PHYS 1401 – General Physics I

Hydrostatic Pressure

 

Leader: ___________________                      Recorder: __________________________

Skeptic: ___________________                     Encourager: ________________________

 

Materials

Laptop

LabPro

Tall plastic cylinder

1/2 meter stick

Pressure sensor attached to long piece tygon tubing

Ring stand with right angle and jaw clamp

600 ml beaker

 

Introduction

      In this lab we will investigate one of the central ideas in the statics of liquids, namely how pressure varies with depth in a liquid.  Our apparatus will consist of a tall plastic cylinder and a pressure sensor.  We will measure the pressure in the liquid at the bottom of the cylinder as we fill the cylinder with water and examine the relationship between the measured pressure and the depth of water.

 

Procedure

1.  Set-up

      Connect the LabPro to the laptop with the USB cable and connect the pressure sensor to CH 1 of the LabPro.  Connect the long plastic tube to the pressure sensor.  Hold the pressure sensor to the jaw clamp and position it with the input facing down just above the graduated cylinder.  Place the long tube so that its end is at the bottom of the graduated cylinder.

 

2.  Start LoggerPro

      Start LoggerPro and open the experiment file by following the path “Probes & Sensors”=>”Pressure Sensors”=>”Pressure Sensor”=>”PS-kPa”.  This will read the pressure in kPa.  Remember atmospheric pressure is approximately 100 kPa.  Click on the sampling button  next to the collect button and change the length of the experiment to 60 s and the sampling rate to 10 samples per second.

 

3.  Collect Data

      With the tube sitting at the bottom of the graduated cylinder, click on the collect button.  Record data for 10 s or so and then autoscale the graph.  You will probably notice that signal is very noisy.  This is due to “least significant bit error”.  The LabPro converts the output of the pressure sensor to a digital form the computer can understand.  It has to round the last digit and sometimes it rounds up and sometimes it rounds down.  Use the STAT button to find the mean value of the pressure and record in the data table below in the first row.  Convert the units to Pa.

      Add water to the graduated cylinder so that the column of water is approximately 10 cm high.  Click on the collect button and determine the mean pressure.  If there is no change in the pressure from the previous reading, contact your instructor.  Find the mean value of the pressure and record the measured height of the column of water and the measured pressure in the data table.  Be sure to convert to the indicated units in the column heading.  Repeat three more times, each time increasing the height of the column of the water by an additional 10 cm.

 

Height of water (m)

Pressure (Pa)

0

 

 

 

 

 

 

 

 

 

 

Data Analysis and Questions

Q1.  The end of the tube doesn’t move appreciable in this experiment.  As you add water does the pressure sensor measure the pressure at the top or the bottom of the column of water?

 

 

Q2.  As the height of the column of water increases what happens to the pressure measured at the bottom of the graduated cylinder?

 

 

 

Q3.  In each step you increased the height of the water by about the same amount.  Did the pressure change in roughly equal increments?

 

 

Q4.  What kind of relationship exists between the pressure at the bottom of the column and the depth of water?  (e.g. linear, proportional, inverse, …)

 

 

Q5.  Use LoggerPro or Excel to produce a properly labeled graph of Pressure vs. Depth.  Add a best fit line to the graph and attach the graph to the report.

 

 

Q6.  Record the slope of the line including units.

 

 

Q7.  Show that the units of the slope can be written as N/m3.

 

 

 

The slope is known as the weight density.  In general the weight density is defined as

Dw =  ρg (1), where ρ is the mass density and g is the acceleration due to gravity.

 

Q8.  Look up the density of water in SI units in your text and use (1) to determine the value of the weight density of water?

 

 

Q9.  Compare the slope of the line to the value of the weight density of water you determined in Q7 by computing the % difference.

 

 

Q10.  What is the pressure at the top of the column of water?  Explain.

 

 

Q11.  One of the data points measured the pressure at the top of the column.  Which one?  Explain.

 

 

Q12.  What is the physical meaning of the y-intercept of your graph?  I.e. the y-intercept is the pressure of what?

 

 

 

Q13.  Using Pb for the pressure at the bottom of the column of water, Pt for the pressure at the top of the column of water, h for the depth of the water, and ρg for the weight density write the expression shown by your graph.

 

 

 

Q14.  In words, explain how the pressure changes with depth in a column of liquid.