Pressure and buoyancy

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

• metal blocks
• metal cans
• electronic balance

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.

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. 

Experiment

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:

Each group has four metal blocks, a small metal can, a can with a spout, and a container to hold extra water.  Each group will determine the density of the metal blocks using a balance only.

Record all your measurements in a table in your log.

For each block:

Set up the balance.  Turn it on and zero it.  Determine the weight of the metal block.
Note:  The readout of the balance is in kg, the weight is m*g.

Determine the weight of the small metal can.

Fill the can with the spout with water until it overflows.  Catch the overflow in the small can and discard it.
Then lower the metal block into the water and catch the displaced water with the small can.
Determine the weight of the small metal can with the displaced water in it using the balance.
Calculate the weight of the displaced water.
Now we will calculate the buoyant force and compare it to the weight of the displaced water.

Place the can with the spout onto the balance.
Make sure there is enough water in it so you can submerge the metal block, but not enough to cause it to overflow onto the balance when you do submerge it.
Zero the balance with the can on it.

Gently lower the block into the water.  Make sure it is totally submerged but is not touching the walls or bottom of the can.  The water is pushing up on the block with a force equal to w_buoyant.  The scale now measures the reaction force with which the block is pushing down, which is equal in magnitude to the buoyant force by Newton's third law.  Record w_buoyant.

Given the mass of the displaced water calculate its volume. 
The density of water is ρ = m/V = 1000 kg/m³, so V = m/(1000 kg/m³).
The volume of the metal block is equal to the volume of the displaced water.
Calculate the density ρ_block = m_block/V_water.

Can you identify the materials your blocks are made of using your result and the table below and the appearance of the blocks?

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

• Table:  Data table

• 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.

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.