MS20 Laboratory
Sediments: origins, composition and transport
Objectives
1. Recognize lithogenous, biogenous and hydrogenous sediments and some of the rock and
mineral particles from which they are composed.
2. Understand the effects of water density, particle density, particle size and viscosity on particle
settling rate as expressed in Stoke’s Law
3. Investigate the effect of particle size on settling velocity
4. Investigate and determine the effects of temperature and salinity induced changes in water
density on particle settling velocity
5. Understand the concept of underwater sediment flows known as turbidity currents
6. Investigate the effects of water density, slope angle, and particle concentration on the speed
of turbidity flows
Introduction
Sediment is composed of particles of loose, un-compacted inorganic or organic material. These
particles may originate from the weathering or erosion of continental or oceanic rocks, biological
activity, chemical processes in seawater, or extra-terrestrial sources. Whatever the source, the
production of sediment and it distribution to the sea floor is tremendous. Some areas of the sea
floor accumulate several centimeters of sediment each year, creating maximum depths of up to
9 km along the continental slope. Along the southern California coast, sediment is created and
transported into basins on the sea floor in the channel between Catalina Island and the
mainland. In today's lab we will analyze and classify sediment based upon origin, particle size,
particle composition, and particle shape and angularity; and we will look at the mechanism of
transport.
There are four possible origins for a sediment particle. Lithogenous sediments arise from the
weathering or breakdown of parent rock into smaller particles. Biogenous sediments are
created through the actions of living organisms. Coral sands, diatomaceous earth, and
foraminiferous ooze are examples. Those spectacular white sand beaches in Polynesia are
eroded from the skeletons of surrounding coral reefs. Hydrogenous sediments are created by
chemical reactions in water. The precipitation of manganese into nodules, the evaporation and
precipitation of salt (sodium chloride), and the precipitation of limestone oolites are good
examples. The final category includes cosmogenous sediments, which are of extraterrestrial
origin. Two sources include inter-planetary dust (silt and sand
sized particles) that results from collisions between asteroids or
comets, and rare impacts from asteroids or comets.
Interplanetary dust represents about 15,000 metric tone of
sediment per year.
Figure One. Plastic reticle to be used
for sediment measurements
Sediment Size
You will be using a microscope in this laboratory. For use with
the microscope you will need a plastic reticle that is specially
made for examining sand sized particles. The reticle, as viewed
through the microscope, is shown in Figure One. For each
sample you will be estimating the average particle size as well
as the range of particle sizes (smallest to largest).
MS20 Sedimentation Lab version 4/4/2005
Page 1 of 15
Sorting
Sorting is a term geologists use to describe the mix of particle sizes in a sample. Sorting results
from sediment transport. For example, if there were small, medium, and large sand grains all in
the same sample, the sample would be poorly sorted. But if all the sand grains were small
(same size) the sample would be well sorted. Figure Two illustrates the three types of sorting
categories we will use to describe our samples.
Figure Two. Examples of sediment sorting
Composition
Composition describes the mineralogical makeup of the sediment sample. A given sediment
sample may have many different kinds of minerals; however, the samples provided in this lab
are relatively simple and usually have no more than three mineral components. You will be
examining the samples and estimating the percentages of minerals that you learned in the rocks
and minerals lab. You should recall these:
Quartz- clear, glassy mineral, looks like smooth broken glass
Feldspar- milky, yellowish or pinkish mineral, mostly opaque; may be confused with quartz.
Garnet- pink to red glassy mineral, very dense; may be confused with quartz.
Carbonates- chalky fragments of shell, sometimes containing pink fragments of coralline algae.
We will also look for dark minerals and dark rock fragments. These represent many mineral
types and are "lumped together" as “darks” for ease of identification.
Procedure 1: Texture and composition of sediment samples
Texture is a term used to describe the size and sorting of a sediment sample. In this
procedure you will observe the texture and composition of 5 different sediment samples. Place
a pinch of each sample (one at a time) in a sample box. Place the sample box under the
microscope. You will only need to use the top
light on the microscope for this exercise. Look at
the sample through the microscope provided and
estimate the size, sorting, and composition of
each sample. Estimate the composition
percentages to the nearest 20%. Enter your data
in Table One. The estimated percentages should
then be displayed in a pie graph. An example of
such a pie graph is shown in Figure Three.
Figure Three. Example of pie graph
MS20 Sedimentation Lab version 4/4/2005
Page 2 of 15
Table One. Texture and composition of sediment samples
Rock
Fragment
Sand
QuartzFeldspar
Sand
Garnet Sand
Quartz Sand
Carbonate
Sand
Average
Size
(mm)
Smallest
size (mm)
Largest Size
(mm)
Range
(L-S)
Sorting
Pie Graph
%
%
%
%
%
Quartz
Feldspar
Darks
Shells
Garnet
Sediment transport: settling rates
The transport of particles to the sea floor often includes a period of sediment “falling” through the
water column. This is often called “settling.” Five basic factors influence the particle-settling
rate:
1. Size. Increasing size (expressed as particle diameter) usually means faster settling.
2. Shape. A sphere-shaped particle is more streamlined and will settle faster than a disk-shaped
particle, which would tend to slide sideways as it settles.
3. Particle density. Quartz, with a density of 2.65 g/ cm3 will settle more slowly than the garnet
with a density of 4.0 g/ cm3.
4. Density of the fluid. The density of seawater is primarily controlled by salinity and temperature.
Seawater density changes only slightly in the second and third decimal places (1.02 to 1.03
g/cm3). However, in a dense salt water solution, the relative "weight" of the particle will be less
and should settle more slowly.
5. Viscosity of the fluid. The viscosity of the fluid, or internal friction, is also controlled by
temperature and salinity. The salinity effects on viscosity, however, are minor compared with the
temperature effects. (Think of warm and cold pancake syrup flowing from a bottle; which is more
viscous?)
A general equation for settling rate was developed by Stokes. This equation (called Stokes Law)
describes the settling velocity of small, spherical particles:
MS20 Sedimentation Lab version 4/4/2005
Page 3 of 15
where
ds
dw
g
D
µ
Vo
=
=
=
=
=
=
density of solid, g/cm3
density of water, g/cm3
gravity, cm/second2
particle diameter in centimeters
molecular viscosity, g/second X cm
terminal settling velocity, cm/second
In the following experiments you will test this equation by directly measuring settling rates. You
will use a 1.5 m long 2.5 cm diameter plastic tube filled with water as shown in Figure Four. In
our experiments we will investigate the effects of particle size (D), particle density (ds), water
density (dw), and water viscosity (µ) on settling rate. Before we begin, we need the densities of
several water samples (dw) to be used in these experiments. Please complete Table Two.
Table Two. Density of water used in settling and turbidity flow experiments
room temp
0 o/oo
room temp
40 o/oo
room temp
80 o/oo
5º C
0 o/oo
5ºC
40 o/oo
Densities
Procedure 2: Effect of Particle Size (D) on Settling Velocity
In this experiment you will be measuring the settling rate of two sizes of glass (quartz) shot. One,
“fine glass shot,” is approximately 0.025 cm diameter; the other, “coarse glass shot,” is
approximately 0.05 cm diameter.
1. Be sure the rubber stopper is firmly in place in the bottom of the tube, the tube is resting on
the bottom of the bucket, and that the tube is held in a vertical position by the grip clamp (use
angle finder if necessary). Fill the settling tube with fresh water at room temperature, by
transferring approximately 800 mL of water from the tap using a plastic 1L beaker. The tube
should be filled to about 2 cm from the top.
2. Place two small pieces of masking tape 100 cm apart on the tube, leaving a space of
approximately 30 cm from the top of the tube before the first tape marker.
3. Using plastic weigh boats and the 200g capacity electronic balance measure two separate
0.66g samples of the fine glass shot.
4. When you are prepared, pour the sediment sample directly from the weigh boat into the tube,
trying to dispense the entire sample all at once. Note that the grains move as a dispersed "cloud".
Using a stopwatch, measure the time it takes for the front of the shot "cloud" to pass between the
two marks on the tube (100 cm). Record the data below. Repeat the experiment with the second
sample. Compute the average velocity for fine glass shot from the distance (100cm) and the
average time:
fine shot settling velocity = 100 cm/average number of seconds
MS20 Sedimentation Lab version 4/4/2005
Page 4 of 15
Table Three. Fine glass shot settling time (100 cm) and velocity
Time (s)
Velocity (cm/s)
fine glass shot 1
XXXXXXXXXXX
fine glass shot 2
XXXXXXXXXXX
Average
5. Without changing the water in the tube, repeat steps 4 and 5 using two 0.66 g samples of the
coarse glass shot. Compute the average velocity for coarse glass shot from the distance
(100cm) and the average time:
coarse shot settling velocity = 100 cm/average number of seconds
Table Four. Coarse glass shot settling time (100 cm) and velocity
Time (s)
Velocity (cm/s)
coarse glass shot 1
XXXXXXXXXXX
coarse glass shot 2
XXXXXXXXXXX
Average
In this experiment, the diameter of the coarse particle is twice as large as the fine particle., Is the
settling velocity twice as fast? If not, how much faster is it? (hint: Divide the settling velocity of the
large shot by that of the small shot and compare that to the Stoke's equation.)
Procedure 3: Effect of Particle Density (ds) on Settling Velocity
In this experiment we will measure the settling rate of two particles of approximately the same
diameter (0.025 cm), but of two different densities. The particles will be glass shot, with a density
of 2.65 g/cm3, and garnet sand, with a density of 4.0 g/cm3.
1. Use the room temperature water from the previous exercise. Don't refill the tube.
2. Measure two 1.00g samples of the fine garnet sand. Using the method from Procedure 2,
measure the settling time over a 100 cm length for the fine garnet sand. Compute the average
velocity for fine garnet sand from the distance (100cm) and the average time:
fine garnet sand settling velocity = 100 cm/average number of seconds
Table Five. Fine garnet sand 100 cm settling time (s) and velocity
Time (s)
Velocity (cm/s)
fine garnet sand 1
XXXXXXXXXXX
fine garnet sand 2
XXXXXXXXXXX
Average
MS20 Sedimentation Lab version 4/4/2005
Page 5 of 15
3. Transfer your average velocity for fine glass shot (Procedure 2, Table Three) and fine garnet
sand to the following table:
Table Six Average settling times and velocities for fine glass and garnet particles
Average Time
(s)
Average Velocity
(cm/s)
fine glass shot
fine garnet sand
The density of garnet is 1.5 times greater than that of the glass shot. Is the settling velocity
1.5 times greater? (hint: divide the settling velocity of the glass shot by the settling velocity of
the garnet)
The Effect of Water Density on Particle Settling Rate
In denser water the sediment particle will settle more slowly because the relative density
(particle density minus the water density) will be lower. If the particle density is less, it
sinks slower. There are, as you already know, there are two important factors that cause
changes in the density of seawater: temperature and salinity. We will investigate each of
these.
Procedure 4: Effect of temperature induced density changes on settling rate
1. First we will need to empty the settling tube. Loosen the grip clamp and raise the tube
a few inches. Slowly ease the rubber stopper out of the bottom of the tube and allow the
water to drain slowly from the tube. Rinse tube with a beaker full of tap water. Replace
the rubber stopper firmly and place the tube so it again rests on the bottom of the bucket.
Make sure the tube is again in a vertical position. Refill the settling tube with water
approximately 5° C, 0 o/oo provided by your instructor. Its density will also be given to you.
Remember, the density of fresh water reaches a maximum at 4º C, so the density should
be very close to 1.000 g/cm3.
2. Using two 0.66g samples of fine glass shot , measure the settling rates. Compute the
average velocity for fine glass shot in cold, fresh water from the distance (100cm) and the
average time:
fine shot settling velocity = 100 cm/average number of seconds
MS20 Sedimentation Lab version 4/4/2005
Page 6 of 15
Table Seven. Fine Glass Shot fall time (100 cm) and velocity in cold, fresh water
Time (s)
Velocity (cm/s)
fine glass shot 1
XXXXXXXXXXX
fine glass shot 2
XXXXXXXXXXX
Average
3. Transfer your densities (from Table One), average velocity for fine glass shot in room
temperature water (from Procedure 2, Table Three ) and fine glass shot in cold, fresh water to
the following table:
Table Eight. Average settling times and velocities for fine glass particles in room and cold temperature fresh water
Water temperature
Density (g/cm3)
Average Time
(s)
Average Velocity
(cm/s)
Room ( ~ 22° C)
Cold ( ~ 5° C)
What was the difference in water density from room to cold temperature? In this
experiment, the cold water made the glass shot a little less dense (density of glass shot
minus the density of the water). Was the reduction in the settling velocity more or less
than you would expect, given the slight change in density from fresh room temperature
water to fresh cold water? Explain!
Procedure 5: Effect of salinity induced density changes on settling rate
1. Once again we will need to empty the settling tube. Follow the instructions in step 1 of
procedure 4. This time refill the tube with cold, salty water provided in the laboratory.
2. Using two 0.66g samples of fine glass shot , measure the settling rates in cold, salty water.
Compute the average velocity for fine glass shot in cold, salty water from the distance (100cm)
and the average time:
fine shot settling velocity = 100 cm/average number of seconds
Table Nine. Fine Glass Shot fall time (100 cm) and velocity in cold, salty water
Time (s)
Velocity (cm/s)
fine glass shot 1
XXXXXXXXXXX
fine glass shot 2
XXXXXXXXXXX
Average
MS20 Sedimentation Lab version 4/4/2005
Page 7 of 15
3. Transfer the densities (from Table One), average velocity for fine glass shot in cold, fresh water
(Procedure 4, Table Eight) and fine glass shot in cold, salty water to the following table:
Table Ten. Average settling times and velocities for fine glass particles in room and cold temperature fresh water
Salinity and
Temperature
Density (g/cm3)
Average Time
(s)
Average Velocity
(cm/s)
0 o/oo, ~ 5° C
40 o/oo, ~ 5° C
What is the difference in the settling velocities of fine glass shot in the cold, fresh water
and the cold salty water?
In the real ocean, would the temperature or salinity have a greater effect on the particle velocity
as it would settle from the surface to the ocean bottom. Explain.
Procedure 6: Effect of Viscosity on Settling
Velocity
In these experiments we have learned that the
settling velocity of a particle is affected by the
particle size, particle density, and water
density. It is difficult to measure is the
viscosity of the fluid. We can think of viscosity
as the ability of a fluid to flow, as viscosity
increases the ability to flow decreases. From
the Stoke’s Law equation we see that
viscosity (µ) has an inverse effect on settling
velocity. In other words, an increase in
viscosity will result in a decrease in the settling
rate of the particle. Viscosity is directly
affected by temperature, as shown in Figure
Four. The change in water density from fresh
water at room temperature (20º C) to fresh
water at 5º C is an increase of approximately
0.002 g/cm3.
Figure Four. Effect of temperature on viscosity
MS20 Sedimentation Lab version 4/4/2005
Page 8 of 15
Examine the change in viscosity from room temperature to 5º in Figure Four. Which of these
factors, density or viscosity, is more important in determining the settling rate of a particle?
Turbidity Currents
So far we have considered the direct settling of particles vertically through the water column.
Much of the abyssal plain is covered by layers of fine particles deposited slowly, grain by grain
onto the open ocean floor. However, sediment laden currents originating from terrestrial rivers,
creeks and estuaries also provide material. These turbidity currents transport particles of several
sizes through submarine canyons in the continental slope far out onto the deep ocean floor.
These currents have been measured at speeds in excess of 20 km/h. As these current loose
energy, the particles deposit in turbidite layers where the finest particles are at the tops and
largest are near the bottom.
The occurrence of deep-ocean turbidity currents is still being debated by geological
oceanographers. These hypothetical currents are thought to be generated by earthquakes, which
in turn cause submarine slumping. This slumping creates a dense suspension of mud, sand, and
water, which flows down slope toward the deep-ocean bottom. Although a deep-ocean turbidity
current has never actually been observed, there are several lines of evidence that suggest such
flows occur.
In the following experiments we will consider the obvious factors that affect the speed of the
turbidity current as it progresses down slope. These include the difference in density difference
between turbidity current and the water and the steepness (angle) of the slope.
Procedure 7: Effect of Density Difference on Speed of a Turbidity Current
In these experiments you will use the other plastic tube. It is 5 cm in diameter and 1.5
m long; it should be mounted in clamps on the desktop. In addition, you will use two
saline solutions, 40 o/oo and 80 o/oo.
1. Carefully draw off 50 mL of the 40 o/oo solution into a 125 mL Erlenmeyer flask. Dye the
water in the flask with a few of drops of yellow food coloring.
2. Fill the 1.5 meter long, 5 cm diameter clear plastic tube with approximately 3.5 liters
of tap water. Make sure one end is properly stoppered and sealed, and not leaking
water.
3. Place the tube on the table with the stoppered end in the green plastic tray and its
open end in the ring stand clamp so that its angle with the horizontal is 20° (Figure Six).
After the tube is fixed in place, add additional water until the water level is 10 cm from the
open end.
MS20 Sedimentation Lab version 4/4/2005
Page 9 of 15
Figure Six. Turbidity tube set-up
4. Mark the tube with small pieces of masking tape at 0, 33.3, 66.6, and 100 cm increments
down the length of the tube. The 0 mark should be where the tube’s entire diameter is filled
with water, about 10 cm from the open end of the tube (see Figure Six).
Note: You will be measuring the maximum thickness of the turbidity current head at the 66.6
cm mark (see "h" in Figure Seven) and the time at each of the tape marks. You should prepare
before you begin step 5.
5. After shaking the 40 o/oo water in the
flask, quickly pour (don't dump! ) the dyed
salt solution into the open end of the tube
and start the stopwatch when the front of
the turbidity current flows by the zero mark.
Record the head height and times in Table
Eleven below. Calculate the velocity of the
turbidity flow at 100 cm. Remember that
Velocity = 100cm / time (s)
7. Repeat the experiment with the 80 o/oo
water-using a different food coloring. You
do not need to replace the water in the
turbidity tube for this measurement.
Record the head height and times in Table Eleven below. Calculate the velocity of the
turbidity flow at 100 cm. Remember that
Velocity = 100cm / time (s)
Figure Seven. Measurement of maximum height of flow
head at 66.6 cm
Table Eleven. Effect of salinity (density) on speed of a turbidity current, angle equals 20°
Salinity
Head Height
at 66.6 cm
(mm)
Time in seconds at each point
33.3 cm
66.6 cm
100 cm
Velocity at 100 cm
(cm/s)
40 o/oo
80 o/oo
8. Graph the turbidity flows in seconds in Figure Eight. Use an "x" for the 40 o/oo water
and a "o" for the 80 o/oo water. Connect your marks to create two lines.
MS20 Sedimentation Lab version 4/4/2005
Page 10 of 15
Figure Eight. Turbidity speed for 40 o/oo and 80 o/oo water at 20° slope
Is the speed constant down the length of the tube?
Does a doubling of the salinity double the speed of the current?
Does the head thickness remain constant relative to the two densities?
Procedure 8: Effect of Slope Angle on Turbidity Flow
1. Slowly lift the stoppered end of the turbidity tube and empty its contents into the bucket used
in the settling tube exercises. Do this slowly or you will give your lab partner a soaking!
Refill the turbidity tube with about 3.5 L of tap water and then adjust the angle of the slope to
10° by carefully lowering the clamp on the ring stand. You will need to adjust your tape marks
so that the zero mark is again where the tube is completely full of water, and the other marks
are at 33.3, 66.6 and 100.0 cm from the zero mark.
MS20 Sedimentation Lab version 4/4/2005
Page 11 of 15
2. Repeat the experiments above for the 40 o/oo and 80 o/oo salinity waters at the new, lower
slope angle. Record the head height and times in Table Twelve below. Calculate the velocity of
the turbidity flow at 100 cm. Remember that Velocity = 100cm / time (s) Graph the turbidity
flows in seconds in Figure Nine. Use an "x" for the 40 o/oo water and a "o" for the 80 o/oo water.
Connect your marks to create two lines.
Table Twelve. Effect of slope angle on speed of a turbidity current, angle equals 10°
Salinity
Head Height
at 66.6 cm
(mm)
Time in seconds at each point
33.3 cm
66.6 cm
100 cm
Velocity at 100 cm
(cm/s)
40 o/oo
80 o/oo
Figure Nine. Turbidity speed for 40 o/oo and 80 o/oo water at 10° slope
What was the effect of a decrease in slope on the flow speeds of the two different
density waters? (compare speeds from Figure Eight with Figure Nine).
Was there any effect on the turbidity current head thickness due to decreasing the slope?
Which effects on the speed of the turbidity flow more, density differences or slope changes?
MS20 Sedimentation Lab version 4/4/2005
Page 12 of 15
Procedure 9: Effect of Sediment Concentration on Turbidity Flow
In this set of experiments you will use two sediment suspensions, one high density, and the other
low density. Your first task is to obtain and determine the density of the suspensions.
1. Carefully tare (zero the weight) an empty 10 mL graduate on one of the balances. Your
instructor will demonstrate this.
2. At the sink, your instructor will dispense 10mL of the low density suspension into your tared
graduate. Your instructor will also dispense 50 mL of the suspension into a 125mL Erlenmeyer
flask which you will use in the flow experiment.
3. Weigh the graduate to the nearest 0.01 gram. Record the weight in Table Thirteen. Calculate
the density and record it in table Thirteen. Remember, density = mass/volume and 10 mL is equal
to 10 cm3, thus
Density = Weight of the suspension
10 cm3
4. Repeat steps 1 and 2 for the high density suspension. Weigh the graduate to the nearest 0.01
gram. Record the weight in Table Thirteen. Calculate the density and record it in Table Thirteen.
Transfer the density values to Table Fourteen, as well.
Table Thirteen. Weight of 10 mLs and density of high and low density suspensions
Weight 10 mL (g)
Density g/cm3
Low Density Suspension
High Density Suspension
5. Empty the turbidity tube using the bucket as you did before. Refill the tube with tap water, readjust the slope to a 20º angle and re-set the tape marks.
6. When you are ready quickly pour the low density suspension into the turbidity tube. (Don't
dump the suspension!) Note the times as the turbidity current head flows past the marked points.
Note the height of the head at 66.6 cm. Record your data in Table Fourteen.
7. Empty the tube. This time you may benefit from rinsing the tube once or twice with a liter of
clear tap water. Repeat the experiment with the high density suspension. Note the times as the
turbidity current head flows past the marked points. Note the height of the head at 66.6 cm.
Record your data in Table Fourteen.
Table Fourteen. Effect of suspension density on speed of a turbidity current, angle equals 10°
Suspension
Density (g/cm3)
Head
Height at
66.6 cm
(mm)
Time in seconds at each point
33.3 cm
66.6 cm
100 cm
Velocity at 100 cm
(cm/s)
Low
High
MS20 Sedimentation Lab version 4/4/2005
Page 13 of 15
8. Graph the turbidity flows in seconds in Figure Ten. Use an "x" for the high density suspension
and a "o" for the low density suspension. Connect your marks to create two lines.
Figure Ten. Turbidity speed for high and low density suspensions at 10° slope
In the box in Figure Eleven draw the head region of the turbidity current, and indicate flow patterns
around the head region.
Before you empty and clean the tube, consider this
question.
Look on the under side of the tube. What do
you see, and how might this be related to
sediment transport in the ocean?
Figure Eleven. Shape and flow around the head
region of the turbidity flow.
These sediment suspensions are much denser than the salt water solutions. Would
you expect them to travel faster and farther in the ocean?
MS20 Sedimentation Lab version 4/4/2005
Page 14 of 15
Procedure 10. Measured versus Theoretical Turbidity Flow Speeds
Your work to this point has shown that turbidity current density is one of the more important factors
controlling velocity, while bottom slope seems to have little effect. In fact, researchers have
determined that the speed or celerity (C) of the turbidity current is governed by the following
equation:
where
d1 =density of the turbidity current
d2 = density of the ambient fluid (in this case the tap water) = use 1.000 gm/cm3
g = gravity, 980 cm/sec2
h = thickness of the head of the current
From the data tables in Procedures 7, 8 and 9, carry forward to Table Fifteen the measured
velocities, head thicknesses, densities, then calculate the theoretical speed of the turbidity current
using the equation shown above.
Table Fifteen. Measured and theoretical velocities for turbidity currents
Experimental
Measured
d2
h
d1 - d 2
Procedure
dl
condition
velocity
o
1.000
40 /oo 20°
7
gm/cm3
slope
o
1.000
80 /oo 20°
3
gm/cm
slope
o
1.000
40 /oo 10°
8
gm/cm3
slope
o
1.000
80 /oo 10°
3
gm/cm
slope
low density
1.000
9
suspension
gm/cm3
high density
1.000
suspension
gm/cm3
Theoretical velocity
(cm/s)
Which are larger, the theoretical or the measured velocities? Why? Where might the errors be in
your experimental results?
MS20 Sedimentation Lab version 4/4/2005
Page 15 of 15