Benjamin Barbaro
12/1/23
Fluids Lab Report: Measuring Vena Contracta and Friction Corrections
Introduction:
To experimentally determine the values of different outlets based on their shape, I tested water
flow through 4 different designs. The designs were determined based on our class lectures and simple
geometric shapes. I will measure the pouring time and poured volume to calculate the flow rate and use
that to calculate the required corrections for each design.
Initial Calculations
H = 18cm - measured
R = 5mm = 0.5cm - designed
Theoretical:
𝑄 = √2𝑔𝐻𝑎 = √2 ∗ 98.1
𝑐𝑚
𝑐𝑚3
2
∗
18𝑐𝑚
∗
0.785
𝑐𝑚
=
46.67
𝑠2
𝑠
𝑎 = 𝜋𝑟 2 = 𝜋(0.5𝑐𝑚)2 = 0.785 𝑐𝑚2
Actual:
𝑄 = 𝑐𝑣 𝑐𝑓 √2𝑔𝐻𝑎
Measured 16oz of tap water – 467 g
𝜌=
𝑚 467𝑔
1𝑜𝑧
𝑔
=
∗
= 0.987
3
𝑉
16𝑜𝑧 29.574 𝑐𝑚
𝑐𝑚3
Methodology:
Cross sections of the 4 designs used are shown below. They were 3D printed and screwed onto the cap
of a large bottle, then flipped over for approximately 5 seconds into a container. The mass of the water
was taken by zeroing the scale on the container and recording the mass of the water. The time was
recorded using a stopwatch, then the calculations for flow rate and constant were done in excel.
Figure 1: Flat Design
Figure 2: Angled Design
Figure 3: Curved Design
Figure 4: Extended Flat Design
Results:
Data is tabulated on a spreadsheet, full results are in appendix 1
Design
1
2
3
4
Avg Q
10.78301
25.7068
34.46043
29.15917
Avg c
0.231048
0.550821
0.738385
0.624795
Design 1 had trouble maintaining steady flow which skewed the data towards the lower end. The rest all
had steady flow, with design 3 being the highest flowrate. This makes sense because during the lecture
on these corrections this curved edge would not need a Vena Contracta correction, only friction.
Surprisingly design 4 had a higher flowrate than design 2, this may be because design 2 causes
conflicting flows at the outlet because all of the fronts meet in one place. I used the average c for design
3 as a value for cf and calculated cv for the other values. These values are shown below.
Design
cv
1
0.31291
2
0.74598
3
1
4
0.846164
Design 1 still has poor flow rate but not exactly the 0.4-0.5 cv predicted during lecture. This is likely due
to the lack of laminar flow. Design 2 and 4 both had relatively large values for cf but designs should favor
design 3 if manufacturing that geometry is not a concern.
Conclusion:
This experiment proved that the highest flow rate out of a nozzle can be achieved by gradually sloping in
a parabola towards the outlet. I noticed that the intake of air into the bottle was also important to
achieving laminar flow out of the bottle which was not consistently achieved for each design. Potential
improvements to the lab may have included air spigots similar to those seen in pour spouts in the
restaurant industry. The shape of the outlet has a great effect on the rate at which water flows through it
so design of parts for fluid flow should account for this. You can see this distinct curved shape on many
commercial bottle caps made for consistent flow.
Appendix 1a: Spreadsheet Tab 1
Appendix 1b: Spreadsheet Tab 2
Appendix 1c: Spreadsheet Tab 3
Appendix 1d: Spreadsheet Tab 4
Appendix 1e: Spreadsheet Tab 5