Bouyancy, temperature, and heat budgets

LAB 4 – Bouyancy, temperature, and heat budgets

Part A. Hands-on exercises: Pressure, buoyancy, convection, ideal gas equation /40

Apparatus:
Wood blocks of different dimensions; Clear or rubber hose siphon tubing and 2 buckets, beakers with different water levels; Alcohol thermometers, table of water densities, dH2O, hot plate for stirring only, Erlenmeyer conical flask, stir bars, rubber stoppers with holes and 1” glass tubing inserts; Saturated salt solution; Two tall cylindrical beakers, water, food coloring, 2 salsa containers, rocks or sand.

Introduction Pressure and Buoyancy

Fluids surround us, and they are particularly well suited to deliver and distribute the heat and chemicals essential to life. We are carbon- and water-based creatures on an ocean planet, breathing the oxygen/nitrogen atmosphere created by our green co-conspirators. In this collection of laboratory encounters with fluids, we will attempt to demonstrate the key properties of fluids, particularly those which pertain to the oceans and atmosphere.

Pressure and buoyancy

Fluids sit, move and accelerate under the action of forces: both body forces like gravity, momentum and surface-contact forces. A small cube-shaped region of fluid feels such surface forces on its “faces”, known as ‘pressure’ and ‘viscous stress’. The average (at a point, over all directions) of such forces normal to the cube’s faces is known as pressure, and the net force (the average of the normal vector force on all six faces) is the pressure gradient. It is this particular surface-contact force that tends to compress, the cube, changing its volume slightly. The surface forces, tangential to the faces of the cube which tend to deform its shape, are known as viscous stress.

It would be wonderful if we could see pressure, perhaps by a change in color of the fluid, but we can see its effects [In fact, specialized paint exists which changes color in response to pressure; it is used in wind tunnels to give a complete picture of the pressure field on the surface of an airplane during high-speed flow].

The pressure at any given point of a non-moving (static) fluid is called the hydrostaticpressure (i.e. the pressure exerted by a fluid at equilibrium due to the force of gravity). This is akin to what a fish feels or you at the bottom of a swimming pool. In open conditions, fluids generally conform to the principles of fluid statics (even in the ocean where there are waves and currents) because water is incompressible and a Newtonian fluid, the fluid motions create only negligible changes in the pressure.

Extreme hydrostatic forces. Despite the gentle nature of hydrostatic pressure force in the lab, one should remember that at the bottom of the sea, say 5000 m depth, the pressure is about 5000 decibars or 500 times the atmospheric pressure. This is 5 x 107 Newton meter-2. It is great enough to crush oceanographic instruments, especially ones sealed with just 1 atmosphere of pressure inside. Submersible vehicles like Alvin or Pisces need really strong walls and designs (think 10 cm thick Titanium spheres!) to avoid being crushed during descent. Remarkable species of fish and cetaceans (whales, dolphins) can move through great changes in pressure without suffering; several species of whales dive rapidly to depths of 800 m or more in search of food.

Experiment 1: The siphon (tubing, clamps, cotton butcher’s cord, beakers, trays)
The hydrostatic pressure principle, and Bernoulli’s equation for more general flows, explain the wonders of the siphon: in an inverted U-tube, water rises a great distance before falling down the other arm and exiting. The siphon is such an important tool in the laboratory that it deserves a brief introduction. It is useful for transferring water from source buckets to experimental apparatus, and in providing a continuous inflow to model jets and rivers.

Make a siphon and test it at different levels (below source, same as source and above source). Making a siphon work is an exercise in humility. Some rules: wide diameter tubing makes for a fast-flowing siphon, yet is difficult to start (and stop!). Thin tubing works fine but is slow. Start a siphon by filling the tube with fresh water, pinching in firmly near the middle (which will prevent flow everywhere in the tube) and immersing one end in the source water. Both ends should be secured, for example guiding them loosely through a pinch clamp. The normal accident is that the tube is not secured, the inflow end flips up above the water surface and the siphon is ‘broken’. Sucking fluid from one end, the siphon can be reestablished but only at the expense of a large mouthful of water. It is not necessary, and may even be dangerous, to suck fluid into tubing. By holding the tube under a water tap or immersed in water, it can be filled without oral contact.

The siphon is rather difficult to get right; wouldn’t it be nice to invent a ‘self-priming’ siphon that would start up whenever the water level exceeded a certain height? Imagine how this might be done. One way is to use capillary fluid-surface effects, which cause fluid to climb up a wick. A piece of string draped over the edge of a beaker of water will eventually drain it out!

1a) Place a full beaker on a dry tray and get a fat piece of butcher’s chord to try it. Draw your results and show the time it took to drain your beaker partly. /3

1b) Draw a tube siphon that works to draw fluid from one reservoir to another and explain how this works (hint: think about atmospheric pressure) or can fail! Draw 2 or 3 positions and the direction of flow /8
Experiment 2. Buoyancy, floating and specific gravityMaterials: buckets in sinks, plastic cups, rectangular and different shaped (sphere, cone, cylinder, prism) wooden blocks, wooden chop sticks, dry foam sponges, plasticine.

Archimedes principle is based on the assumption that if we place a rigid body in a fluid, the molecular rebounds from its surface will have the same momentum as would the molecular flux from the fluid previously there, and hence the vertical force on the rigid body must equal (minus) the weight of the fluid previously there. This is simply a symmetry argument for an ideal gas, but is a more touchy assumption for a fluid. Perhaps we should just say that if it is not true, we can blame some ‘chemical or physical reaction’ between the fluid and solid molecules like hydration or water-logging. But nonetheless, it seems to work: the net ‘buoyancy’ (the force due to pressure exerted on an immersed object) is equal to the weight of fluid replaced by it.

Specific gravity is the basis of floatation and buoyancy. A partially immersed ‘buoy’ of mass M has a hydrostatic pressure force supporting it. For the buoy to float, the force exerted by the mass must be less than the hydrostatic pressure. Questions of the stability of floating objects, whether they float ‘vertically’ or ‘horizontally’, can be worked out using simple hydrostatic pressure and moment of inertia ideas, and have application to the rolling over of icebergs, and the floating of ‘dead-heads’ (logs that float nearly vertically in local waters). Sailboats need weighted keels to keep them floating upright. The floating and bobbing of deadheads principle has been used to generate electrical power, by using the mechanical energy of flotation and waves, to power an instrument package or to even generate larger amounts of electricity in “wave power generators”. Long deep buoyant floats have also been used to stabilize large offshore floating platforms strung between them.

Stability of floating objects. If a rectangular polyhedron floats on a water surface, will it also float happily, after being rotated 900 to the vertical? A log floats lying horizontally on the sea-surface, yet sometimes you see logs floating vertically (‘dead heads’) or at an angle. A very light solid of foam rubber floats either way. The stability can be studied by tipping the solid slightly, and seeing whether it erects itself or tips completely over. This can be worked out by calculating the moment of the hydrostatic pressure about the center of mass of the object: this torque will either restore equilibrium or cause a tip-over. Play with wooden blocks of various dimensions in the sink and study this phenomenon qualitatively. Try an empty a plastic cup and then add ballast (water or plasticine) and compare stability.

2)Draw and describe your findings showing dimensions and the directions of the forces, stability or rotations involved which act on 4 floating objects of different shapes & characteristics. /8

Experiment 3: Convection
Apparatus: large beaker, food coloring, disposable pipettes, hot plates, rocks and tongs to put hot rocks in cold beaker. 100°C Alcohol Thermometers. White screen for back of beaker to see convection.

Simple convection. A ball of fluid with density less than its surrounding fluid will rise, for the same reason that objects float. Archimedes’ argument holds. Heating a fluid from below will cause this to happen, in diverse and complex ways. You will see at the beginning a ‘mushroom’ shaped buoyant ‘thermal’ rising, followed by a continuous ‘pipe’ of warm fluid. (Think of starting a fire in a cold fireplace.) Even with gentle heating this will likely go unstable and produce turbulent convection. A large-scale upwelling is driven, as the rising thermal plume drags nearby fluid upwards along with it. Eventually the thermal will produce stratification in the fluid as a whole. Ironically, heating the fluid from below can create stable stratification (warm layer on top), provided the heat source is not uniformly distributed along the bottom.

Procedure: Heat some very hot water and rocks to use for secondary heat sources, using 1 per cold beaker. In a beaker of cold water, measure and record the initial temperature profile (i.e. top, middle and bottom of beaker). Using tongs, place a hot rock into the beaker and quickly squirt a little dye directly on the submerged rock using a disposable pipette before it cools. Measure and record the final temperature profile.
3) Draw and label the temperature profiles at 3 or more stages, record the cumulative time and temperatures for each stage and describe the final stratification. /8
Experiment 4: Heat transfer – convection and conduction

Equipment:
Plastic cups, water, food coloring, rock pieces.

Early Preparation:
Freeze a little water with food coloring in half the cups and water with rocks/sand and food coloring in the other half. Place cups in the freezer until the water is frozen.

Procedure:
1) Two tall beakers, A and B, are filled with hot water (3/4 full only).
2) Take the ice out of the plastic cups and carefully place it in the tall beakers: The ice with rock/sand in Beaker A; the ice without rock/sand in Beaker B.
What happens in each beaker a) immediately, b) after 10 minutes /8

4-1) Beaker A and Coloured Ice
a)

b)
4-2) Beaker B and Coloured Ice with Rocks
a)

b)
Experiment 5: Ideal Gas Equation (Equation of state)
Apparatus: Erlenmeyer flask (sloping sides), rubber stopper with hole, glass tubing, Alcohol glass thermometer, magnetic stir bar and stirring hot plate, insulating material to wrap flask, ruler

Water is composed of H2O molecules in close proximity, with weak dipolar (hydrogen) bonds between them. Polar molecules like this behave very differently than non-polar substances like oily or gassy hydrocarbons. The ‘hydrogen bond’ is an unusual form of molecule and bond, and water is thus, an usual substance. The two hydrogen atoms are covalently bonded to the central oxygen atom with an angle of 104.50. This gives the water molecule an electrostatic dipole moment. It is like a partially ionized substance. For ocean water which is salty, the ions from the salts additionally provide ion-dipole forces to make the salt water hold together even denser and to freeze at lower temperatures and boil at higher temperatures. If an electric field is applied by putting two charged conducting plates in water, (holding them at different voltages) the water molecules orient themselves, causing an induced field that opposes the applied one: water is thus a dielectric material.

Most ordinary non-polar substances have solidification and boiling points that increase with molecular weight. Basically the bigger the atom or molecule, the stronger the intermolecular forces, so they stick and tangle with each other. Based on its place in this mass and size sequence, ice should melt at –100°C and water should boil at –80°C. The “error” of 180°C in the boiling point is due to the hydrogen bonds that form, holding water molecules in a loose matrix so that they are not individual particles but little nets and clumps of them. Hydrogen bonds are known to be weaker than normal covalent bonds which hold molecules together (say, in a H2 molecule) yet can be stronger than monovalent ionic bonds like that which holds Na+Cl- together as a solid salt crystal. For this reason many natural ionic substances like most rocks and minerals dissolve or weather, going into solution in water. This polar dissolution mechanism is where the salts really come from.

Fresh water has a nonlinear equation of state, with a maximum density at about 40 C. This property determines the temperature and density at the bottom of the ocean. The curvature (non-linearity) of water’s physical properties as a function of temperature, causes a mixture of hot and cold water to have a density different from the average of the two original densities. This is because there is a balance at any temperature for the tendency of water molecules to swim around freely and individually, versus being attracted to each other in clumps by hydrogen bonds. The lower the temperature, the more the hydrogen bonding and the large the molecular clumps of water. At lab temperatures, water molecules stick together in clumps of a few tens of molecules. This changes the availability of water to dissolve other substances, making solubility an entirely empirical property (we can’t predict it, we have to measure it). This also limits the size of droplets that form under condensation or spraying of aerosols.

Procedure:
The shape of the density/temperature/salinity curve for water is worth exploring. Take a flask with sloping sides and fit a stopper with a hole. Insert through the hole a glass tube to act as a ‘chimney’. Determine the proper filled volume of your flask with the stopper fitted (i.e. with no air gap) by using a graduated cylinder.
5-1 Now fill the flask with equal volumes of hot and cold tap water, ensure the volumes you use are exactly half of the total flask volume you just measured. Measure the half volumes of hot and of cold water with a graduated cylinder and note down their initial temperatures. Record data below.
5-1a Total volume of flask to 0.1 mL ______________ (1)

5-1b Cold tap water initial volume ______ temperature to 0.1°C ______ (2)

5-1c Hot tap water initial volume _______temperature to 0.1°C _______ (2)

Drop the stir bar into the flask. Insert the stopper so that there is no air gap inside. Press down until water rises half way up the tube.

4-1d Measure the height of the water above the stopper.____ (1)

Now place the flask on the lab temperature stirrer. Watch the height of the water column in its glass chimney. It may slowly fall, as the hot water cools (this effect can be minimized by balancing the hot and cold temperatures, or by wrapping insulation round the flask).
Switch on the stirrer, and watch the column height change as the hot and cold waters mix. Just use the stir function and your hot plate should be turned off and cool to the touch.

4-1e Record the height after stirring _____ & the change in height ______ (2)

4-1f What does this tell you about the relationship between the temperature and density of fresh water? Is it linear or not? Can you tell whether the colder water was disproportionately dense or the hot water disproportionately ‘fluffy”? (4)

5-2 A companion experiment investigates the effect of salinity on density. Put a layer of salty water beneath a fresh layer, at the same temperature. When the stirrer is turned on, what happens and why? /2
5-2a Total volume of flask to 0.1 mL ______________ (1)

5-2b Deionized water initial volume ___ & temperature to 0.1°C _____ (2)

5-1c Salt water initial volume ______ & temperature to 0.1°C _______ (2)

Drop the stir bar into the flask. Insert the stopper so that there is no air gap inside. Press down until water rises half way up the tube.

5-1d Measure the height of the water above the stopper.____ (1)

Now place the flask on the lab temperature stirrer. Watch the height of the water column in its glass chimney. Switch on the stirrer, and watch the column height change as the salt and fresh waters mix. Just use the stir function and your hot plate should be turned off and cool to the touch.
5-1e Record the height after stirring _____ & the change in height ______ (2)

5-1f What does this tell you about the relationship between the salinity and density of fresh water? Is it linear or not? Can you tell whether the saltier water was disproportionately dense or the fresh water disproportionately ‘fluffy”? (4)
5.3 Draw and label your flask experiments with the 2 water temperatures and 2 water salinities. Label the volumes and temperatures or salinities of water you used. Estimate the volume change of mixing in each case. Explain your diagrams with captions or labels. /8

This says something about the way salt molecules hide among water molecules. A simple ideal fluid without the hydrogen bonding and ion-dipole forces would not change in total volume when low-density and high-density fractions are mixed together.

These two experiments give us two ‘cuts’ across the equation of state, ? as a function of Temperature, Salinity (actually T, S and P, the pressure, but we are staying near atmospheric pressure). The shape of ?(T,S; P) is a sloping plane, which is slightly curved (see the two color figures provided separately that show the oceanic range of salinity (above) and a larger range of salinity, down to zero (below); note the density maximum at 4°C which exists only near zero salinity. Salinity is expressed in kg salt/kg seawater x 10-3 or ‘parts per thousand’. Oceanic salinities are typically 2 to 3.6 % or 20 to 36 parts per thousand. Salinity decreases where fresh water enters oceans at river mouths or from rainfall. Salinity increases by evaporation, by freezing (salt exclusion from ice) and by mineral solutions from weathering, hot springs and other submarine discharge of high pressure waters all involving rocks.

Look on My course website at the “Graphs for Water” file below this lab posting to visualize and answer the questions with a little deeper understanding. I have assembled some graphs and written a few notes below them for you to use.

Below is a flow chart for how salinity, temperature and density vary in the ocean system in response to some common processes.

For more background information on density and salinity changes in Earth’s oceans go to: http://sciencelearn.org.nz/Contexts/The-Ocean-in-Action/Science-Ideas-and-Concepts/Ocean-density

From the pull down menu on this site, explore how salinity and temperature vary in the world’s oceans. When these simple physical relationships occur in a real ocean basin with variations in: depth, coastlines, insolation, season, climate etc., it gets irregular and complicated looking!

What happens when density changes

Part B – Web based exercise using interactive maps & computer videos

PURPOSE: The purpose of this web-based laboratory exercise is to review the fate of solar energy as it passes through the earth’s atmosphere and contacts the earth’s surface.
We know that temperatures at the earth’s surface vary in space and time. Here we consider the global and local factors that influence temperature, we compare trends throughout a day and throughout a year, and compare temperatures between continental and maritime locations.

1. Global Energy Patterns

A) The solar energy that reaches the earth’s surface is either absorbed or reflected. Go to:
http://geography.uoregon.edu/envchange/clim_animations/index.html
Look at the first image (run the animation), the Net Short-Wave Radiation file.
After examining the image, explain the relationship between net shortwave radiation (the images) and insolation. /2

B) Now look at the Net Radiation on the same website, which combines short and long wavelengths. In the December view, we know that the Southern hemisphere is tilted towards the sun, and south of the Antarctic circle there is daylight for 24 hours a day, but Antarctica is still barely ‘soaking up’ the sun. One reason for this is that the angle of the sun on Antarctica is still fairly acute. What is another reason why Antarctica is only slightly above a positive net radiation at this time of year? /1

C) The proportion of insolation that is reflected or absorbed varies according to the physical properties (color, texture etc.) of the surface. Albedo is a measure of the reflectivity (intrinsic brightness) of a surface. A surface with high albedo will have high reflection and low absorption of insolation. Use your textbook to list some natural Earth surfaces that have high albedo and some that have low albedo. /6

Low Albedo High Albedo

1 1

2 2

3 3
2. Global Effects of Water
Now, on http://geography.uoregon.edu/envchange/clim_animations/index.html
go down to the Non-Radiative Components. Read the paragraph next to Change in Heat Storage. Keep in mind, as this paragraph explains, that a positive change in heat storage means that heat is being released from the substance, and a negative change in storage means that the substance is absorbing heat from the atmosphere.

A) What is the range of the changes in heat storage of continents throughout the year? (give units from map differences) /2
B) What’s the range for the oceans? /2
The reason for this difference is the different specific heats of water and soil/rock.
Recall that specific heat is the amount of energy necessary to raise the temperature of 1 cubic cm of a substance by 1 degree Celsius.

C) So which substance has a higher specific heat? (Circle it) Continents, Oceans List the specific heat of “Land” ________ and Ocean ________ /3

D) Which one of these requires more energy to raise its temperature?
(Circle the higher one) Continents, Oceans /1

E) Which one has a higher heat storage capacity: (Circle it) Land, Ocean /1
F) Now, take a look at the Northern Atlantic and Pacific Oceans, and the Arctic Ocean on this website. Pay particular attention to the contours as the cross the land-sea boundaries.

What is the effect on air temperature of the oceans’ changein heat storage in the months of November to February? (Circle the correct two below) /2
F-1) 1. Raising or 2. Lowering
F-2) 1. Moderating (less extreme) or 2. Emphasizing (enhancing differences)
G) The high specific heat of water is one reason for the effect water has on the continents and on global weather in general. Give two other reasons for the ocean’s moderating effect on temperature compared to the continents. /4
G-1.

G-2.

Using what you now know about specific heat, take a look at the global temperatures farther down the http://geography.uoregon.edu/envchange/clim_animations/index.html
page. Notice that both the hottest and coldest places throughout the year are landmasses.

Isotherms are lines on a map that connect points of equal temperature and are useful to show temperature patterns. Here, the isotherms are delineated by different colors.
Compare North America in December and in June.

H) In December, which direction do the isotherms bend when they enter North America from the Pacific Ocean – North or South? /1

I) Which way do they bend in June – North or South? /1

This effect on the warmth of the coastal areas relative to the rest of the continent is called the maritime influence, or the marine effect.
J) Briefly describe what is happening by comparing summer and winter. /2

K) What is the result of the continental effect or “continentality” in summer and winter? /2
L) What’s one reason why this pattern is not as clear in the British Columbia/Alaskapanhandle region of North America, or on the west coast of the South American continent? /2
3. Daily Temperature Variations

A) At what time of day does the maximum insolation normally occur? /1
B) But, in the summer, when is the average maximum daily temperature? /1
11am-1pm or 1pm-3pm or 3pm-5pm

C) Why? /2
20) The minimum daily air temperature generally occurs at sunrise. Why? /2

4. City Comparisons

Go to http://www.climate.weatheroffice.ec.gc.ca/Welcome_e.html

Go to“Climate Normals & Averages.”Enter the names in the location box for Victoria, BC International airport and Winnipeg, Manitoba (airport).

A) Describe the annual temperature trend for Victoria and Winnipeg, including their temperature range, and explain the reason for their difference. /4

B) Just looking at the average maximum temperatures, Victoria and Winnipeg have similar monthly means for May, but conditions for this period are
probably not the same. Describe temperature differences that likely exist between Victoria and Winnipeg during this time. For example, what about differences between the beginning and the end of May, as well as the differences in daily temperature fluctuations that are also not readily apparent in the monthly averages. Explain. /4

5. Canada – Coast to Coast Comparisons

Continuing on the theme of spatial influences on temporal differences in temperature, go to the site for Halifax airport.

A) Compare the data for Victoria and Halifax, and give a brief summary of similarities. Explain the reasons for this. /4
B) Compare the data for Victoria and Halifax, and give a brief summary of differences. Explain the reasons for this. /4