Result and Discussion of Bernoulli Theorem fluid mechanics
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Transcript of Result and Discussion of Bernoulli Theorem fluid mechanics
Results
Flowrate (Q) = 10L / 0.7665min = 2.175 x 104m/s
Cross sectionUsing Bernoulli equationUsing continuity equationDifference
Ih* = h8hiVib = 2 x g x (h hi)
Ai = Di/4Vic= Q/Ai
(Vib - Vic)/ Vic
mmmmm/smm2m/s%
A217.0209.00.396530.930.409-0.032
B215.0195.00.626366.440.5940.052
C213.0142.01.180201.061.0810.093
D210.0178.00.792314.160.6920.145
E208.0183.00.700380.130.5720.224
F206.0190.00.560530.930.4090.369
Flowrate (Q) = 10L / 0.6107min = 2.729 x 10 4m/s
Cross sectionUsing Bernoulli equationUsing continuity equationDifference
Ih* = h8hiVib = 2 x g x (h hi)
Ai = Di/4Vic= Q/Ai
(Vib - Vic)/ Vic
mmmmm/smm2m/s%
A246.0230.00.560530.930.5140.089
B242.0209.00.805366.440.7450.081
C240.0119.01.541201.061.3570.133
D233.0181.01.010314.160.8690.162
E232.0191.00.897380.130.7180.249
F230.0201.00.754530.930.5140.467
Flow rate (Q) = 10L/0.4628min = 3.601 x 10 4m/s
Cross sectionUsing Bernoulli equationUsing continuity equationDifference
Ih* = h8hiVib = 2 x g x (h hi)
Ai = Di/4Vic= Q/Ai
(Vib - Vic)/ Vic
Mmmmm/smm2m/s%
A285.0260.00.700530.930.6780.032
B284.0229.01.039366.440.9830.056
C279.085.01.950201.061.7910.089
D278.0184.01.358314.161.1460.185
E278.0203.01.213380.130.9470.280
F268.0222.00.950530.930.6780.401
Where:
Cross sectionDistance (mm)Diameter of cross section (mm)
A60.026.0
B83.021.6
C105.016.0
D148.620.0
E166.422.0
F215.026.0
*The distance is from the beginning tip to the respective tapings
Discussion
Based on the experiment, the results achieve the objective. The objective of doing this experiment is to determine the fluid velocity using the Bernoullis theorem and the continuity equations. When the inlet flow control valve open from the small and repeated from step 1-12 for another two different flowrate and it obtain the flowrate of the first trial is 10L / 0.7665min, second trial 10L / 0.6107min and the last trial is 10L / 0.4628min.it was calculated below
Calculation for flowrate (Q)Convert:= 45.99sec 1min / 60secFlowrate= 10L / 0.7665min
This experiment was repeated about three times to get accurate results. After get the flowrate, the Bernoullis equation and Continuitys equation was used as a method to fine the velocity that can give two different readings. As a results the velocity that shows the highest velocity is the faster flowrate 10L / 0.7665min that velocity for Bernoulli equation are A=0.396, B=0.626, C=1.180, D=0.792, E=0.700, F=0.560 and for continuity equation the velocity are A=0.409, B=0.594, C=1.081, D=0.692, E=0.572 F= 0.409 while the slowest flowrate 10L / 0.4628min give the lowest velocity which for Bernoulli equation are A=0.700, B=1.039, C=1.950, D=1.358, E=1.213, F=0.950 and for Continuity equation the velocity are A=0.678, B=0.983, C=1.791, D=1.146, E=0.947 F= 0.678 . It calculated by below
Bernoullis equation:ViB = 2 x g x (h hi)Where:Gravity, g = 9.81 m/s2 hi = the total headh = pressure head
ViB = 2 x 9.81m/s2 x (21 20cm) =0.396Continuitys equation:Vic= Q/AiWhere:Q = flow rate averageAi = area of cross sectionVic= Q/Ai = 2.175 10-4 m3 /s (530.93 10-3)-2 = 2.175 10-4 m3 /s (530.93 10-6) = 0.409 m/sDifference
(Vib-Vic)/ Viv Where:Vic = continuitys equationVib = Bernoullis equation = (0.396 0.409) / 0.409 = -0.032From the result of experiment, we know that we can calculate velocity by using Bernoullis equation and continuity equation. We can see the velocity is relaying on the flowrate. That mean, high flowrate can give high velocity. After we calculate the velocity using Bernoullis equation and continuity equation there have a big difference of readings. So, the hypothesis was correct proven that using Bernoullis equation is better than continuity equation because the result given by Bernoullis equation is smaller than continuity equation.
There are several possibilities why the result does not perfect that must be avoided during the experiment. Firstly, the air bubbles still in the manometers. It can disturb the result obtained, as the result is inaccurate. Besides, the parallax error is the one of the fact why the result is inaccurate. It happens when process of manometer reading that the reading was taken incorrect way, when the meniscus of fluid was not stabilized yet or still moving.
Table 1: Manometer Reading Vs Velocity
MANOMETER READING (H)VELOCITY (M/S)
2170.36
2150.626
2131.18
2100.792
2080.7
2060.56
Table 2: Manometer Reading Vs Velocity
MANOMETER READING (H)VELOCITY (M/S)
2460.56
2420.85
2401.541
2331.01
2320.897
2300.754
Table 3: Manometer Reading vs Velocity
MANOMETER READING (H)VELOCITY (M/S)
2850.7
2841.039
2791.95
2781.299
2781.213
2680.95