Pressure and buoyancy

In this laboratory you will investigate properties of fluid pressure.  You will also determine the density of a metal block by applying Archimedes' principle.

Open a Microsoft Word document to keep a live journal of your experimental procedures and your results.  Include all deliverables, (data, graphs, analysis, outcome).  Write a 'mini-reflection' immediately after finishing each investigation, experiment or activity, while the logic is fresh in your mind.

Experiment

Archimedes' Principle states that an object partially or wholly immersed in a gas or liquid is acted upon by an upward buoyant force B equal to the weight w of the gas or liquid it displaces.  In this experiment you will measure the apparent loss of weight of several submerged objects and find the weight of the displaced fluid.  You will use your measurements to determine the density of the objects.  A PASCO Force Sensor is used to measure the weights.

Equipment that was used to produce the experimental data below:

• Force Sensor
• Two containers, one with and one without overflow spout
• Various solid objects

Before making the measurements, draw a free-body diagram of an object hanging in the air.  Now, imagine it is submerged in water.  What new force appears?  Will the tension in the string increase, decrease, or stay the same?  Write down your prediction before making the measurements.

Procedure:

Use the data below.  Click on a small picture if you want to see an enlarged picture.

	(a)	(b)	(c)	(d)
Object 1:
Object 2:
Object 3:
Object 4:

For each of the objects:

(a)  Determine the weight W_c of the empty container with the handle.  When the container is suspended from the force sensor, the force sensor measures the force of gravity (weight) acting on the object, and the program displays the magnitude of this force (in N) on the computer screen.

(b)  Determine the weight of an object W_o when it is suspended above the container with the overflow spout.  This container is completely filled with water, and the container with the handle standing below the spout is empty.

(c)  Determine the apparent weight of the object W_ow after it has been lowered into the water.  As the object is lowered into the water, water pours out of the overflow spout.  The container with the handle has collected this water.

(d)  Determine the weight W_cw of the container with the handle holding the collected water.

Record the weights in a spreadsheet as shown below.

For each of the objects, your goal is to determine if the 'missing weight' of the object (F_b) is exactly equal to the weight of the water (W_w) it pushed out of the way.  Design a mathematical comparison using your data to test this hypothesis.  Record F_b and W_W in the spreadsheet.

Determine the density of the objects.

• Determine the mass m_o of each object and record it in the spreadsheet. (Remember the difference between mass and weight.)
• From the weight of the water displaced by the object calculate its mass m_w and record it in the spreadsheet.
• Use the density of water, 1000 kg/m³, and the mass of the displaced water, to calculate the volume V_w of the displaced water.  Record this volume in the spreadsheet.
• The volume of the displaced water is the same as the volume of the object.  Calculate the density ρ_o of the object  (ρ = m/V) and record it in the spreadsheet.
• Compare the density you found with the density of the materials ρ_t given in the table below.  Try to identify the material each object is made of.  If you cannot identify the material based on the density alone, also consider the appearance of the material.  (Brass and steel have a different color.)

Experiment Deliverables: (to be included in the your journal)

• Table:  Data table (both parts)

• Analysis:  According to Archimedes' principle, the buoyant force is equal to the weight of the displaced fluid.  Do your experimental results verify Archimedes' principle?  Comment on your results.
  Do your experimentally determined densities of the various materials agree with the densities given in the table?  Comment on your results.

Exploration

Open the simulation Under Pressure.

The interface

• You will see an underground basin containing a liquid  The top of the basin is at sea level.
• You can use multiple tools to make measurements.
• Sensors are very sensitive, so you may expect some variations in the readings.
• The "Grid" option makes it easier to estimate the height of the fluid.

Explore how the pressure in the liquid changes as a function of depth, liquid density, filling level, and external conditions.  Determine the densities of the mystery fluid B and the gravitational acceleration on mystery planet B.

Exploration Deliverables: (to be included in the your journal)

• Analysis:

  • As the pressure sensor is moved deeper into the liquid, how does the pressure change?
  • As liquid is added or removed from the basin, how does the pressure near the bottom of the tank change?
  • How does the pressure in the water change when the atmosphere is removed?
  • Keeping all other conditions the same, does the pressure a given distance below the surface depend on the shape of the basin?
  • How is the density of the fluid related to the pressure it exerts?
  • How does increasing gravity change the pressure in the fluid?
  • When g = 9.8 m/s², how does pressure (in Pa) change for each meter of water depth?
  • What measurements of depth and pressure do you need to collect to determine the densities of the mystery fluid B and the gravitational acceleration on mystery planet B?   Explain your reasoning.

• Results:  Densities of the mystery fluid B and the gravitational acceleration on mystery planet B. 

In the next module we will study Bernoulli's equation.  Bernoulli's equations describes the behavior of static fluids and ideal fluids in motion.  For static fluids it tells us how the pressure in a fluid column depends on the position above the bottom where the pressure is measured.
P₁ + ρgh₁  = P₂ + ρgh₂.
For fluids in motion it it gives us a relationship between fluid pressure, speed, and vertical position.  If, for example,  a liquid (or a gas which is not being compressed) is flowing frictionless in a steady state through a horizontal pipe with a varying cross-sectional area, then the pressure depends on the speed of the fluid.

The faster the fluid is flowing, the lower is the pressure at the same height.

This may seem counterintuitive to you, but it is a consequence of conservation of energy.  The molecules of a fluid at room temperature are always in motion, even if the fluid as a whole is at rest.  This disordered motion is responsible for the pressure exerted by the fluid, even in gravity-free space.  In a pipe, it results in collisions with the walls.  If a fluid is flowing trough a horizontal pipe at a steady rate, then the molecules also have ordered motion.  In a narrow section of the pipe the fluid is flowing faster, and more of its energy goes into the ordered motion.  This leaves less energy for the random motion and therefore results in softer collisions and lower pressure.

Exercise

• (i)  Lay your hands on the table in front of you and locate a bulging vein.  Slowly raise your hand until it is well above your head while constantly watching that vein.  What happens?  What height above your shoulders do you first notice a change?   Describe your observations.
  Slowly lower your hand while still watching the vein.  Repeat the process.
• (ii)  Lay two thick books about 10 cm apart.  Place a sheet of paper on the books so that it bridges the gap between them.  Try to blow the paper off the books by blowing underneath it.  Describe what happens.  Do you have an explanation for your observations?
• (iii)  Hold two sheets of paper vertically about 5 cm apart.  Blow the sheets apart by blowing hard between them. 
• (iv)  Hold a straw upright in a glass of water so that the top of the straw projects over the top of the glass.  Place a second straw perpendicular to the first so that the end of the second straw is almost touching the opening of the first, but is not blocking it.  Blow hard through the second straw.

Exercise Deliverables: (to be included in the your journal)

• Analysis:  Describe your observations for parts (i) - (iv).  Do you have explanations for your observations?
  Most people think blowing between two sheets of paper will push them apart.  Why does the result contradict common sense?   How does the speed of the air relate to the 'strength' of the air pushing on the sides of the paper?"

Convert your log into a lab report.

Name:
E-mail address:

Laboratory 7 Report

• Make sure you completed the entire lab and answered all parts.  Make sure you show your work and inserted and properly labeled relevant tables and plots in your journal.
• Add a summary reflection at the end of your report in a short essay format.

Save your Word document (your name_lab7.docx), go to Canvas, Assignments, Lab 7, and submit your document.