A $19 desktop constant head tank

I have been planning on doing some pipe flow demonstrations in class using straws and rubber connectors. However, to do that I need a constant head tank that will drive the flow. Ideally the entire system would sit on a desktop so that no special mounting would need to be brought into the classroom. I am still working on the pipe flow demonstration but I thought that the budget desktop constant head tank design may be helpful to share.

Equipment

You will need:

  1. A small aquarium pump $8 
  2. A funnel $1
  3. 2 plastic tubs with straight sides (I used plastic shoe boxes) $4
  4. A small tube of silicone sealant $3
  5. A binder clip $1
  6. A short length of tubing to connect to the pump $1
  7. A hard plastic straw $1

20180530_140256

Figure 1: Materials needed for construction (binder clip missing).

Design

The basic idea is that there is a lower reservoir tank that feeds the upper tank via a pump. The upper tank contains a constant height weir overflow, with return to the reservoir tank, and an outlet below the overflow that will have a constant head. Provided the weir length on the overflow is large and the flow rate through the pump is substantially larger than the flow rate out of the constant head outlet then there will always be water flowing over the weir and the head over the weir will be relatively constant. In this budget design the reservoir and upper tank are plastic shoe boxes and the weir overflow is a funnel. Water is pumped using an aquarium pump from the lower to the upper tank and returns through the funnel to the lower tank. The upper tank rests on the lower so that the entire system can sit on a desk.

CH Tank

Construction

  1. Drill a hole in the center of the base of one of the shoe boxes with a diameter equal to that of the middle of the funnel neck.
  2. Drill a hole in the side of the same shoe box with a diameter a fraction smaller than the straw.
  3. Push the straw through the side hole (it should be a tight fit) and then seal around the hole with the silicone sealant on both sides
  4. Place the funnel inside the same shoe box with the neck protruding through the hole and seal around the funnel neck on both sides of the hole. The top of the funnel should be below the rim of the box so that water will flow into the funnel before it overflows out of the box.
  5. Attach the tubing to the aquarium pump and place it in the second shoe box.
  6. Attach the binder clip to the box with the funnel and use it as a mount for the tubing such that the tubing is pointed into the box but not into the funnel
  7. Place the box containing the funnel on top of the box containing the pump with the funnel outlet draining into the lower box.

Figure 2: (a) fully assembled constant head tank system. The yellow straw is the constant head outlet. (b) close up of the upper tank showing the inflow tube mounted (from the pump) through the binder clip and the funnel overflow back into the lower reservoir tank. (c) alternate view of the entire system.

Operation

  1. Block the end of the outlet straw or connect it to the test rig to be used.
  2. Fill the lower box until it is almost overflowing and the upper box until it is about to overflow into the funnel.. This is most easily done by pouring water into the upper tank and allowing it to overflow through the funnel into the lower tank.
  3. Turn on the pump. The water will be pumped into the upper box and drain through the funnel back into the lower box. The head in the upper box will remain essentially constant provided there is water overflowing into the funnel.

Comments

The $19 budget is approximate. You will use only a fraction of the $3 tube of sealant and may need to buy a box of binder clips to get the one you want. The whole thing takes about 15 minutes to assemble provided you have an electric drill with the appropriate drill bits for cutting the holes.

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Video of “Compressible vs incompressible flow and conservation of mass”

Below are GIFs of the compressible and incompressible versions of the “Compressible vs incompressible flow and conservation of mass” demonstration. The full videos are linked from the GIF headings.

Compressible flow (air)

Incompressible flow (water)


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.

Compressible vs incompressible flow and conservation of mass

This is a really simple demonstration of how conservation of volume can be used for incompressible fluids but not for compressible fluids. The demonstration was suggested by Dr. Baburaj of IIT Madras. I teach in a civil engineering department where practically everything is incomopressible and we mostly talk about conservation of volume. The demonstration below is so simple yet so clear.

Equipment

You will need:

  1. Two identical syringes,
  2. A few feet of clear tubing that fits tightly over the end of each syringe,
  3. Some water, and
  4. Food dye (optional)

Demonstration

Compressible flow

  1. Have one syringe (A) with the plunger fully pushed in and the second plunger (B) fully pulled out.
  2. Connect each end of the tube to the syringes
  3. Slowly press the plunger on syringe (B)

Assuming that the syringe plunger’s are a little stiff you should be able to push the plunger on (B) all the way in before the plunger on (A) is pushed all the way out. Mass is conserved because there are no leaks but volume is not conserved as the plungers move different distances on identical syringes. This works better with stiffer syringe plungers.

Incompressible flow

  1. Have one syringe (A) with the plunger fully pushed in and the second plunger (B) fully pulled out and the syringe full of water.
  2. Fill the tube with water (food dye can help with visualization) and connect the tubes in the same way as for the previous version. This is tricky as you want to ensure that there are no air bubbles in the lines.
  3. Slowly push in the plunger on syringe (B). The plunger in syringe (A) should move out at exactly the same speed. you can show this clearly by having the syringes pointing away from each other with the plunger ends next to each other. As you push one in the other should move right next to it.

Analysis

There is no analysis for this demonstration. The gas is compressible so volume is not conserved whereas the liquid is incompressible so volume is conserved. Analysis of the change in pressure in the compressible case and resulting motion of the plungers is complex as you need to know about the friction in the syringe.

Thanks again to  Dr. Baburaj for suggesting the demonstration.


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 “‘Rotational buoyancy’ – Hydrostatic pressure in solid body rotation”

Here is a video from the “‘Rotational buoyancy’ – Hydrostatic pressure in solid body rotation” demonstration. The GIF is a little hazy but clearly shows the cork staying centrally located under rotation and the marble being pushed to the end of the jar (and up next to the lid). The full video is here.

Video Apr 13, 3 04 54 PM 00_00_55-00_01_10


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.

‘Rotational buoyancy’ – Hydrostatic pressure in solid body rotation

Solid body rotation of a fluid about a vertical axis results in a horizontal pressure variation which provides the centripetal force required to rotate the fluid particles. The pressure gradient is, therefore, given by

dp/dr=ρw2r                                              (1)

Where ρ is the fluid density, w is the angular velocity and r is the distance from the center of rotation.

This is easily demonstrated by spinning a cup of water and showing the paraboloid surface that forms with the low point at the center of pressure. However, the pressure gradient exists regardless of the free surface and, just as with the non-rotating hydrostatic pressure variation, an immersed object will experience a net force in toward the region of lower pressure. This can be demonstrated using a sealed container

Equipment

  1. A small cork
  2. A marble
  3. A Lazy Susan or some other cheap turntable
  4. A mason jar
  5. Some Velcro strips or something else to secure the Mason jar to the turntable.

Photo Apr 13, 3 04 44 PM

Demonstration

  1. Place the cork and marble in the jar and fill it with water
  2. Seal the jar so that there are no bubbles (or at least no bubbles that are large compared to the size of the cork) and attach it to the turntable so that its long axis is horizontal and it is centered on the turntable (see figure above).
  3. Shake the jar until the marble and the cork are near the center of the jar (this is so that when the marble moves it is clearly due to the rotation of the jar).
  4. Rapidly spin the turntable. The marble should be pushed to one end of the jar while the cork should remain centered.

Analysis

The horizontal hydrostatic pressure gradient (equation above) means that any submerged object will experience a net pressure force acting toward the center of rotation. For a rectangular object of width s in the radial direction and area A normal to the radial direction located a distance r  from the center of rotation, the net pressure force toward the center of rotation is given by

FpAw2((r+s/2)2-(r-s/2)2)/2                      (2)

See figure below.

rotation

Expanding leads to

Fp=ρAw2rs= ρ∀w2r                                          (3)

where is the volume of the object. Therefore, the net force toward the center of rotation is the angular acceleration multiplied by the mass of water displaced by the object. This is directly analogous to the buoyancy force in a stationary fluid. Therefore, if the object displacing the fluid has a lower density than the fluid then the centripetal pressure force will exceed that needed to maintain the angular velocity of the object and it will be pushed toward the center of rotation (as in the cork). If the object is denser than the fluid the centripetal pressure force will not be enough to maintain rotation and the object will move radially outward (note that this is a somewhat simplified linearized analysis and the integration constant is left out of the pressure equation used in (2) but it gets the appropriate result).


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.