How Fast can Water Flow Through a Hole?

That Dam Weir Problem

Scenario:
We are designing a dam to control flood water. The dam needs an overflow and an outlet pipe. How large should this pipe be? If we build larger dams how should this scale?

The Dripping Faucet Problem

Scenario:
To keep from going nuts listening to a dripping faucet while trying to sleep we need to understand why drops form from a leaking faucet.
Or:
We are designing an apparatus requiring the formation of drops. How are the drops formed? How fast do they flow? How does the system scale should we want to use different liquids and a different size apparatus?

A Series of Questions

  1. How fast does a fluid flow through a hole?
  2. How does a fluid flow through an orifice?
  3. Does the viscosity of the fluid matter?
  4. Is the flow smooth or turbulent?
  5. When do drops form and what is their behavior?
  6. How does the behavior depend on the fluid? Does water flow differently than glycerol and alcohol?
  7. What happens to the flow if angular motion is imparted to the liquid in the reservoir?

    Equipment:

  8. three stop watches
  9. plastic tube 10 cm dia x 20 cm high 4 each clear plastic
  10. plastic base 14 cm dia x 1/4" thick
  11. plastic inserts 4 ea
  12. plastic orifices: tubes with ID 0.1 cm, 0.2 cm, 0.5 cm, 1.0 cm x 5 cm long.
  13. Fluids:
    1. water
    2. glycerol
    3. alcohol (isopropanol)
  14. dye such as fluorescene, methlyene blue, or perhaps veg. coloring
  15. strobe for "stopping" and timing drops.

Invariances

return to Scissors