#2 Fluid dynamics:

Objective: 

Using application problem to verify Bernoulli Equation.

Procedures:

1.      Set the equipment as instructed and record all values needed.

2.      Measure time for releasing certain amount of water.

3.      Calculate the theoretical value and compare with the actual measured data.

Bernoulli Equation:

Results:

Value obtained:

       Volume emptied: 450 mL  Height of the water surface: 7.6 cm

       Height of the hole: 2.5 cm       Radius of the hole: 2.6 mm

       We stick paper to the hole and draw the shape of the hole using pencil on the other side of the bucket. The radius of the hole is roughly determined to be the value above.

       T_theoretical  = V / (A·(2·g·h)^0.5)

= 450 ·10^-6 / (π·(2.6·10^-3)²·(2·9.8·(0.076-0.025))^0.5)

= 21.40 s

       Time measured:

      

# of run	1	2	3	4	5	6
Time / s	21.88	21.86	22.61	21.67	22.66	22.55
Average time / s:	22.205
Percent difference / %:	3.762
Theoretical hole radius / mm :	2.591

Discussion:

       The result is very close to theoretical value, proving the ideal equation works. However, by assuming the velocity of fluid is constant and water surface remains constant, the error can be created in the system. The actual data is with in 5 % of the theoretical one, the experiment conducts successfully.