Wright State University
Department of Mechanical and Materials Engineering
Fall 2004
ME 317: FLUID DYNAMICS LABORATORY
Experiment 2: Continuity Equation Demonstrator
Objective: The objective of this experiment is to compare measurements of flow draining from a
tank with predictions from a quasi-steady frictionless flow analysis.
Reference: Fox, McDonald and Pritchard, Introduction to Fluid Mechanics, 6th edn., Section 4.3:
Conservation of Mass
Preparation: Read the reference material and these instructions, and solve the following text
problem: A cylindrical tank of diameter D = 50 mm drains through an opening d = 5 mm in the
bottom of the tank. The speed of the liquid leaving the tank may be approximated by V  2 gy ,
where y is the height from the tank bottom to the free surface. If the tank is initially filled with
water to a depth y0 = 0.4 m, determine the water depth at time t = 12 s. Answer: y = 0.134 m.
Equipment Needed: Stopwatch and experimental apparatus (inner diameter of tank D =
inches, diameter of hole d = 0.25 inches).
Experimental Procedure:
1. Measurements
a. Use the four attached data sheets to record the data, noting whether the hole is
rounded or sharp-edged, with or without the porous media insert.
b. Completely fill the tank, start the stopwatch, remove the stopper and record the times
required for the free surface to reach the levels indicated on the data sheets. Make
sure to use the bottom of the free surface to be consistent and to avoid parallax error.
For the experiments without the porous media insert, y = 0 occurs when the free
surface “breaks through” into the hole.
c. Place the porous media insert into the bottom of the tank and hold it in place with the
copper rings. Carefully fill the tank so as not to disturb the porous media insert. Data
for y = 0 is not required for these tests.
d. Repeat each test four times to determine the repeatability of the experiment.
2. Data Reduction
a. For each data set, you will need to tare the initial time (at y0 = 16 inches) from the
subsequent times.
b. Create four separate graphs (one for each data sheet) by plotting the time on the yaxis and the height on the x-axis for each of the four trials.
c. If you find a data set that is obviously bad, do not present it in the graphs, but discuss
it in the report.
Report: Prepare a brief written report in the usual format. On each of the four graphs, plot the
analytical solution for d = 0.25 inches. If the analytical solution does not match the data well,
vary the hole diameter d in the analysis until it does. This can be thought of as an equivalent hole
diameter. Plot this curve on the graph, and indicate what d was for each situation. Turn in the
spreadsheet that you used to reduce the data. Answer the following questions:
1. Are the t = 0 data points predicted well by the analysis? Why or why not?
2. Are the data for the sharp-edged hole predicted well? Why or why not? See page 342.
3. How repeatable is the data?
4. What is the effect of the porous media?
5. If you deleted a data set, what was done wrong in the experiment?
Wright State University
Department of Mechanical and Materials Engineering
Fall 2004
ME 317: FLUID DYNAMICS LABORATORY
Experiment 2: Continuity Equation Demonstrator Data Sheet
Rounded Hole
Time (sec)
y (inches)
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2.5
2
1.5
1
0.5
0
Trial 1
Trial 2
Trial 3
Trial 4
Wright State University
Department of Mechanical and Materials Engineering
Fall 2004
ME 317: FLUID DYNAMICS LABORATORY
Experiment 2: Continuity Equation Demonstrator Data Sheet
Sharp-Edged Hole
Time (sec)
y (inches)
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2.5
2
1.5
1
0.5
0
Trial 1
Trial 2
Trial 3
Trial 4
Wright State University
Department of Mechanical and Materials Engineering
Fall 2004
ME 317: FLUID DYNAMICS LABORATORY
Experiment 2: Continuity Equation Demonstrator Data Sheet
Rounded Hole with Porous Media
Time (sec)
y (inches)
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Trial 1
Trial 2
Trial 3
Trial 4
Wright State University
Department of Mechanical and Materials Engineering
Fall 2004
ME 317: FLUID DYNAMICS LABORATORY
Experiment 2: Continuity Equation Demonstrator Data Sheet
Sharp-Edged Hole with Porous Media
Time (sec)
y (inches)
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Trial 1
Trial 2
Trial 3
Trial 4