Physics II Basic Flow Experiment

The picture below shows a uniform cylinder filled with water, and set upon a box about a foot high (you will use a soft drink bottle).

• A ruler is taped to the tube (you can use a ruler, a tape measure, or marks made at carefully measured intervals on the tube).
• The idea is to be able to measure the depth of the water above the hole at regular time intervals as it flows out of the hole near the bottom of the tube.
• The instructor is holding his thumb over the hole.

Based on your knowledge of physics, answer the following, and do your best to justify your answers with the physical reasoning and insight:

• Would you expect the rate of flow to increase, decrease or remain the same as water flows from the cylinder?
• As water flows out of the cylinder, an imaginary buoy floating on the water surface in the cylinder would descend.

• Would you expect the velocity of the water surface and hence of the buoy to increase, decrease or remain the same?
• How would the velocity of the water surface, the velocity of the exiting water, the diameter of the cylinder and the diameter of the hole be interrelated?  More specifically how could you determine the velocity of the water surface from the values of the other quantities?

• The water exiting the hole has been accelerated, since its exit velocity is clearly different than the velocity it had in the cylinder.  

• Explain how we know that a change in velocity implies the action of a force?
• What is the nature of the force that accelerated it?

In the next sequence of pictures the water is flowing out of the hole.

The water stream is just barely visible. 

• The pictures are taken at fairly but not precisely regular time intervals.

From the pictures, answer the following and justify your answers, or explain in detail how you might answer the questions if the pictures were clearer:

• Does the depth seem to be changing at a regular rate, at a faster and faster rate, or at a slower and slower rate?
• What do you think a graph of depth vs. time would look like?
• Does the horizontal distance (the distance to the right, ignoring the up and down distance) traveled by the stream increase or decrease as time goes on?
• Does this distance change at an increasing, decreasing or steady rate?
• What do you think a graph of this horizontal distance vs. time would look like?

You can easily perform this experiment in a few minutes using a 2- or 3- liter soft drink bottle.  

• Poke a hole about 1/4" in diameter about an in the side of the bottle about an inch above the bottom.  
• You want the size of the hole to be such that a full bottle will empty through the hole in a minute or two.   A smaller hole and a longer time give better results, but don't go to extremes.  Ideally it should take about a minute or two for the water to exit the bottle.
• Fill the bottle about 3/4 of the way full.  
• The bottle, between the filling point and the hole, isn't a perfectly uniform cylinder, but it's reasonably close.  
• Use a ruler or tape measure to measure distance.
• Use a watch to measure the time.
• We will use 'clock time' to refer to the time since the very first reading. The very first reading will therefore be at clock time 0.

You can take data in one of two ways.

• You can write down the clock time every time the water crosses another centimeter line on the ruler.
• Or you can write down the reading on the ruler at regular time intervals, e.g., every 10 seconds.
• You will want about 10 readings, spread out over the time required for the bottle to empty.

You will obtain data which can be put into the following format:

clock time (in seconds, measured from first reading)	Depth of water (in centimeters, measured from the hole)
0	14
10	10
20	7
etc.	etc.

Your numbers will of course differ from those on the table.

Get a ruler, a watch, set the experiment up, and take a careful set of measurements.

The following questions were posed above.  Do your data support or contradict the answers you gave above?

• Is the depth changing at a regular rate, at a faster and faster rate, or at a slower and slower rate?

• What does the graph of depth vs. clock time look like?

Analyze the motion of the water surface:

• For each time interval, find the average velocity of the water surface.
• Assume that this average velocity occurs at the midpoint of the corresponding time interval.
• Make a table of average velocity vs. clock time, and for each time interval of this table determine the average acceleration of the water surface.
• Do you think the acceleration of the water surface is constant, increasing or decreasing?