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FLUID MECHANICS BTD

BERNOULLI’S PRINCIPLE LAB REPORT

LECTURER

AT-TASNEEM BINTI MOHD AMIN

NOR FATIHA BINTI HISAMUDEN

TK

INTRODUCTION

Bernoulli's Principle is a fundamental concept in fluid dynamics that describes the behavior of fluids, such as liquids and gases, as they flow through various conditions. Bernoulli's Principle asserts that as the speed of a fluid increases, its pressure decreases. To understand the derivation of Bernoulli's Principle, we can begin by considering the conservation of mass.

1 2

2

Conservation of mass : ρ = 1

1

1 ρ 2

2

2 Conservation of momentum :

1 1 2

1 2

1

2 1 2

2 2

2

1 1 2

1 2

1

2 1 2

𝐴 1

2

2

2

𝑑𝑦𝑛𝑎𝑚𝑖𝑐

𝑑𝑦𝑛𝑎𝑚𝑖𝑐

OBJECTIVE

● To investigate the validity of the Bernoulli equation when it is applied to a steady flow of water through a venturi device. ● To understand how the Bernoulli equation relates to conservation of mass.

HYPOTHESIS

● The expected outcome from this experiment is to get the velocity from the total and static head ( 𝑉 ) and the velocity determined from the flow rate ( ). 𝑐𝑎𝑙𝑐

𝑚𝑒𝑎𝑠 ● Initially, there is a decrease in the static head trend followed by a subsequent increase. ● The dynamic head shows an initial growth followed by a reduction.

RESULT & ANALYSIS

Table 1. Static head measurements Measurement Flow rate, Q (l/s) Static head (mm water) ℎ1,𝑠𝑡𝑎𝑡𝑖𝑐 ℎ2,𝑠𝑡𝑎𝑡𝑖𝑐 ℎ3,𝑠𝑡𝑎𝑡𝑖𝑐 ℎ4,𝑠𝑡𝑎𝑡𝑖𝑐 ℎ5,𝑠𝑡𝑎𝑡𝑖𝑐 ℎ6,𝑠𝑡𝑎𝑡𝑖𝑐 1 0.273 200 180 0 95 150 160 2 0.286 220 205 15 110 170 180 3 0.294 235 220 30 130 180 195 Table 2. Total head measurement Measurement Flow rate, Q (l/s) Static head (mm water) ℎ1,𝑡𝑜𝑡𝑎𝑙 ℎ2,𝑡𝑜𝑡𝑎𝑙 ℎ3,𝑡𝑜𝑡𝑎𝑙 ℎ4,𝑡𝑜𝑡𝑎𝑙 ℎ5,𝑡𝑜𝑡𝑎𝑙 ℎ6,𝑡𝑜𝑡𝑎𝑙 1 0.273 290 288 290 279 270 265 2 0.286 310 305 308 292 289 284 3 0.294 324 323 325 315 312 309 Table 3. Inner diameter and area of venturi at each point Point ID(mm) (^) Area, A ( 10 −4𝑚^2 ) 1 28.4 6. 2 22.5 3. 3 14.0 1. 4 17.2 2. 5 24.3 4. 6 28.4 6.

Table 4. Data Collections Cycle Q (l/s) Description Point 1 2 3 4 5 6 1 0.273 ℎ𝑡𝑜𝑡𝑎𝑙 (𝑚𝑚) 210 208 210 199 190 185 ℎ𝑑𝑦𝑛 (𝑚𝑚) 10 28 210 104 40 25 ℎ𝑠𝑡𝑎𝑡 (𝑚𝑚) 200 180 0 95 150 160 𝑣𝑚𝑒𝑎𝑠 (𝑚/𝑠) 0.0431 0.0688 0.1773 0.1177 0.0593 0. 𝑣𝑐𝑎𝑙𝑐 (𝑚/𝑠) 0.4429^ 0.7412^ 2.0298^ 1.4285^ 0.8859^ 0. 2 0.286 ℎ𝑡𝑜𝑡𝑎𝑙 (𝑚𝑚) 230 225 228 212 209 204 ℎ𝑑𝑦𝑛 (𝑚𝑚) 10 20 213 102 39 24 ℎ𝑠𝑡𝑎𝑡 (𝑚𝑚) 220 205 15 110 170 180 𝑣𝑚𝑒𝑎𝑠 (𝑚/𝑠) 0.0452 0.0720 0.1857 0.1233 0.0622 0. 𝑣𝑐𝑎𝑙𝑐 (𝑚/𝑠) 0.4429 0.6264 2.0443 1.4147 0.8747 0. 3 0.294 ℎ𝑡𝑜𝑡𝑎𝑙 (𝑚𝑚) 244 243 245 235 232 229 ℎ𝑑𝑦𝑛 (𝑚𝑚) 9 23 215 105 52 34 ℎ𝑠𝑡𝑎𝑡 (𝑚𝑚) 235 220 30 130 180 195 𝑣𝑚𝑒𝑎𝑠 (𝑚/𝑠) 0.0464^ 0.0741^ 0.1909^ 0.1267^ 0.0639^ 0. 𝑣𝑐𝑎𝑙𝑐 (𝑚/𝑠) 0.4202 0.6718 2.0539 1.4353 1.0101 0. Sample Calculation To calculate ℎ , using formula To calculate , using formula 𝑡𝑜𝑡𝑎𝑙

𝑑𝑦𝑛 ℎ𝑡𝑜𝑡𝑎𝑙 = ℎ𝑡𝑜𝑡𝑎𝑙,𝑟𝑒𝑎𝑑𝑜𝑓𝑓 − 80 𝑚𝑚 ℎ𝑑𝑦𝑛 = ℎ𝑡𝑜𝑡𝑎𝑙 - ℎ𝑠𝑡𝑎𝑡 ℎ cycle 1 = 290 - 80 cycle 1 = 210 - 200 𝑡𝑜𝑡𝑎𝑙

𝑑𝑦𝑛 = 210 mm = 10 mm

DISCUSSION

● Change in diameter had a notable impact on pressure/head and velocity along the tube.

We can see this by calculating the 𝑉 from our experiment. Based on my experiment, 𝑚𝑒𝑎𝑠 the analysis of the data received is similar to my hypothesis. ● Based on my experiment, the higher the flow rate, the pressure and the velocity are also increasing. For example, the 𝑉 calculated from flow rate 0.273 is 0.0431 while 𝑚𝑒𝑎𝑠

𝑚𝑒𝑎𝑠 calculated from flow rate 0.294 is 0.0464. This is similar to my hypothesis that 𝑉 and 𝑚𝑒𝑎𝑠 𝑉 are increasing in trend. 𝑐𝑎𝑙𝑐 ● After conducting the experiment, a clearer understanding of Bernoulli's Principle emerged. The experiment emphasizes the inverse relationship between fluid velocity and pressure. ● We can improve the accuracy and precise measurements of pressure, velocity, and flow rate to ensure the reliability of the data. Additionally, controlling variables, such as temperature fluctuations or preventing air leaks can be minimized to enhances the consistency of data of the experimental results.

CONCLUSION

In conclusion, the experiment confirmed that changes in diameter affect pressure and velocity as predicted by Bernoulli's Principle. Higher flow rates also led to increased pressure and velocity, aligning with the hypothesis. To improve future experiments, focus on precise measurements and control variables like temperature fluctuations and air leaks for more consistent results.

REFERENCE

1. Bernoulli’s Principle Lab sheet, by At-Tasneem binti Mohd Amin (2023) 2. Bernoulli’s Principle Lab Report, by Kee Tze San (2017, 6 november) , Bernoulli's Principle Lab Report.docx