Name Lab Section Date. Investigating Stokes Law Sediment Lab ds = density of solid, g/cm dw = density of water, g/cm g = gravity, 980 cm/second 2 D = particle diameter in centimeters μ = molecular viscosity, g/second X cm V o = terminal settling velocity, cm/second You will investigate Stokes Law by measuring settling rates. You will use a 1.5 m long 2.5 cm diameter plastic tube filled with water. Table 1 records the densities of several water samples. room temp room temp room temp 5º C 5ºC 0 o / oo 40 o / oo 80 o / oo 0 o / oo 40 o / oo Densities 0.997 1.027 1.058 0.999 1.02 Table 1. Density of water (dw) used in settling and turbidity flow experiments 1. Effect of Particle Size (D) on Settling Velocity In this experiment you will measure 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. A. Be sure the rubber stopper is firmly in the bottom of the tube, the tube is resting on the bottom of the bucket, and that the tube is held vertically 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 side table using a plastic 1L beaker. The tube should be filled to about 2 cm from the top. B. Place two small pieces of masking tape 100 cm apart on the tube, leaving a space of approximately 0 cm from the top of the tube before the first tape marker. C. Using plastic weigh boats and the 200g capacity electronic balance measure two separate 0.66g samples of the fine glass shot. D. When you are prepared, pour the sediment sample directly from the weigh boat into the tube, trying to dispense the entire sample at once. Note that the grains 2/29/2009 1
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 (Table 2). Repeat the experiment with the second sample. Compute the average velocity for fine glass shot from the distance (100 cm) and the average time (velocity = 100 cm/average number of seconds). fine glass shot 1 fine glass shot 2 Average Time (s) Velocity Table 2. Fine glass shot settling time (100 cm) and velocity E. Without changing the water in the tube, repeat steps 4 and 5 using two 0.66 g samples of the coarse glass shot (Table ). Compute the average velocity for coarse glass shot from the distance (100 cm) and the average time )velocity = 100 cm/average number of seconds). coarse glass shot 1 coarse glass shot 2 Average Time (s) Velocity Table. Coarse glass shot settling time (100 cm) and velocity 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 Stokes equation.) 2. Effect of Particle Density (ds) on Settling Velocity In this experiment you 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/cm, and garnet sand, with a density of 4.0 g/cm. A. Use the room temperature water from the previous exercise. Don t refill the tube. B. Measure two 1.00g samples of the fine garnet sand (Table 4). Measure the settling time for the fine garnet sand. Compute the average velocity for fine garnet sand (velocity = 100 cm/average number of seconds). 2/29/2009 2
fine garnet sand 1 fine garnet sand 2 Average Time (s) Velocity 4. Fine garnet sand 100 cm settling time (s) and velocity C. Transfer your average time and velocity for fine glass shot (Table 2) and fine garnet sand to Table 5. Average Time Average Velocity (s) fine glass shot fine garnet sand Table 5. Average settling times and velocities for fine glass and garnet particles 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 garnet by the settling velocity of glass shot). The Effect of Water Density (dw) on Particle Settling Rate Sediment particles settle more slowly In denser water the because the relative density (particle density minus the water density) is lower. If the particle density is less, it sinks more slowly. As you already know, two important factors cause changes in the density of seawater: temperature and salinity. We will investigate each of these. A. Effect of temperature-induced density changes on settling rate 1. Empty the settling tube. a. Loosen the grip clamp and raise the tube a few inches. b. Slowly ease the rubber stopper out of the bottom of the tube and allow the water to drain slowly from the tube. c. Replace the rubber stopper firmly and place the tube so it rests on the bottom of the bucket. d. Make sure the tube is vertical. e. Refill the settling tube with water approximately 5 C, 0 o / oo provided by your instructor. Its density will be given to you. The density of fresh water reaches a maximum at 4º C, so the density should be close to g/cm. 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 (settling velocity = 100 cm/average number of seconds) (Table 6). 2/29/2009
Time (s) Velocity fine glass shot 1 fine glass shot 2 Average Table 6. Fine Glass Shot fall time (100 cm) and velocity in cold, fresh water. Transfer your average velocity times and velocities for fine glass shot in room temperature water (Table 2) and fine glass shot in cold, fresh water (Table 6) to Table 7: Water temperature Density (g/cm ) Room ( ~ 22 C).997 Cold ( ~ 5 C).999 Average Time (s) Average Velocity Table 7. Average settling times and velocities for fine glass particles in room and cold temperature fresh water 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 expected, given the slight change in density from fresh room temperature water to fresh cold water? Explain! B. Effect of salinity-induced density changes on settling rate 1. Empty the settling tube (carefully, as previously instructed). 2. Refill the tube with cold, salty water.. Using two 0.66g samples of fine glass shot, measure the settling rates in cold, salty water (~5 o C, 40 0 / 00 ). 4. Compute the average velocity for fine glass shot in cold, salty water from the distance (100 cm) and the average time (fine shot settling velocity = 100 cm/average number of seconds). 2/29/2009 4
Time (s) Velocity fine glass shot 1 fine glass shot 2 Average Table 8. Fine glass shot fall time (100 cm) and velocity in cold (~5 o C), salty (40 0 / 00 ) water 5. Transfer the densities (from Table 1), average velocity for fine glass shot in cold, fresh water (Table 7) and fine glass shot in cold, salty water (Table 8) to Table 9. Salinity and Temperature Density (g/cm ) Average Time (s) Average Velocity 0 o / oo, ~ 5 C 40 o / oo, ~ 5 C Table 9. Average settling times and velocities for fine glass particles in cold (5 degree C) fresh (0 o / oo ) and cold salty (40 o / oo ) water. 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. 2/29/2009 5
Effect of Density Difference on Speed of a Turbidity Current In these experiments, you will use a 5 cm-diameter 1.5 m-long tube and two saline solutions, 40 o / oo and 80 o / oo. 1. Carefully measure 50 ml of 40 o / oo dyed solution in a 125 ml Erlenmeyer flask. 2. Fill the tube with approximately.5 liters of tap water. Make sure one end is stoppered and sealed, and not leaking water.. Place the tube on the table with the stopper 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 2). 4. After the tube is fixed in place, add additional water until the water level is 10 cm from the open end. Figure 2. Turbidity tube set-up 5. Mark the tube with small pieces of masking tape at 0,., 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 (Figure 2). Note: You will be measuring the maximum thickness of the turbidity current head at the 66.6 cm mark (see h in Figure ) and the time at each of the tape marks. You should prepare before you begin step 7. Figure. Measurement of maximum height of flow head at 66.6 cm 2/29/2009 6
6. After shaking the 40 o / oo water in the flask, quickly pour (don t dump!) the dyed salt solution (from the side table) 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 10. Calculate the velocity of the turbidity flow at 100 cm. (Velocity = 100 cm / time (s).) 7. Repeat the experiment with the 80 o / oo water-using a different food coloring. Do not replace the water in the turbidity tube for this measurement. Record the head height and times in Table 10. Calculate the velocity of the turbidity flow at 100 cm. (Velocity = 100 cm / time (s).) Head Height Time in seconds at each point at 66.6 cm Salinity (mm). cm 66.6 cm 100 cm Velocity at 100 cm 40 o / oo 80 o / oo Table 10. Effect of salinity (density) on speed of a turbidity current, angle equals 20 8. Graph the turbidity flows in seconds in Figure 4. 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. Is the speed constant down the length of the tube? Figure 4. Turbidity speed for 40 o / oo and 80 o / oo water at 20 slope Does a doubling of the salinity double the speed of the current? Does the head thickness remain constant relative to the two densities? 2/29/2009 7
Effect of Slope Angle on Turbidity Flow 1. Slowly lift the stoppered end of the turbidity tube and empty its contents into the bucket. Do this slowly or you will soak your lab partner! 2. Refill the turbidity tube with about.5 L of tap water and then adjust the angle of the slope to 10 by lowering the clamp on the ring stand.. 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., 66.6 and 100.0 cm from the zero mark. 4. Repeat the experiments above for the 40 o / oo and 80 o / oo salinity waters at the new, lower slope angle. 5. Record the head height and times in Table 11. 6. Calculate the velocity of the turbidity flow at 100 cm. (Velocity = 100 cm/ time (s).) Head Height Time in seconds at each point at 66.6 cm Salinity (mm). cm 66.6 cm 100 cm Velocity at 100 cm 40 o / oo 80 o / oo Table 11. Effect of slope angle on speed of a turbidity current, angle equals 10 7. Graph the turbidity flows in seconds in Figure 5. 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. Figure 5. Turbidity speed for 40 o / oo and 80 o / oo water at 10 slope 2/29/2009 8
What was the effect of a decrease in slope on the flow speeds of the two different density waters? (Compare speeds from Figure 4 with Figure 5.) Was there any effect on the turbidity current head thickness due to decreasing the slope? Which affects the speed of the turbidity flow more, density differences or slope changes? Effect of Sediment Concentration on Turbidity Flow Obtain two sediment suspensions, one high density and the other low density from your instructor at the side table. Low Density Suspension 1.07 High Density Suspension 1.16 Density g/cm Table 12. Density of high and low density suspensions 1. When you are ready quickly pour the low density suspension (50 ml) 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 1. 2. 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 1. Suspension Density (g/cm ) Head Height at 66.6 cm (mm) Time in seconds at each point. cm 66.6 cm 100 cm Velocity at 100 cm Low High Table 1. Effect of suspension density on speed of a turbidity current, angle equals10 2/29/2009 9
. Graph the turbidity flows in seconds in Figure 6. Use an x for the high density suspension and a o for the low density suspension. Connect your marks to create two lines. Figure 6. Turbidity speed for high and low density suspensions at 10 slope Draw the head region of the turbidity current, and indicate flow patterns around the head region in Figure 7. Before emptying and cleaning the tube, look on the under side of the tube. What do you see, and how might this be related to sediment transport in the ocean? These sediment suspensions are much denser than the salt water solutions. Would you expect them to travel faster and farther in the ocean? Figure 7. Shape and flow around the head region of the turbidity flow. 2/29/2009 10
Measured versus Theoretical Turbidity Flow Speeds Your work shows 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 of the turbidity current is governed by the following equation: where d 1 =density of the turbidity current d 2 = density of the ambient fluid (in this case the tap water) = use g = gravity, 980 cm/sec 2 h = thickness of the head of the current Carry forward to Table 14 the measured velocities, head thicknesses, and densities, from Tables 10--1 then calculate the theoretical speed of the turbidity current using the equation above. Procedu re 7 Experiment al condition 40 o / oo 20 slope Measured velocity d l d 2 h d 1 - d 2 Theoretical velocity 80 o / oo 20 slope 8 40 o / oo 10 slope 80 o / oo 10 slope 9 low density suspension 10 slope high density suspension 10 slope Table 14. Measured and theoretical velocities for turbidity currents Which are larger, the theoretical or the measured velocities? Why? Where might the errors be in your experimental results? 2/29/2009 11