Demo: My Buckets Got A Hole In It



Experiment: Pressure and Velocity

Carol Brunjes

Leonard Freise

Objective:

To show the velocity of a liquid leaving a spigot has the same velocity as a falling object dropped from the same height.

Equipment:

• Photogate timers

• Lead ball

• Coffee can with small hole drilled in the side near the bottom

• Waterproof marker

• Meter stick

• Centimeter ruler

• Catch basin (if inside)

• Water

Procedure:

Setup photogate to measure the time of a falling object through a specific distance (i.e. 10 cm). Using this time and distance calculate the average velocity of the falling object. Repeat 5 times and record in data table.

Measure off the same specific distance used for the falling object on the inside of the coffee can with the hole at the origin (i.e. 10 cm). Place a mark at this point. Fill the coffee can above mark with water and place on table ledge. Align small ruler with bottom edge of cup directly below the hole. Measure the vertical distance between the hole and the ruler. Record in data table. Allow water to flow through hole and center the ruler under the flow. Record the distance the water stream hits the ruler when the water level in cup reaches the mark that corresponds to the height of the dropped object. Calculate the velocity of the flow when it reaches the mark on the ruler using the projectile motion equations. Repeat five times and record in data table.

Falling Object Data Table

|Trial # |Distance (m) |Time (s) |Velocity (m/s) |

|1 | | | |

|2 | | | |

|3 | | | |

|4 | | | |

|5 | | | |

Water Data Table

|Trial # |Distance (m) |Time (s) |Velocity (m/s) |

|1 | | | |

|2 | | | |

|3 | | | |

|4 | | | |

|5 | | | |

Vertical Distance from Hole to Ruler

Discussion:

Bernoulli’s equation can be applied to many situations. One example is to calculate the velocity, v1, of a liquid flowing out of a spigot at the bottom of a reservoir. Since the diameter of the container is large in comparison to the hole then the velocity at the top is negligible. The hole and the top of the cup are both open to the atmosphere; therefore P1 and P2 cancel each other. The hole is the reference point so the gravitational potential energy component is zero.

Bernoulli’s Equation:

[pic]

Becomes:

[pic]’

This is the same equation that you would get for the velocity of a falling object:

P.E. = K.E.

[pic][pic]

The mass cancels:

[pic]

Questions for Students:

1. Using the velocity calculations calculate the amount of error in your results.

2. Would your results be different if the cup were cone shaped instead of cylinder shaped?

3. Would your results change if the hole in the cup were larger?

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