FACULTY OF ENGINEERING AND TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING MMB 324 FLUID MECHANICS LAB REPORT TITLE: FLOW THROUGH A PIPE ORIFICE METER AUTHOR: SEITAAKGOBATI. O ID NO: 200901885 Deadline: 16/04/2012 LECTURER: DR MOTSAMAI
OBJECTIVE To calibrate an experimental orifice flow meter b y determining the experimental coefficient Cor. APPARATUS A scheme of the experimental stand is shown on figure 1 below 1. 2. 3. 4.
Orifice plate installed in a horizontal pipeline Piezometers installed upstream and downstream of the plate Water supply pump Flow-rate measuring device
Figure 1.Showing a scheme of the experimental stand THEORY By definition an orifice is a thin plate with a hole in the middle and it is used for measuring the volumetric flow rate, while in use it is placed in a pipe in which fluid flows. Moreover, when the fluid reaches the orifice at the upstream the fluid is forced to converge as it goes through the small hole however, maximum convergence occurs just downstream and beyond this point the fluid expands hence pressure and velocity changing. Nozzle and orifice meters are based on the same principle of energy head conversion and head loss as venturi meters, namely Bernoulli’s principle which relates the pressure of the fluid and its velocity thus, velocity is inversely proportional to pressure. Therefore, the discharge (Q) equations have the same form. However, the coefficient of discharge Cd would be different from the theoretical value, calculated based on the area ratios, due to separation of the stream flow from the pipe wall boundary immediately downstream from the obstruction (orifice) and the formation of vena co ntracta.
Where; Cd – coefficient of discharge (based on literature sources Cd = 0.6 – 0.65) Cv – coefficient of velocity (note, that this coefficient differs from the coefficient of velocity applied to discharges through small orifice) 2
1/2
Cc – coefficient of contraction – Cc = 1/[(A1/A2) – 1] ] A1 – cross sectional area of the pipe (internal diameter) A2 – cross sectional area of the orifice ΔP – pressure difference up and downstream the dev ice – ΔP// ρg = h1 – h2 = Δh Rearranging: 1/2
Q = Cor . (Δh)
(1) 1/2
Where: Cor = Cv . Cc . A1 . (2g)
1/2
= Q/(Δh)
(2)
Representing equation (1) in logarithmic format allows for linear graphical presentation of the relationship, where the intercept of the experimentally obtained straight line with the “Y” axis will give the numerical value of “ln Cor .” 1/2
lnQ = ln Cor + ln [ (Δh) ] METHODOLOGY The experiment was started off by recording both cross sectional areas A1 and A2. Thereafter an adjustment of the flow rate was done up to its maximum value then conditions were allowed to be steady hence enabling values to be read and recorded thus, Q, h1 and h2. The flow rate was then reduced, repeating the procedure to take several readings for different flow rates. RESULTS Table 1: Showing experimental results N
Q
1 1 2 3 4 5
L/min 2 50 45 40 35 30
Q
m /s mmHg 3 6 0.000833 547 0.000750 464 0.000667 355 0.000583 280 0.000500 197
mH2O 7 7.4349 6.3067 4.8252 3.8058 2.6776
Cor -
8 2.7267 2.5113 2.1966 1.9508 1.6364
10 9 0.000297 0.000256 0.000276 0.000247 0.000283
[] In
10 1.0030 0.9208 0.7869 0.6682 0.4924
InQ
11 -7.1196 -7.3486 -7.4073 -7.6372 -7.6769
Sample calculations
Conversion of mmHg to mH2O
= (547
-3
10 ) (13.6) = 7.4392mH2O 1/2
= 7.4392 = 2.73
Equation 1 is used to calculate Cor in column 9
Cor =
=
= 2.97
10
-4
[]
In
= In (2.7267) = 1.003
1/2
InQ = In Cor + In [( ] -4 = In (2.97 10 ) + (1.00309) = -7.1196
( ) √
Area 1 (A1) =
=
Area 2(A2) =
=
Cc =
-2
=
= 3.02033 10
Cv =
Cd = Cv
=
Cc = 3.361
-2
3.02033 10 = 0.1015
= 3. 36
Graph oF lnQ against ln(Δh)1/2 -7 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1 -7.1 -7.2 -7.3
Q n l
-7.4 -7.5 -7.6 -7.7
ln(Δh)1/2
Figure 2.Graph of lnQ against ln(Δh)
1/2
Graph of Q [l/s] Vs Δh [mmH2O] 0.9 0.8 0.7 0.6 ] s 0.5 / l [ Q0.4
0.3 0.2 0.1 0 0
0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 Δh
[mmH2O]
Figure 2.Graph of Q [l/s] against Δh [mmH2O]
-7.8
Table 2.Sowing average value of Cor
Cor.
Average
0.000297 0.000256 0.000276 0.000247 0.000283
0.0002718
DISCUSSION 1/2
A value of ln Cor. was found to be -7.1 from Figure 2, the Graph of lnQ against ln(Δh) . 1/2 Therefore, it can be commented that lnQ has an inverse proportion to ln(Δh) . From the previously used equations values of (Cv), (Cc) and (Cd) were found to be Cc = 0.174, Cd = 0.625 and CV = 3.59. Moreover, the specific equation for the device has been found to be Q = 1/2 (0.00091) (Δh) . There could have been errors during the experiment in terms of improper timing while measuring the flow rate. CONCLUSION
It can be pointed out that the aim of this experiment has been met and therefore the theoretical Cd is 0.625 and it falls within the theoretical range o f 0.6 – 0.65. REFERENCES rd
John F. Douglas, Janusz M. Gasiorek, John A. Swaffield, Lynne B. Jack; Fl uid Mechanics, 5 Edition, ISBN 0-13-129293-5
FACULTY OF ENGINEERING AND TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING
MMB324-FLUID MECHANICS
TITLE: EXPERIMENT 2: FLOW THROUGH A PIPE ORIFICE METER
NAME: OTLADISA TLHALERWA ID NUMBER: 200901854
