  Irrigation Training Manual: Planning, Design, Operation and Management of Small-Scale Irrigation Systems (Peace Corps, 1994, 151 p.)  Training session  Section 1: Introduction to irrigation principles and practices  (introduction...) Exam: Section 1 - Math skills assessment

### Exam: Section 1 - Math skills assessment

The following questions can assist Trainees to identify math skills that they might want to acquire or strengthen in order to work confidently with technical problem solving at their sites. The questions are intended to increase in complexity as one proceeds through the self-examination. In presenting the skills assessment to Trainees, it is important to emphasize that this is not a pass-fail test but rather an opportunity for them to conduct a self-assessment of their own skill levels.

1. A storage tank holds 1.5 cubic meters of water.

- How many gallons is this?
- How many liters?

2. 3 cubic meters of gravel + 2 cubic meters of sand + 1 cubic meter of cement = 3 cubic meters of concrete. You will pour a concrete slab that measures 3 meters by 5 meters by 10 centimeters.

- Approximately how many cubic feet of concrete will you need?
- How much gravel, sand, and cement (in meters) will you need?

3. You are planning to construct a concrete water storage tank. Each wall measures 2 meters high by 3 meters wide. You will need to purchase reinforcing bar to reinforce the walls. The bars are to be spaced 20 centimeters apart both horizontally and vertically.

- How many 2 meter lengths are needed? How many 3 meter lengths? (for 4 walls)
- If reinforcing bar can only be purchased in 6 meter lengths, how many bars will you need to purchase?

4. A hollow block measures 20 centimeters high and 40 centimeters wide. You want to build a retaining wall 2 meters high by 4 meters wide. Approximately how many blocks will you need, assuming none break in transport?

5. A truck carries 4 cubic meters of sand/gravel. You estimate that you will need 30 cubic feet of gravel and 100 cubic feet of sand. Can it bring you the sand and gravel in one trip?

6. 16 gallon wire sells by the kilo (one kilogram = 54 meters). A kilo sells for 20 pesos. You estimate that you will need 200 meters of wire. How much will it cost?

7. The flow from a spring is 8 liters per minute (Lpm). Assuming a constant rate, how many liters per hour and cubic meters per hour is this? How many gallons per hour?

8. Find the volume of this tank in cubic meters: inside depth = 5 m, outside walls = 6 m, wall thickness = 0.25 m.

How many liters of water will it hold?

9. The flow rate in a stream is estimated to be approximately 50 L/sec. or 180 m3 /hr. You want to divert the stream to irrigate 1 hectare (10,000 m2) of pasture. The hay requires 10 cm (0.1 m) of water to be applied in an irrigation. How long will you need to maintain the diversion to fulfill these water requirements?

Bonus Question

10. After surveying, you find that the difference in elevation between a water source and an irrigation distribution canal is 30 meters. The horizontal distance from the water source to the canal is 120 meters. Approximately how long a length of pipe will be needed to run from the source to the canal, assuming the slope of the hill is constant?

Sample Completed Test

1. A storage tank holds 1.5 cubic meters of water.

- How many liters is this?

Answer: 1.5 m3 x 1000 liters/m3 = 1500 liters

- How many gallons is this?

Answer: 1500 liters/3.8 = 395 gallons

2. 3 cubic meters of gravel + 2 cubic meters of sand + 1 cubic meter of cement = 3 cubic meters of concrete. You will pour a concrete slab that measures 3 meters by 5 meters by 10 centimeters.

- Approximately how many cubic meters of concrete will you need?

Answer: 1.5 cubic meters x (3.28 ft/1 m)3 = 52.9 ft3

- How much gravel, sand, and cement (in cubic meters) will you need (using the given ratio of 3:2:1)?

Answer: 1.5 m3 gravel, 1 m3 sand, 0.5 m3 cement

3. You are planning to construct a concrete water storage tank. Each wall measures 2 meters high by 3 meters wide. You will need to purchase reinforcing bar to reinforce the walls. The bars are to be spaced 20 centimeters apart both horizontally and vertically.

- How many 2 meter lengths are needed? How many 3 meter lengths? (for 4 walls)

- If reinforcing bar can only be purchased in 6 meter lengths, how many bars will you need to purchase?

4. A hollow block measures 20 centimeters high and 40 centimeters wide. You want to build a retaining wall 2 meters high by 4 meters wide. Approximately how many blocks will you need, assuming none break in transport?

Answer: Number of blocks = area of wall / area of individual blocks = (2 m x 4 m)/(0.2 m x 0.4 m) = 100 blocks

* Note: This assumes the mortar joints take up no space

5. A truck carries 4 cubic meters of sand/gravel. You estimate that you will need 30 cubic feet of gravel and 100 cubic feet of sand. Can it bring you the sand and gravel in one trip?

Answer: Volume of sand and gravel = 30 cubic feet + 100 cubic feet

130 cubic feet/35 cubic feet per cubic meter = 3.7 m3; thus, yes.

6. 16 gauge wire sells by the kilo (one kilogram = 54 meters). A kilo sells for 20 pesos. You estimate that you will need 200 meters of wire. How much will it cost?

Answer: 200 m/54 m = 3.7 kg x 20 = 74 pesos

7. The flow from a spring is 8 liters per minute (Lpm). Assuming a constant rate, how many liters per hour and cubic meters per hour is this? How many gallons per hour?

Answer: 8 x 60 = 480, 480 liters/hr = 0.48 m3/hr
480/3.8 = 126 gallons/hr

8. Find the volume of a tank in cubic meters if the inside depth is 5 meters and the lengths of the outside walls are 6 meters. Wall thickness is 0.25 meters.

- How many liters of water will it hold?

Answer: 5.5 x 5.5 x 5 = 151.25 m3 = 151,250 liters

9. The flow rate in a stream is estimated to be approximately 50 L/sec. or 180 m3 /fur. You want to divert the stream to irrigate 1 hectare (10,000 m2) of pasture. The pasture requires 10 cm (0.1 m) of water to be applied in an irrigation. How long will you need to maintain the diversion to fulfill these water requirements?

Answer: Area x depth = flow rate x time
Time = (area x depth)/flow rate
Time = (10,000 m2 x 0.1 m/180 m3 /fur) = 5.6 hrs

Bonus Question

10. After surveying, you find that the difference in elevation between a water source and an irrigation distribution canal is 30 meters. The horizontal distance from the water source to the canal is 120 meters.

Approximately how long a length of pipe will be needed to run from the source to the canal, assuming the slope of the hill is constant?

Answer: (30)2 + (120)2 = x2
x2 = 900 + 14,400
x2 = 15,300
x2 = 123.7 meters