Result and Discussion of Bernoulli Theorem fluid mechanics

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Results Flowrate (Q) = 10L / 0.7665min = 2.175 x 10 4 m³/s Cross section Using Bernoulli equation Using continuity equation Difference I h* = h8 hi Vib = 2 x g x (h –hi) Ai = πDi²/4 Vic= Q αν /Ai (Vib - Vic)/ Vic mm mm m/s mm 2 m/s % 217.0 20!.0 0."!6 5"0.!" 0.40! #0.0"2 $ 215.0 1!5.0 0.626 "66.44 0.5!4 0.052 21".0 142.0 1.1&0 201.06 1.0&1 0.0!" ' 210.0 17&.0 0.7!2 "14.16 0.6!2 0.145 20&.0 1&".0 0.700 "&0.1" 0.572 0.224 F 206.0 1!0.0 0.560 5"0.!" 0.40! 0."6! Flowrate (Q) = 10L / 0.6107min = 2.72! x 10 4 m³/s Cross section Using Bernoulli equation Using continuity equation Difference I h* = h8 hi Vib = 2 x g x (h –hi) Ai = πDi²/4 Vic= Q αν /Ai (Vib - Vic)/ Vic mm mm m/s mm 2 m/s % 246.0 2"0.0 0.560 5"0.!" 0.514 0.0&! $ 242.0 20!.0 0.&05 "66.44 0.745 0.0&1 240.0 11!.0 1.541 201.06 1."57 0.1"" ' 2"".0 1&1.0 1.010 "14.16 0.&6! 0.162 2"2.0 1!1.0 0.&!7 "&0.1" 0.71& 0.24! F 2"0.0 201.0 0.754 5"0.!" 0.514 0.467

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fluid mechanics

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