SURFACE DRAINAGE: SLOPE
AND VELOCITY OF OVERLAND
FLOW
in Agriculture Lesson B1–4 • Page 1
Student Learning Objectives. Instruction in this lesson should result in
students achieving the following objectives:
1 Quantify the relationship between slope and velocity.
2 Describe the impact of roughness (friction) on velocity.
3 Make design decisions relative to slope and roughness to control water
velocities in surface drains.
Anticipated Problem: How does slope affect velocity?
I. Velocity, distance divided by time, increases at a ratio of v to the square root of the
slope.
A. Slope is the amount of rise divided by the amount of run or distance traveled.
B. Manning’s equation can help estimate the velocity of a fluid in a channel with many
variables.
Illinois Physical Science Applications in Agriculture Lesson B1–4 • Page 2
C. The steeper the channel the higher the velocity.
D. The shape of the channel also affects the velocity with a parabola allowing for the
greatest velocity.
E. The differences in slope and velocity is not a straight-line relationship. It is caused by
exponential differences which is a non-linear relationship.
Anticipated Problem: What affect does friction have on velocity?
II. Friction affects the velocity of water in a channel.
A. The roughness coefficient determines the speed of the water.
B. Winding, sluggish and weedy banks slow water down more than smooth straight
channels.
C. Runoff is water and soil that travel along the soil surface.
1. The runoff of a land area is dependent on the infiltration and percolation rates of the
soil as well as the precipitation levels.
2. The precipitation levels cannot be controlled. The soil characteristics will change
over time, and as erosion increases the soil characteristics will differ.
Anticipated Problem: How can changing slope and friction control water velocity in
surface drains?
III. The roughness, slope, and velocity of a channel all impact erosion and surface
drainage.
A. As the roughness of a channel increases the velocity of the water decreases. This
forms an indirect relationship. Roughness is difficult to change in an existing waterway
but can be affected in a newly created waterway situation.
Illinois Physical Science Applications in Agriculture Lesson B1–4 • Page 3
B. The velocity of water flowing overland in an open channel varies as the square root of
the slope in ft/ft. The relationship is nonlinear. Slope is topographical and cannot easily
be changed in a large channel but may be altered in smaller channels.
SURFACE DRAINAGE: SLOPE AND
VELOCITY OF OVERLAND FLOW
Part One: Matching
Instructions: Match the word with the correct definition.
a. velocity
b. friction
c. slope
d. runoff
_______1. Rise/Run
_______2. Overland water Flow
_______3. flow of water based in feet/second
_______4. Force that prevents the flow of water over a surface
Part Two: Fill-in-the-Blank
Instructions: Complete the following statements with increase or decrease.
1. As slope increases velocity of water in an open channel will _________.
2. As friction in the channel increases velocity will __________.
Part Three: Multiple Choice
Instructions: Write the letter of the correct answer.
_______1. The overland flow of water is called _______.
a. percolation
b. run off
c. leaching
d. erosion
Illinois Physical Science Applications in Agriculture Lesson B1–4 • Page 6
_______2. The formula for slope is _______.
a. run/rise
b. velocity/rise
c. rise/run
d. rise/velocity
_______3. As slope increases velocity _____.
a. increases
b. decreases
c. stays the same
d. none of the above
_______4. If a soil drops 18 inches in 50 feet, what is the percent slope?
a. 18%
b. 9%
c. 3%
d. 1%
_______5. Level and nearly level land has a _____ percent slope.
a. 0–2
b. 2–6
c. 6–12
d. 12–20
_______6. Surface drainage is the removal of excess water by which of the following?
a. land grading
b. ditches
c. row cropping
d. a & b
_______7. Which of the following is a critical factor to successful drainage designs?
a. velocity
b. stabilization of the waterway
c. slope
d. all of the above
_______8. Which of the following statements is not true?
a. Grasses are often used to stabilize waterways.
b. Vegetative cover has little effect on the velocity of water.
c. Grasses help to limit the amount of erosion along waterways.
d. Proper design of surface drainage systems is essential for control of erosion.
Part Four: Short Answer
Instructions: Answer the following questions.
1. What is the relationship of slope and velocity of water in an open channel?
Illinois Physical Science Applications in Agriculture Lesson B1–4 • Page 7
2. How does roughness/friction affect water velocity?
3. Is roughness and slope readily altered in channels?
Illinois Physical Science Applications in Agriculture Lesson B1–4 • Page 8
Assessment
TS–A