FLUID MECHANICS
CALIBRATION OF AN ORIFICE
RESULTS AND DISCUSSION
ORIFICE 1 | |||||
|
|
|
|
|
|
DESCRIPTION |
|
| PARABOLIC |
|
|
Diameter of orifice | 13 | mm |
|
|
|
Area of orifice | 0.000133 | m2 |
|
|
|
|
|
|
|
|
|
Run Number | Volume | Time | Flowrate “Q” | Head “H0” | Cd |
| L | Sec | m3/sec | m |
|
1 | 10 | 32.4 | 0.0003 | 0.33 | 0.9567 |
2 | 10 | 34.3 | 0.0003 | 0.3 | 0.9466 |
3 | 10 | 35.3 | 0.0003 | 0.288 | 0.9382 |
4 | 10 | 36.8 | 0.0003 | 0.267 | 0.9337 |
5 | 10 | 38.3 | 0.0003 | 0.249 | 0.9281 |
6 | 10 | 40.6 | 0.0002 | 0.223 | 0.9237 |
7 | 10 | 42.5 | 0.0002 | 0.198 | 0.9349 |
8 | 10 | 44.8 | 0.0002 | 0.168 | 0.9606 |
Table 1 data recorded in the lab for the orifice 1 and the value of Q calculated
In the table 1, the discharge Q(m3/s) is calculated by dividing the volume of water(m3) to time (s).
Figure 1 plot Q vs. H0
“n” for Orifice 1 from plot = 0.486
“R^2” for Orifice 1 from plot = 0.984
“Cd” for Orifice 1 = Displayed on the last column of table 1
ORIFICE 2 | |||||
|
|
|
|
|
|
Run Number | Volume | Time | Flowrate “Q” | Head “H0” | Cd |
| L | Sec | m3/sec | m |
|
1 | 10 | 36 | 0.0003 | 0.321 | 0.3322 |
2 | 10 | 40.3 | 0.0002 | 0.304 | 0.3137 |
3 | 10 | 44.6 | 0.0002 | 0.288 | 0.2996 |
4 | 10 | 49.3 | 0.0002 | 0.254 | 0.3083 |
5 | 10 | 45.2 | 0.0002 | 0.228 | 0.3755 |
6 | 10 | 52.6 | 0.0002 | 0.216 | 0.3411 |
7 | 10 | 62.1 | 0.0002 | 0.201 | 0.3110 |
8 | 10 | 68.2 | 0.0001 | 0.188 | 0.3032 |
9 | 10 | 70.2 | 0.0001 | 0.172 | 0.3227 |
10 | 10 | 74.4 | 0.0001 | 0.166 | 0.3158 |
Table2 data recorded in the lab for the orifice 2 and value of Q calculated
Figure 2 plot Q vs. H0
“n” for Orifice 2 from plot = 1.024
“R^2” for Orifice 2 from plot = 0.928
“Cd” for Orifice 2 = Displayed on the last column of table 2
Figure 3 plot Cd vs. Re for orifice 1
Figure 4 plot Cd vs. Re for orifice 2
- The three practical applications where orifices are used in engineering process design are
- Water treatment plants
- Natural gas industries
- Refineries
- Petrochemical plants
- If the plan area of the tank is 4.12 x 10-2 m2, what is the approach velocity when the discharge is 1.97 x 10-4 m3/sec? What velocity head does this correspond to?
Q=A x V
1.97 x 10-4 m3/sec = 4.12 x 10-2 m2 x V
Approach Velocity V=4.7815 x 10-3 m/s
V =
4.7815 x 10-3 =
H=1.165 x 10-6 m
- Is it negligible compared to the velocity head associated with the jet velocity, uo at the same discharge?
Yes, the above H is value very small.
- Is the assumption (that the velocity of fluid in the tank is negligible) justified?
Yes it can be justified upto some extent. Because the value V0 becomes for the fluid inside the tank.
- Define the term vena contracta. Calculate the velocity in the vena contracta at the highest flowrate for each orifice. Make any assumptions needed but clearly state them.
Vena contracta is the point in a fluid stream where the diameter of the stream is the least, and fluid velocity is at its maximum, such as in the case of a stream issuing out of a nozzle (orifice) (Evangelista Torricelli, 1643). It is a place where the cross-section area is minimum.
For orifice 1, Consider diameter of jet is 1mm = 0.001m and area of jet = 7.853 x 10-4 m2.
Q = Cd Ao(2∆p/ρ)½
This formula neglects the approach velocity. The kinetic energy up stream of the orifice is not usually neglected.
Where, Q=0.0003m3/s
Cd = 0.3322
A0= 0.000133 m2
ρ = 998 kg/m3
∆p = 0.23 x 105 m/m2
Therotical Velocity = (2∆p/ρ)½ = 6.789 m/s
Actual velocity = 2.255 m/s
Cv = Actual velocity/Theoretical velocity
Cv = 0.3322
Cc = 7.85 x 10-4 / 0.000133
Cc=5.90
β=d0/d1=0.013/0.001
Velocity at Vena contracta u2 = 2.255 m/s (actual velocity)
CONCLUSION
In this experiment, it is found that the value of theoretical n=0.5 which is close to the experimental n=0.486 for the orifice 1. While in orifice 2, the n=1.024, which is twice the theoretical value.
From the plot, Cd and Re for the orifices the value of n is 1.058 and 1.001which is very close to each other.
REFERENCES
Çengel, A., and J. M. Cimbala. Fluid Mechanics: Fundamentals and Applications. 2nd ed. Boston: McGraw-Hill Higher Education, 2010. Print.
“Fundamentals of Orifice Metering.” Afms.org. Smith Metering, Inc, n.d. Web. 30 Sept. 2013. <http://www.afms.org/Docs/gas/Fundamenatls_of_Orifice.pdf>.
“Orifice, Nozzle and Venturi Flow Rate Meters.” Engineeringtoolbox.com. N.p., n.d. Web. 30 Sept. 2013. <http://www.engineeringtoolbox.com/orifice-nozzle-venturi-d_590.html>.
