the flow rate; the smaller value in equation 4 is due to a smaller area. But from the two graph plotted in figure 1 have a constant mass flow rate when equation 4 were used to calculate them (that is there value are the same due to constant area, coefficient of discharge) and both the graph increases when using equation 2c.

The experimental value darcy friction and calculated darcy friction value are approximately the same in both Blasius, Stanton and panel with a value 0.004 .and so therefore the pipe is a smooth pipe. The two curve in figure 1 are characteristic of laminar and turbulent flow, the marked scatter in the result in region of Re=138088 being due to transition.

Apparatus used for the experiment Fan motor Manometer Pitot tube Diaphragm valveProcedure A fan motor is switch on to a maximum speed The diaphragm vale is open to allow a maximum flowZero error are corrected from all the manometer readings as to check the datum level of the manometers.The reading of the static pressure head along the pipe wall (1-14), the exit static pressure head, the temperature, barometric pressure were all taken and tabulated as it is showing in table 1.

Principle of of operation of micro-manometerA device in which of a suitable liquid are used to measure the deference in pressure between a certain point and the atmosphere, or between two point neither of which important at atmospheric pressure is known as manometer Micro-manometer ; this are used to measure a very small pressure difference. Variety of them has been developed. Several devices are use to increase the accuracy of the reading. Example Scale on the surface of a liquid may be optically magnified.when many micro-manometers is used the pressure difference to be measure is balance by the slight raising or lowering one of the arm of the manometer whereby a meniscus is brought back to its original position. (B.S.Massey, Mechanics of fluids).

Error that can affect the result in this experiment Error due to parallax when taking reading from the measuring instrument. Calculation and approximation error that could affect the calculation. Error due to losses in the pipe as fluid flow; these are Expansion losses This occour when a fluid flows past and obstacle with sharp edge, a surface of dis continuity spring from the latter. This surface being unstable , rolls up so forming and eddy wake. If the reynoilds is high the velocity distribution upstream will at least for steady flow be fairly uniform, a vigorous turbulent mixing process will ocour in a downstream and will tend to produce a uniform velocity distribution Losses due to shock in which kinectic energy of their relative motion is destroyed. Losees due to contraction and restriction.(A.C Walshaw and D.A.Jobson, Mechanics of Fluids)

ConclusionThe aim of the experiment as to examine the physical behaviour of real fluid flow using the air flow was achieved the darcy friction factor were calculated and compare with the value obtained from smooth pipe laws ,and the result were equal. Reference:B.S.Massey(1989) Mechanics of Fluids Sixth Edition chapman and Hall ISBN 0 412 342804Robert W.Fox, Alan T.McDnald, Philip J. Pritchard(2004) Introduction to Fluid mechanics Sixth Edition John Wiley & Sons, INC ISBN 0-471-37653-1A.C.Walshaw and D.A.Jobson(1979) Mechanics of Fluids Third Edition A.C.walshaw, D.A.Jobson ISBN 0-582-44495-0Robert L.Streeet, Gary Z.Watters,John k.Vernard(1996) Elementay Fluid Mechanics,Seventh Edition John Wiley & Sons, INC