In this experiment you’ll study fluid dynamics using a plastic bottle full of water. The bottle has a marked fill line, three equally-sized (1/8″ diameter) holes at different heights, and three differently-sized holes (1/16″, 1/8″, and 1/4″) all at the same height.

Objectives

1. Make qualitative predictions for each of the questions listed below, and test your predictions. If they prove incorrect, explain how you correct your thinking.
2. Calculate where the stream of water from each of the 1/8″ holes will land if the water level in the bottle is at the fill line.
3. Measure the landing point for the water stream from each 1/8″ hole and compare to your calculation.

Resources

• Water bottle with holes as described above
• Tray for catching water
• Cup for refilling bottle to fill line
• Ruler

Predictions

• Which 1/8″ hole will project a stream of water the farthest when the water level is at the fill line?
• Of the holes at equal heights, which will project a water stream the farthest when the water level is at the fill line?
• Which hole will drain the bottle the fastest?
• Will water stream out slower or faster if you put the cap on the bottle?

Background

In an incompressible flowing fluid, the following holds true:

\tfrac{1}{2}\rho v^2 + \rho g h + P = \textrm{constant}

where \rho is the fluid density, v is the fluid velocity, h is the height of the fluid column above the point in question, and P is the external pressure. For fluid streaming from a hole at a height y in a reservoir, such as a bottle of water, filled to a height h, the above equation can be used to show that the velocity of the fluid streaming out of a hole is

v=\sqrt{2g(h-y)}

This can be combined with simple kinematics to show that the distance from the bottle at which the stream lands should be

D = 2\sqrt{y(h-y)}