Experiment 2: Fluid Dynamics

Purpose:
To experimentally measure what effects the height of water above a hole has on the flow rate of water out of that hole.  This  will be conducted six times with varying heights and the results compared.

Equipment:

• Bucket with small hole near bottom
• Beaker
• Meter Stick
• Stopwatch
• Tape
• Water

Experiment:

 

Measure and record the dimensions of the hole in the bucket.  Place bucket above the beaker so that the stream of water exiting the hole enters the beaker.  Place tape over the hole so that water does not leak out.  Fill the bucket to a certain depth and record the water height above the hole.  Remove the tape and allow 300 mL to flow into the beaker from the bucket while recording the time that it takes using a stopwatch. 

 

Below is the data that was recorded from the six trials.

 

0.0072	±	0.0005	Hole Diameter (m)
4.072E-05	±	0.000006	Hole Area (m^2)
0.0003	±	0.000025	Water Removed (m^3)
0.02	±	0.0075	Hole Above Bottom (m)
Trial		Initial Height (m)			Final Height (m)			Avg Height Above Hole (m)			Time (s)
1		0.080	±	0.005	0.074	±	0.005	0.057			9.8	±	0.2
2		0.080	±	0.005	0.076	±	0.005	0.058			9.6	±	0.2
3		0.073	±	0.005	0.063	±	0.005	0.048			10.8	±	0.2
4		0.069	±	0.005	0.060	±	0.005	0.045			11.1	±	0.2
5		0.065	±	0.005	0.055	±	0.005	0.040			11.9	±	0.2
6		0.094	±	0.005	0.086	±	0.005	0.070			9.0	±	0.2

The data below shows the calculation of the theoretical times that it would take to drain the same amounts of water for trials one through six.  In addition, the % error was calculated for each trial.

3.506E-05	Min Hole Area (m^2)
4.637E-05	Max Hole Area (m^2)
0.000275	Min Water Removed (m^3)
0.000325	Max Water Removed (m^3)
0.013	Min Hole Above Bottom (m)
0.028	Max Hole Above Bottom (m)
Experimental					Theoretical
Trial	Min Height (m)		Max Height (m)		Min Time (s)	Max Time (s)		Theoretical Time(s)			% Error
1	0.045		0.070		5.1	9.9		7.5	±	2.4	30.7%
2	0.046		0.071		5.0	9.8		7.4	±	2.4	29.3%
3	0.036		0.061		5.4	11.1		8.3	±	2.8	30.5%
4	0.032		0.057		5.6	11.7		8.7	±	3.0	28.3%
5	0.028		0.053		5.8	12.6		9.2	±	3.4	28.9%
6	0.058		0.083		4.7	8.7		6.7	±	2.0	34.4%

 

The data below shows the calculations of how big the hole should theoretically by in order to drain the water in the time experimentally measured plus the % error associated. 

0.0003	±	0.000025	Water Removed (m^3)
0.02	±	0.0075	Hole Above Bottom (m)
Experimental								Theoretical
Trial		Time (s)			Height (m)			Min Hole Diameter (m)			Max Hole Diameter (m)			Hole Diameter (m)			% Error
1		9.8	±	0.2	0.057	±	0.013	0.0055			0.0068			0.0061	±	0.00066	17.4%
2		9.6	±	0.2	0.058	±	0.013	0.0055			0.0068			0.0062	±	0.00066	16.7%
3		10.8	±	0.2	0.048	±	0.013	0.0054			0.0068			0.0061	±	0.00072	17.6%
4		11.1	±	0.2	0.045	±	0.013	0.0054			0.0069			0.0062	±	0.00075	16.7%
5		11.9	±	0.2	0.040	±	0.013	0.0053			0.0069			0.0061	±	0.00080	17.3%
6		9.0	±	0.2	0.070	±	0.013	0.0055			0.0067			0.0061	±	0.00059	18.8%

Conclusion:



The experimental values obtained for time to drain are higher than the theoretical values calculated but are the same within the experimental error.   The drill bit calculations show that the hole diameter should be about 0.0061 meters with some error.  The hole size is within the error but the average comes out smaller than the measured valued of the hole. 

Experiment 1: Fluid Statics

Purpose: 
To experimentally measure the buoyant force acting on an object.  This will be done three different ways and then compared. 

Equipment: 

• Force Probe
• String
• Beaker
• Flask
• Caliper
• Cylinder to be tested

Experiment:

A)  Underwater Weighing Method

 

With the force sensor in the vertical position, a string connects the cylinder to the sensor.  Logger Pro will measure the tension in the string due to the cylinder.  Measuements will be taken with the cylinder in air and in water (as shown above).  The buoyant force is the weight minus the tension. 

 

Below are the measurements taken from Logger Pro. 

Trial	Sensor Readings
	Air	Water
1	1.140 ± .01 N	0.769 ± .01 N
2	1.148 ± .01 N	0.759 ± .01 N
3	1.138 ± .01 N	0.763 ± .01 N
Avg	1.142 ± .01 N	0.764 ± .01 N
Min	1.132 N	0.754 N
Max	1.152 N	0.774 N

The minimum buoyant force is:

1.132 N - 0.774 N = 0.358 N.

 

The maximum buoyant force is:

1.152 N - 0.754 N = 0.398 N.

 

Buoyant Force:

0.368 ± .01 N

B) Displaced Fluid Method

 

 

Measure and record the mass of the empty beaker.  Place a flask filled to the top with water into the beaker.  Place the cylinder into the flask and allow the water to flow over the top and into the beaker.  Remove the cylinder and flask allowing the water that overflowed to remain in the beaker.  Measure the beaker plus water.  The buoyant force is equal to the weight of the water dispaced according to Archimede's principle. 

0.14999 ± 0.00005 kg	Mass of Empty Beaker (kg)
Trial	Mass of Beaker + Overflow Water (kg)		Mass of Water Overflow (kg)
1	0.18776 ± .00005 kg		0.03777 ± .0001 kg
2	0.18764 ± .00005 kg		0.03765 ± .0001 kg
Avg			0.03528 ± .002 kg

The minimum buoyant force is:

0.03671 kg * 9.81 m/s^2 = 0.36895 N

The maximum buoyant force is:

0.03871 kg * 9.81 m/s^2 = 0.37975 N

Buoyant Force:

0.374 ± .005 N

C) Volume of Object Method
Using this method, simply measure the cylinder's diameter and height using calipers and then calculate the volume.  Using the stated density of water (1000 kg/m^3), caluclate the weight of water that would be displaced by the cylinder and that would equal the buoyant force. 

Height of Cylinder:  0.0765 ± .00005 m
Diameter of Cylinder:  0.0254 ± .00005 m

pi * (0.0254 m / 2)^2  = 0.0005067 ± .000002 m^3

Area of Cylinder:  0.0005067 ± .000002 m^3

0.0005067 m * 0.0765 m = 0.00003874 m^3 ± .000002 m^3

Calculated Volume of Cylinder:  0.00003874 m^3 ± .000002 m^3
 

3.874 x 10^-5 m^3 * 1000 kg / m^3 = 0.03874 ± .002 kg

Mass of Water Displaced:  0.03874 kg
 

0.0374 kg * 9.81 m/s^2 = 0.380 N ± .02

Buoyant Force:  0.380 N ± .02 N

Conclusion:





The three values are the same within the experimental error.  The most accurate method was Experiment B (Displaced Fluid Method) with the error was only ± .005 N.  The error was based off of the scale measurments which have a precision to five decimal places.

In experiment A, had the cylinder been resting on the bottom of the container, it would have reduced the force read from the sensor.  The original force would have remained the same.  Since the buoyant force is the weight (in air) minus the weight (in water), it would have given a bigger buoyant force.