LAB 8: CALCULATION OF STREAM DISCHARGE AND CHANGE IN
CROSS-SECTION AREA
OBJECTIVES:
-To use the data collected in Lab 7 (the field survey) to
calculate stream discharge.
-To calculate the change in cross-sectional area as a result
of a flood.
MATERIALS NEEDED: Graph paper, calculator.
QUESTION 1: COMPUTING THE DISCHARGE ALONG YOUR CROSS-SECTION
PART A: DISCHARGE MEASUREMENT
1. Calculate the area of the stream cross-section.
To do this:
i) Count the total number of graph-paper squares
contained within your cross-section (see example below). You will have to
estimate the fractions of squares that are partly contained.
ii) Determine the area one square represents in
the field. To do this multiply the real-world vertical depth for a square by
the horizontal distance covered by the same square. Make sure you have the
measurements in the same units for both (see example below).
iii) Multiply the total number of squares by the
area of one square to get the total cross-sectional area.
Total number of squares: 25.5
Area of one square: 0.02 m2
Total cross-section area: 25.5 x 0.02 m2 = 0.51 m2
Data for your cross-section:
AREA OF ONE SQUARE:_______
NUMBER OF SQUARES:_______
AREA OF YOUR CROSS-SECTION:_______
2. Compute the stream discharge using one of the two averages
of velocity (current meter or floats) calculated last week.
Justify your selection (current meter or floats).
NOTE: Often there are errors/problems with measurements,
it is important to develop judgment to be able to select which is the best/ most
appropriate to use.
YOUR CROSS-SECTION AREA:
VELOCITY YOU SELECTED: (floats or current
meter?)
DISCHARGE:
See the first page of Lab 7 for how to calculate
discharge.
Why did you select this velocity measurement?
3. In measuring stream velocity in the field, you noted the
positions of the floats. Using this information, draw a velocity curve for the
stream, as seen from above (see example below).
You can do this on the same graph as your cross-section:
you just have to add another Y axis to the right of your graph with the velocity
measurements.
Draw lines, at the correct positions across the channel, with
lengths proportional to velocity. For example, if we had made measurements at 2
m, 4 m, 6 m, and 8m from the bank on a 10 m wide stream, the profile might look
like this:
QUESTION 2: INTERPRETATION OF THE DATA
First you need to compare your data with the data collected
by the other teams. List the results of the other teams in the table below and
use these to answer the following questions.
|
Name of team |
Area of
cross-section (m2) |
Average velocity
(floats or current meter) (ms-1) |
Discharge (m3s-1)
|
| YOUR DATA |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1. Should discharge at each of the cross-sections measured in
your lab by the different groups be the same? Why?
HINT: Think about the volume of water entering this
section of stream channel and the volume leaving it.
2. What factors, other than measurement errors, could cause
stream discharge to vary from one place to another along a reach?
3. Suppose that discharge is the same at all points
along the channel, but just downstream from your measured cross-section the
channel becomes much larger. What effect should this increase have on stream
velocity? Explain your answer.
4. Describe the shape of the velocity curve drawn in the
previous section.
5. What factors account for the shape of the velocity curve?
Why is the curve displaying this shape?
QUESTION 3. CROSS-SECTIONAL CHANGES
In the spring of 2000, a cross section of a river was surveyed before the
spring flood (next table: column 2). The same section was resurveyed after the
spring flood (column 3).
SURVEY OF BED EROSION AND DEPOSITION
AS A RESULT OF THE SPRING FLOOD
| DISTANCE (m) |
Depth (m) before
spring flood |
Depth (m) after
spring flood |
| 0 |
0 |
0 |
| 0.2 |
0.02 |
0.02 |
| 0.4 |
0.045 |
0.03 |
| 0.6 |
0.075 |
0.08 |
| 0.8 |
0.09 |
0.10 |
| 1 |
0.12 |
0.13 |
| 1.2 |
0.15 |
0.13 |
| 1.4 |
0.16 |
0.15 |
| 1.6 |
0.19 |
0.16 |
| 1.8 |
0.22 |
0.18 |
| 2 |
0.22 |
0.23 |
| 2.2 |
0.20 |
0.24 |
| 2.4 |
0.25 |
0.27 |
| 2.6 |
0.255 |
0.30 |
| 2.8 |
0.27 |
0.32 |
| 3 |
0.28 |
0.29 |
| 3.2 |
0.29 |
0.28 |
| 3.4 |
0.29 |
0.26 |
| 3.6 |
0.28 |
0.19 |
| 3.8 |
0.22 |
0.18 |
| 4 |
0.10 |
0.10 |
| 4.2 |
0.05 |
0.07 |
| 4.4 |
0 |
0 |
1. Plot the two cross-sections (before and after the flood).
Draw them on top of each other.
2. What is the vertical exaggeration of your plot? Show your calculations.
3. What was the net change in the cross-sectional area of the river as a
consequence of the flood? Show how you arrived to your answer.
4. What was the average gradient before the flood (from distance 0 to 2m)
expressed as feet per mile.
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