Video of “Drag, added mass, and Spring-Mass systems”

Here are the videos of the “Drag, added mass, and Spring-Mass systems” demonstration. The full videos are linked to the GIF captions.

0.15 kg oscillating in air

0.15 kg oscillating in water (lower frequency than in air)

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Drag, added mass, and Spring-Mass systems

The concept of added mass can be a useful but perhaps a little hard to visualize (either the added mass or the impact of added mass on a system). This is a simple demonstration adapted from Granger’s Experiments in Fluids to illustrate the impact. The basic idea is that a solid accelerating in a fluid will accelerate fluid in its wake effectively increasing its inertia. The method for demonstrating this is to use a spring-mass system that is released and oscillates in air and then water. The added mass in water is much larger than that in air, increases the system inertia, and reduces the frequency of oscillation.

Equipment

1. Container of water
2. Spring
3. Mass
4. Support structure
5. Stop watch

Demonstration

1. Mount the mass on the spring in air, extend the spring, and release.
2. Measure the time taken for the mass to oscillate 20 times (may be more or less depending on the losses in the system and frequency of oscillation).
3. Mount the mass on the spring and place it in the water container (ideally only the mass on a long cord with the spring dry), extend the spring and release.
4. Measure the time taken for the mass to oscillate 20 times (this may be harder and you may have to have fewer oscillations this time as the water damps out the motion fairly quickly).

Analysis

The frequency of oscillation (f) of the system is

f~(k/m)1/2

where k is the spring constant and m is the mass. There are a number of methods for getting to this result. Dimensional analysis is an easy method where the dimensions of the parameters are [f]=T-1, [k]=MT-2, and [m]=M. Alternatively one can write down the equation of motion

m(d2x/dt2)=-kx

and solve to get

x=x0cos((k/m)1/2t+Θ)

giving an oscillation frequency of

f=(k/m)1/2/2π.

Regardless of how you get there, the main result is that the frequency of oscillation is inversely proportional to the square root of the mass, i.e.

(2πf)2=k/m.

When the mass is immersed in the water the effective mass of the system increases due to the added mass. Therefore, the Frequency of oscillation of the system will also drop. Denoting the added mass by ma the frequency in water (fw) is given by

(2πfw)2=k/(m+ma).

For a known mass, the spring constant can be calculated from the frequency of oscillation in air. The added mass can then be calculated from this data and the frequency of the system in water.

I ran a test using the equipment shown above. In this case the mass was 0.15 kg and the frequency in air was f=1.6 hz giving a spring constant of

k=(2πf)2m=15 N/m.

The frequency of the system when immersed was fw=1.45 hz giving and added mass of

ma=(k/(2πfw)2)-m=0.031 kg

or 20% of the original mass.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Video of “Flow attachment, wakes, and blowing a candle out around a cup”

Here is animated GIF of the “Flow attachment, wakes, and blowing a candle out around a cup” demonstration. The full video is here.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Flow attachment, wakes, and blowing a candle out around a cup

Most undergraduate engineering textbooks have a schematic diagram of the flow around a cylinder at different Reynolds numbers. The one below is styled on the diagram from Munson et al.  However, the implications of the diagram can seem a little abstract. Here is a simple demonstration that illustrates how, at the right Reynolds number and positioning, you can blow out a candle with a glass or cup between your mouth and the candle.

Schematic diagram of flow regimes for flow around a cylinder for increasing Reynolds numbers. From left to right and down Laminar fully attached wake, steady separation bubble, von Karmen vortex street, wide turbulent wake, flow reattachment with narrow turbulent wake (drag crisis). Adapted from Munson et al.

Equipment

1. A candle
2. Matches
3. A cylinder such as a drinking glass

Demonstration

1. Light the candle
2. Place the glass a few diameters away from the candle
3. With your mouth a similar distance from the glass as the glass is to the candle, blow out the candle.

Explanation

The main point of the demonstration is that the glass does not create and endless wind shadow but rather there is a wake behind the glass that gradually decays as the flow moves downstream. Therefore, provided the glass is not too close to the candle, the velocity in the wake regains sufficient velocity to extinguish the candle. The only exception to this would be if the candle were a low flow portion of the steady separation bubble that exists for low to moderate Reynolds numbers. However, it is difficult to achieve this Reynolds number while still blowing hard enough to blow out the candle. I found that my peak air speed is around 25 mph (11 m/s). The glass diameter was approximately 3” (7.5 cm) which gives a Reynolds number of 55,000. This places the flow squarely in the wide turbulent wake (pre drag crisis) regime (or it would if it were a uniform flow as opposed to a round air jet coming from a small opening). The demonstration takes a little practice.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.