Fluid Dynamics

Objective: Verify Bernoulli's Equation-- P+Dgh+1/2Dv^2=constant

When delta P=0, V=sqrt(2gh)

Flow rate = Volume per seconds = speed * area
Therefore, A=Volume/(speed * time)
                     =V/sqrt(2gh)*t

We measure the Volume, time, and water depth to find the area of the little hole and verify the Bernoulli’s Equation.

Measure the hight

Measure the time

 

Measure the area of the hole

Compare to the theoretical Area

 

Test #	1	2	3	4	5	6
Time (s)	8.60	8.25	8.78	8.33	8.78	8.40

Run	Time to empty (s)	Theoretical Time (s)	% Error
1	8.60	7.01	22.68%
2	8.25		17.69%
3	8.78		25.25%
4	8.33		18.83%
5	8.78		25.25%
6	8.40		19.83%

  
Measured diameter: 6.0mm
calculated diameter: 5.3

Percent Error = 13.2%

Conclusion
There is about 20% error on time and 13% error on the area of the hole. We used v=sqrt(2gh) to find the time; however, the water depth h is changing during the process. I think the error is mainly caused by the changing of h. Also, our reaction time also effect the result, and the hole might not be a circle so A is not equal to [pi]r^2. Other than those, we verify the Bernoulli's equation.