Home Experiments in Mechanical Engineering
Latif M. Jiji, Feridun Delale and Benjamin Liaw
The City College of The City University of New York
<back to content> Introduction <next chapter>
This publication describes 14 experiments in mechanical engineering which students can perform at home using readily available supplies. The experiments are designed for integration with lecture courses in thermodynamics, fluid mechanics, heat transfer and solid mechanics. They represent applications of theoretical concepts taught in mechanical engineering courses. In each experiment theoretical predictions are compared with experimentally obtained results. Although crude measuring techniques are used at home, comparison between theoretical and experimental results is usually satisfactory.
Many theoretical undergraduate engineering courses involves concepts, conditions, processes and approximations that are not familiar to students but can be elucidated and clarified through experiments. Although one of the functions of laboratory experiments is to complement lecture courses, it is often difficult to fully exploit them as learning instruments. The ever increasing sophistication and complexity of instrumentation and data acquisition tend to obscure the phenomenon under study, making it difficult for students to exercise their intuition and experience and thus fully benefit from laboratory experiments. Furthermore, unfamiliarity with operating conditions, calibration procedures, uncertainty about the role of theory, and above all, the painful process of report writing, combine to inhibit enthusiasm about laboratory courses. Thus both the opportunity to use experiments to illustrate and reinforce theory, and to rely on theory to explain and motivate experiment are lost.
A new approach is developed in which very simple experiments which students perform at home using common materials and supplies are integrated with lecture courses and used as a learning device. The use of home experiments was inspired by our experience in teaching our undergraduate lecture course in heat transfer. It was found that when the instructor performs a crude experiment in class to illustrate an application of a theoretical topic, such as transient conduction or fin analysis, students exhibit unusual interest and enthusiasm. Suddenly theoretical ideas take on new meaning and significance. Encouraged by students' responses, the practice was institutionalized in a modified form. Students were asked to perform the experiments at home using household supplies and tools such as a wire hanger, scale, ruler, watch, boiling water, etc. Although they were surprised and amused by such an unorthodox approach to the study of theoretical topics, they reacted even more positively to this arrangement. Performing the experiment motivated students to look more carefully at the theory and examine the assumptions involved.
The concept of performing simple experiments at home is of course not limited to heat transfer. It can be applied to many engineering courses. Recognizing its general nature and utility we have extended its application to courses in thermodynamics, fluid mechanics and solid mechanics through an NSF grant. The project was formalized by organizing the material for each experiment into modules which can be used by other schools. An important component of each module is a presentation of a laboratory version of the experiment with the corresponding results. A sample module is given in Section IV.
<back to content>Concept Description <next chapter>
The simple experiment concept is distinguished by several important features. First, it addresses a broad segment of the undergraduate engineering curriculum affecting lecture courses in several disciplines. Second, it can be easily integrated with existing lecture courses and does not require curriculum changes. Third, it makes minimal demands on the instructor's time. Fourth, it increases students' involvement and thereby increases their motivation to learn. Fifth, it trains students in the processes of simplification, approximation and modeling. Sixth, it creates an environment which inspires innovation and improvisation.
Each experiment is skillfully designed to engage and involve students, capture their attention and motivate them to raise questions and seek answers. Experiments are carefully selected to meet the following critical requirements:
back to contentDescription of Home Experiments next chapter
The following are descriptions of 14 experiments in Thermodynamics, fluid mechanics, heat transfer and solid mechanics. Included are typical results and comparisons between experimental measurements and theoretical predictions.
Thermodynamics next topic
Results: Home experiment: latent heat = 338 kJ/kg Error = 1.5%
Published value: latent heat = 333 kJ/kg
Results: Home experiment: DU/(Q-W) = 1.15 Error =15%
Published value: DU/(Q-W) = 1
Results: Home experiment: V1 /V2 = 1.42 Error = 3.6%
Ideal gas law: V1 /V2 = T1 /T2 = 1.37
Fluid Mechanics next topic
Results: Home experiment: Vo =137 cm/s
Bernoulli's equation: Vo = 108 cm/s
Error = 26.8%
Results: Home experiment: drop time = 3 s Error = 4.9%
Newton's law: drop time = 2.86 s
Results: Home experiment: flow rate = 0.98 g/s
Theory: flow rate = 1.04 g/s
Error = 5.8%
Results: Home experiment: film thickness = 1.2 mm Error =9.1%
Theory: film thickness = 1.1 mm
Heat Transfer next topic
Results: Home experiment: distance from base = 4.5 cm
Fin theory: distance from base = 7.3 cm
Error = 38.4%
Results: Home experiment: cooling time = 118 s Error = 33%
Lumped capacitance: cooling time = 176 s
Results: Home experiment: h = 133 W/m2-°C Error = 22%
Correlation equation: h = 170 W/m2-°C
SolidMechanics back to content
Results: Home experiment: deflection at Pt D = 16.5 mm Error = 1.2%
Theory: deflection at Pt D = 16.3 mm
Results: Home experiment: failure load = 1.9 kg Error = 2.7%
Theory: failure load = 1.85 kg
Results: Home experiment: failure load = 6.2 kg Error = 8.4%
Theory: failure load =6.77 kg
Results: Home experiment: deflection at Pt A = 5.69" Error = 11%
Theory: deflection at Pt A = 5.12"
Evaluation.
Course rating form were filled out by students in four courses: Thermodynamics, Fluid Mechanics, Heat Transfer, and Mechanics of Materials in the Department of Mechanical Engineering, City College of New York, in both the fall and spring semesters, 1994-95, allowing them to judge the quality of the home experiment along several dimensions. Results of these surveys are summarized in the figure below. The questions included in the survey were:
Whether the experiment was easy or hard to do (UNDERSTAND, 1 = easy);
Whether the experiment was easy or difficult to perform (PERFORM, 1 = easy);
Whether the experiment helped understand theory (THEORY, 1 = yes, a lot);
Whether distraction was a problem at home (DISTRACT, 1 = yes, very much):
Whether the experiment was enjoyable (ENJOY, 1 = yes, a lot);
Whether the experiment took longer than they expected (TIME, 1 = a lot
less time); Whether the experiment encouraged wanting to learn more about
the theory (LEARNING, 1 = not at all).
Means, standard deviations and a bar graph represeng mean difference
for each rating in each of four courses are shown in the figure. A MANOVA
revealed significant effects for three of the ratings: easy to understand
(UNDERSTAND), helped understand theory (THEORY), how long it took (TIME).
Students in the "SOLID" and "THERMO" courses found
the home-experiment instructions more difficult to understand and more
difficult to perform than did students in the "FLUID" and "HEAT"
courses. The "SOLID" students found that the experiments took
significantly more time than they expected when compared to all other students
and the "FLUID" students found they took less time than all other
students. There were no differences between course ratings along the remaining
dimensions. Most students found home experiments to be somewhat enjoyable;
to encourage them to seek out more information about the underlying theory;
and they were able to implement them without significant distraction. These
findings help establish the usefulness of this teaching method and the
need to understand its differential use in different content areas of the
engineering curriculum.
back to contentSample Module
EXPERIMENT TITLE: CONSTANT AREA FIN next topic
Supplies: (1) Wire hanger, (2) ruler, (3) pot for boiling water.
| Cut a 35 cm long section from a metal wire hanger and use it as a fin. Bend a 5 cm section at one end and immerse it into boiling water. Position the wire horizontally by resting one end on the water pot and supporting the other end on a knife edge as shown in Fig. 1. Allow the wire to exchange heat by natural convection with the surrounding air and reach steady state. Determine the distance from the heated end to a "point" on the wire where the surface temperature is 37 °C. |
|
Describe how you carried out this experiment and compare your results with theory.
Note that metal wire hangers are usually made out of low carbon steel such as AISI 1010. The average heat transfer coefficient, h, for this configuration can be estimated from appropriate correlation equations. For free convection over a horizontal wire, h depends on the surface temperature, the wire diameter, and the ambient fluid and its temperature. For this special case under typical indoor ambient air temperature, values of h corresponding to different wire diameters are tabulated below.
TABLE I
APPROXIMATE FREE CONVECTION HEAT TRANSFER COEFFICIENT
FOR A HORIZONTAL WIRE SIMULATING A FIN IN AIR UNDER
TYPICAL CONDITIONS FOR THIS EXPERIMENT
wire diameter, cm h, W/m2 - °C
0.05 41.5
0.10 26.4
0.15 20.8
0.20 17.8
0.25 15.8
0.30 14.5
0.35 13.5
THEORETICAL ANALYSIS next topic
This problem can be easily solved by introducing the assumption that the temperature distribution is one dimensional. For this simplification temperature variation over each cross section is neglected. This approximation is valid if the Biot number, hd/2k, is smaller than unity. Here h is the average heat transfer coefficient, d is the fin diameter and k is the thermal conductivity. For a constant area fin with a uniform heat transfer coefficient, negligible radiation, specified temperature To at the base and insulated tip, the solution to the temperature distribution is:
T(x) = Tinf+(To - Tinf)*coshm(L-x)/coshmL (1)
where L is the length of the fin, x is the distance along the fin measured from the base and m is defined as
m2 = hp/kA = 4h/kd (2)
In equation (2) p is the perimeter and A is the cross section area of the fin.
HOME EXPERIMENT next topic
Procedure
| A medium size pot was filled with water to within 1/2 cm and placed on a stove to boil. The short leg of the fin was immersed in the water while the other end was supported with a knife edge. It was noted that heat from the burner, by both convection and radiation, was strongly affecting the fin. To eliminate this factor aluminum foil was placed between the pot and the fin (see Fig. 2), which significantly contained hot air vapor motion as well as radiation from the burner. | 
Fig. 2 |
The fin was periodically touched near the hot end to determine if a steady state condition was reached. After approximately 20 minuets no changes in temperature were perceptible. The fin was then touched along its length to establish the location where the temperature is approximately the same as body temperature, i.e. 37 °C. It was not possible to accomplish this accurately due to the simplicity of the method used to measure temperature. The extent of the region along which the temperature was perceived as being the same as body temperature was recorded. Boiling temperature was assumed to be at 100 °C and room temperature was estimated at 26 °C. A ruler was used to measure all distances.
Data
The following data were recorded:
d = fin diameter = 0.18 cm
L = fin length (portion of fin which is in air) = 30.7 cm
Tinf = ambient temperature = 26 °C (estimated)
To = base temperature = 100 °C (assumed)
x = distance from the base, cm
Results
(1) Experimental Results
The value of x where the temperature was perceived to be the same as body temperature was estimated to range from 4 cm to 5 cm.
(2) Theoretical Results
To establish the validity of the fin approximation leading to equation (1) the Biot number, hd/2k, for this case should be determined. Since the surface temperature varies along the fin, it follows that the free convection heat transfer coefficient h also varies. An average value is obtained based on an average temperature defined as
T = (Tinf + To )/2 = (26 + 100)/2 = 63 °C
The above assumes that the tip is at the ambient temperature. It should be noted that both T and To are estimated since neither one was measured. Thus according to Table 1 the heat transfer coefficient h for a horizontal wire of diameter 0.18 cm at 63 °C is 19 W/m2 -°C. The thermal conductivity k for AISI 1010 carbon steel at 63 °C is 62 W/m-°C. The corresponding Biot number is 0.00057. Since the Biot number is small compared to unity, it follows that the fin approximation is valid. Substituting the values of h, k, d, Tinf , and To into equation (1) and solving for x where the temperature is 37 °C, one obtains x = 7.3 cm. The home experiment gave 4 < x < 5 cm.
LABORATORY EXPERIMENT next topic
Procedure
The fin used in the home experiment was instrumented with thermocouples to measure the surface temperature. Eleven thermocouples were soldered to the fin surface at various locations along its length. One thermocouple was positioned at the base just below water level. The ambient air temperature was measured with a thermocouple placed in the vicinity of the experimental setup. All surface thermocouples were connected to a data acquisition system to record their outputs and determine the corresponding temperatures. Aluminum foil was used to shield the fin from the burner and pot, preventing hot air currents from influencing the fin and reflecting radiation from the burner. To determine if a steady state condition was established, the thermocouples were monitored every 10 seconds. Changes in temperature readings almost ceased after few minutes. Once steady state was reached all thermocouple readings were recorded.
A caliper was used to measure the fin diameter and the positions of surface thermocouples. A fine ruler was used to measure the distance L from the base to the tip of the fin.
Data
The following data were recorded
d = fin diameter = 0.196 cm
L = fin length = 30.7 cm
Tinf = ambient temperature = 21.1 °C
To = base temperature = 98.9 °C
Measured surface temperature T at various distances x from the base is tabulated below:
TABLE 2
x (cm) T ( °C)
0.0 98.9
1.0 89.9
1.5 78.6
2.0 68.4
2.9 48.0
3.9 41.8
4.9 37.8
5.8 33.5
7.8 31.8
9.8 27.4
15.0 24.6
Results
(1) Experimental Results
Table 2 shows that the fin reaches a temperature of 37 °C at x = 5.06 cm.
(2) Theoretical Results
Since Tinf , To and the wire diameter d were measured in the laboratory experiment, the corresponding theoretical solution can be expected to be different from that which is based on home data. For this case the average fin temperature is (21.1 + 98.9)/2 = 60 °C and the heat transfer coefficient is 18.1 W/m2 - °C. Using this value for h and the measured values of Tinf , To and d, equation (1) gives the predicted value of x where the temperature reaches 37 °C as 6.5 cm.
DISCUSSION next topic
Fig. 3 compares the theoretical temperature distribution along the fin with data from the home and the laboratory experiments. Although there was uncertainty in determining the location where the temperature is 37 °C in the home experiment, the agreement with the laboratory data is surprisingly good. The difference between laboratory data on surface temperature and theoretical predictions is not uniform along the fin, ranging from zero to 30%. Various factors can account for this difference, including radiation, non-uniform heat transfer coefficient, error in thermocouple readings and uncertainty in the wire material.
Fig. 3 Comparison between theory, home, and laboratory experiments
NOTES TO INSTRUCTOR back to content
(1) The choice of wire hanger as a fin is dictated by availability and convenience. It is in fact not a good choice since the material is not exactly known and the diameter is too small, making it difficult to measure accurately at home. Furthermore, for a typical wire hanger fin the surface temperature drops from 100 °C to 37 °C over a short distance (approximately 5 cm). It is recommended that a rod of known material and larger diameter be distributed to the class. A 1/4 inch diameter rod of AISI steel can be purchased from McMaster-Carr Supply Co., P.O. Box 440, New Brunswick, NJ. 08903, Tel. (908) 329-3200.
(2) Students should be alerted to deal with radiation and free convection from the burner and shield it from the fin.
(3) The temperature and distance variables in Fig. 3 are presented in dimensionless form. The only parameter in the problem is mL. However, for values of mL greater than 4.6, this parameter plays a very minor role in the solution since the fin acts as though it were semi-infinite. Thus students can superimpose their experimental and theoretical results on Fig. 3 regardless of the conditions of their experiments, as long as mL is greater than 4.6.
