Lab 2: Fluid Dynamics (2) x

Purpose:

In this lab we will examining the validity of Bernoulli's equation through determining the dimension of the water drain hole using the Bernoulli's equation.   

Method:

Table 1: Dimension of the apparatus

Diameter of the hole (m)	Theoretical volume of water (L)	Theoretical height of water (m)
(0.7± 0.1)*10-2	0.473	6.7*10-2

Table 2: Time measured to empty the water in the bucket
 

Runs	1	2	3	4	5	6
Time to Empty the Water (s)	17.55	17.08	17.54	17.50	17.50	17.46

Figure 1: Experiment apparatus set up

Figure 2: Close up view of experiment apparatus

Figure 2: Water flowing in accordance to Bernoulli's equation 

 

v = sqrt (2gh)

Rate = Av = V/t 

D = sqrt(4V/vtpi)

D measured = 0.62 cm

D calculated = 0.55 cm

Uncertainty range = 0.083 cm

Error = 11%

Conclusions:

In this lab we determined the hole of a water bucket through fluid dynamics. We found that the calculated diameter has an error of 11% but is within the uncertainty of the value. We believe the error is mostly contribute by the inaccuracy of the experiment.

Lab 1: Fluid Statics (1) s

Purpose: 

In this lab we will examine and determine the value of buoyant force using a variety of methods.

Method:

• Underwater Weighing Method
• The buoyant force will be determine by performing a vector analysis on the force acting on the object
• B = W - T

Table 1: Measurements of Silver Block

Mass (g)	Weight (N)	Tension (N)
112.42 ± 0.01	1.10 ± 0.01	2.0 ± 0.1

Figure 1: The apparatus for measuring buoyant force.

B = 0.329 ± 0.01 N

• Displaced Fluid Method
• The buoyant force will be determine by the Archimede's principle in which the weight of the displaced fluid will be measured to solve the value of buoyant force.
• W = m_w*g

Table 2: Measurements of Archimedes’s principle

Mass of Beaker (kg)	Mass of Beaker and Water (kg)	Mass of Water (kg)	Weight of Water (N)
142.57*10-3 ± 0.05*10-3	181.25*10-3 ± 0.05*10-3	38.68*10-3 ± 0.05*10-3	0.374 ± 0.0059

Figure 2: .Logger pro program used for this lab.

B =  0.374 ± 0.0059 N

• Volume of Object Method
• The buoyant force will be determined by finding the weight of the displaced water through physically measuring the dimension of the silver cylinder to obtain the volume of the water.
• V = πr²
• W = ρVg

Table 3: Measurements of the dimensions of the cylinder

Height of Cylinder (m)	Diameter of Cylinder (m)	Volume of Cylinder (m3)
(7.7± 0.3)*10-2	(2.5± 0.1)*10-3	(3.8 ± 0.1)*10-5

Figure 2: The lab in process.

B =  0.37 ± 0.01 N

• To account for uncertainties, we set a numerical boundary by determining the maximum and minimum value of the buoyant force.
• We believe that the underwater measuring method is the most accurate since the method has the least variable to contribute to the uncertainties, hence the propagation of error is the least.
• If the metal cylinder in part A has been in contact with the beaker, the measured buoyant force will be less than the true buoyant force. The decrease in buoyant force will be replaced by a normal force to maintain equilibrium. 

Conclusion:

In this lab we have attempted to measure the buoyant force on the metal cylinder using a variety of methods.   Although all methods are equally valid in determining the buoyant force, we believe that the under water weighing method is the most accurate method among all three methods. We think that because under water weighing method has the least measurements that creates uncertainties in the calculations, the method remains the most accurate method for determining the buoyant force. In addition, we have include error propagation in our lab by calculating the range of the maximum and minimum buoyant force and let it become our uncertainty range.