Density-driven Flows

Developed by Brendan Hanger, Penelope King, Stephen Eggins, Ross Griffiths & Andy Hogg.

Research School of Earth Sciences, Australian National University

This practical includes exercises to demonstrate how flow on the Earth can be driven by gravity acting on density differences between fluids. The flow is driven by buoyancy forces. Buoyancy is the driving force for the ventilation of the deep oceans, seasonal overturning in lakes, the Hadley circulation of the atmosphere and convection in the Earth’s mantle (which drives plate tectonics).

Aim: This practical will enhance your understanding of salinity and density of a salt solution, and develop your skills in making simple laboratory measurements; data entry, calculation, graph plotting in a spreadsheet; and comparing experimental data with a theoretical relation.

For this practical you will need to form groups of 3-4 people. Group members will need to cooperate in carrying out the experiments and recording the data. A spreadsheet has been provided (Density Flow_Resultsblank) for you to use for recording your results and performing the calculations.

Equipment:

Each group will have:

•A Plexiglas tank with a sliding barrier

•Salt (sodium chloride)

•Food dye (multiple colours)

•Spoon, ruler, buckets

•Electronic weighing scales and jug/beaker

•Digital density meter (shared by class)

Access to a laptop is desirable (bring your own or borrow one in the lab).

Experimental Procedures:

The full experimental procedure is described in the pre-lab video:

Part A

The aim of Part A is to determine how the speed of a buoyancy driven flow depends on the density difference. This will require flow speed data from multiple experiments that use a range of density differences.

  1. Fill the tank with freshwater to about 150 mm[1] depth. Insert the barrier about 100 mm from one end. Weigh out about 5 g of salt (about 1 teaspoon) and dissolve it in the smaller compartment created by the barrier. Add a few drops of food dye to the same compartment. Mix the salt and dye thoroughly.

The density of dilute sodium chloride solutions at 20˚C (⍴solution) is given approximately by:

⍴solution = ⍴0 (1+ β S)(1)

where⍴0= 998.2 kg/m3 is the density of freshwater at 20˚C,β= 0.716 is a constant ‘contraction coefficient’ and S is the ‘salinity’ (measured in kg of salt/kg of water). Typical seawater for example, has S ≈ 0.035 kg/kg (or S ≈ 3.5%) and density⍴sea water≈ 1022 kg/m3 at 20˚C. ρ0 will change if the water in the tank is not fresh, for later runs it will relate to total amount of salt added. Remember that density (ρ) is mass (m)/volume (V), and V = L x W x H.

  1. Record the water depth in the tank, the length of the small chamber behind the barrier, the amount of salt added, and the densities[2] on both sides of the barrier [using the digital density meter and equation (1)]. Carefully and quickly pull the barrier out vertically. The salty solution will flow along the bottom of the tank as a density (or gravity) current.
  1. Use a timer (e.g. phone) and record the elapsed time (to nearest 0.1 s) for the current to pass the positions along the tank. (The group will need to cooperate to record these readings.) A spreadsheet for collecting your results has been provided in Wattle in the practical section.
  1. Thoroughly mix the tank, insert the barrier again and add a larger amount of salt to the small chamber, plus some dye, and mix. Record your measurements again, including the two densities. Release the current and measure speed again.
  1. You should perform four successful experiments using varying amounts of salt between 5 and 150 g, noting both the amount of salt added for each run and the total that has been added since the beginning. Refill the tank with clean tap water when you have too much dye. Try to use the same depth and record the time for the density flow to pass the same distances in all experiments.
  1. Provide a table of results from your four experiments, also please calculate the density of the salty water in the first run using equation (1).

Data Analysis – required for the assessment – please do this duringthe practical time, after completing Part B.

a)A spreadsheet is available in Wattle for this exercise. Enter the data for each experiment from which you have valid measurements (title the columns, show units). The data will be:

  • Experiment number #
  • The water depth H,
  • Length of the small chamber L,
  • The amount of salt added M,
  • Density of liquid in large compartment (⍴1) before the barrier is removed,
  • Density of liquid in small compartment (⍴2) before the barrier is removed,
  • A series of measured positions x and elapsed times t.

In other columns calculate 1) the fractional density difference Δ⍴/⍴=(⍴2 − ⍴1) / ⍴1 (in kg/m3) and 2) the speed u of the current (in m/s), along with an average speed U for each experiment.

The Density Flows Results blankspreadsheet gives an example of how to set out your data table.

b)A theoretical prediction for the speed of the front of the current is:

(2)

where a is a constant, U is the average speed of the current (in m/s), g = 9.8 m/s2 is the acceleration due to gravity, H is the depth of water (in m), ⍴1 is the density of the water in the larger chamber (in kg/m3) and Δ⍴=⍴2 − ⍴1 the density difference between the two chambers (small minus large in kg/m3).

c)Plot YOUR group’s results for the average speed (U) as a function of the fractional density difference (Δ⍴/⍴) using one symbol.

Goals and Hints for teaching staff:

  • Don’t wear white or easy to stain clothes, we’ll be playing with food dye.
  • Keep an eye out for water spills, and make students clean them up. Mops will be available, as well as wet floor signs. Hot water is better for mopping up than cold water.
  • Watch out for electronics (phone, laptops, etc.) and water
  • Make sure all wet work is on bench coat
  • Ensure they don’t use massive amounts of dye or salt
  • Make sure students record density to as many significant figures as possible, many of the difference s are relatively small.
  • Ideally the barrier should be set up 10cm from the end of the tank.
  • Encourage students to work together as teams
  • Record data as a team, share by email,
  • Split duties: timing, data recording, pulling barrier out, etc.
  • Record who their team is.
  • Ideally they should do the data analysis in the lab, after completing Part B.
  • Emphasise that the assessment involves this data

Part B

The experiment in Part A does not simulate all ocean processes – it is time to design your own experiment to test/mimic another ocean circulation/current phenomenon (process) you have learned about during oceans week! You may access any of the materials that you used in previous labs as long as it does not cause an OHS risk or damage the tanks – just ask a demonstrator or staff member if they can help provide you with what you need.

You may consider using:

another barrier, rocks, a battery-driven fan, ice, warm water (not too hot), thermometer, recording the experiment on video, etc.

Record your experiment: you can record your experiment in several ways including by providing a data table, taking a video or photos or other methods, however you should have some record of it.

Note information from this experiment is required for one of the questions in the Assessment.

Goals and Hints for teaching staff:

  • Encourage students to think about what they learnt in the lecture and workshop when designing their experiments, examples include:
  • Different densities colliding
  • Stratification (layers)
  • Effects of topography (use rocks)
  • Multiple temperatures (ice, hot water)
  • Wind interactions (fans, egg-beaters)
  • Make sure they record what they do well
  • Video it
  • Take pictures
  • Make measurements
  • Share records with whole group
  • Have fun and be creative
  • This is one of the most enjoyable practicals in the course

Tank Description

The tanks we use for this activity have been constructed by our workshop, however any long tank could be used. The tanks have internal dimensions of 80 mm (W) x 200 mm (H) x 800 mm (L), and are constructed from 10 mm thick clear rigid plastic, as shown in Figure 1.

Figure 1: Tank using in density-driven flows experiment

The barriers are made from the same materials, and sized to provide a watertight fit once inserted (Figure 2). They feature a cut-out handle, and have a rubber door seal around the edge, on occasion silicone grease may be needed to allow easy removal. Dimensions are 270 mm (H) x 76 mm (W), the hole is 55 mm (W) x 30 mm (H), and is designed to fit 3-4 fingers.

Figure 2: Barrier used to separate water masses

Figure 3 shows how the experiment is set-up immediately prior to the removal of the barrier.

Figure 3: Experimental set-up at time of barrier removal

1

[1]For the International System of Units (SI units) you can use multiples of the basic unit (in this case metre (m) is the basic unit for length, mm is a thousandth of the metre = 10-3 m).

[2]The digital density meter reads the actual density ⍴ in g/cm3, which you will need to convert to kg/m3.