How Fast Does a Plume Rise? Convection Speed and Earth's Layers · Chapter 10

Learning target: I can calculate convection speed from a teaching dataset, graph how it depends on the temperature difference, and use real layer thicknesses to see why mantle convection takes millions of years.

Directions

Part A uses a teaching dataset from an imaginary tank experiment; the numbers were written to be realistic, not measured in a real lab. Part B uses the rounded layer thicknesses from this lesson, which are real reference values. Show every calculation with units, graph with a ruler, and write complete sentences for the interpretation questions.

You will need: This worksheet, Pencil, Ruler, Calculator

Part A: A plume in a tank

Imagine a tall, clear tank of still water 30 cm deep with a small electric warming plate under the center of its base. A thermometer sits on the plate and another sits just under the water surface. The operator sets the plate so that the water at the plate is warmer than the water at the top by a chosen number of degrees, waits two minutes, then releases a drop of dye at the plate and times how long the dye plume takes to rise 20 cm. Each setting was run twice. With the plate switched off (no temperature difference), the dye just spread out slowly on the bottom and no plume formed in 120 seconds.

Time for a dye plume to rise 20 cm (teaching dataset)
Simulated teaching dataset: the numbers are invented to be realistic, not measured.
Temperature difference, plate minus top water (°C)	Trial 1 time (s)	Trial 2 time (s)
0	no plume in 120 s	no plume in 120 s
2	47	49
4	31	33
6	24	26
8	20	22
10	17	19

1.Complete the table. Average the two trials, then divide the 20 cm distance by the average time to get the plume speed. Write one full calculation below the table.

Average time (s)	Plume speed = 20 cm ÷ average time (cm/s, to two decimals)
2 °C
4 °C
6 °C
8 °C
10 °C

2.Describe the shape of your graph in two sentences: what happens to plume speed as the temperature difference grows, and does each extra 2 °C add the same amount of speed, more, or less?

3.The temperature difference at 10 °C is five times the difference at 2 °C. Calculate how many times faster the plume is at 10 °C than at 2 °C. Is speed growing as fast as the temperature difference?

5.Extend your curve to predict the plume speed at a 12 °C difference. Give a value with units and say whether you trust it more or less than the measured points, and why.

6.What does this dataset suggest about convection in the ocean or the mantle: what should happen to the speed of a convection loop if the difference between the warm end and the cool end gets bigger? Then name one important way the tank is not like the mantle that limits how far you should trust the comparison.

Part B: Scaling up to the geosphere

The thicknesses below are the rounded model values used in this lesson for the geosphere's three main layers. Together they add up to the distance from the surface to Earth's center, about 6,370 km.

Thickness of the geosphere's layers (rounded reference values)
Layer	Thickness (km)
Crust (continental average)	35
Mantle	2865
Core (top of the core to Earth's center)	3470
Total: surface to center	6370

7.Complete the table to find what percent of the distance from the surface to the center each layer takes up. Check that your three percentages add up to about 100.

Thickness ÷ 6,370 km	Percent of the distance to the center (to one decimal)
Crust
Mantle
Core

8.Mantle rock creeps at roughly 3 cm per year. Calculate how many years it would take rock to travel the full 2,865 km thickness of the mantle at that speed. Convert kilometers to centimeters first (1 km = 100,000 cm). Give your answer in millions of years.

9.In the tank, the plume crossed 20 cm in about 20 seconds. Compare that with your answer to q8. Explain why a tank model can show the pattern of mantle convection correctly while giving a completely misleading idea of its speed.

Keeping the units straight

Speed is distance divided by time, so cm ÷ s gives cm/s. In q8 the distance is in kilometers and the speed is in centimeters per year, so convert the distance first: multiply the kilometers by 100,000 to get centimeters. Then divide centimeters by centimeters-per-year; the centimeters cancel and years are left. Write each unit next to each number as you go, and cross out the units that cancel.

Halve the distance, halve the time?

Suppose the operator repeats the 6 °C run but times the plume over only the first 10 cm and then over the second 10 cm separately. Predict whether the two times would be equal, and explain why a plume might speed up or slow down as it rises (think about what happens to its temperature and density as it moves away from the plate and mixes with cooler water). Then design one more measurement that would test your prediction.