Water in a canal 1.5m wide and 6m deep is flowing with a speed of 10km/hr. How much area will it irrigate in 30 minutes if 8cm of standing water is desired?
As given here the canal is in the shape of a cuboid with dimensions, length(l), breadth(b), and height/depth(h).
Answer: The area that will be irrigated in 30 minutes by a water canal that is 1.5m wide and 6m deep flowing with a speed of 10km/h with standing water of 8cm is 56,2500 m2
Let's use the condition given in the question to find the required area.
Let's first note down the given dimensions in the case of the canal.
Width or breadth, h = 1.5 m
Depth or height, b = 6 m
Since we know that the water is flowing at 10 km/hr through the canal, then:
In 1 hr or 60 mins, length of canal, l = 10 km
In 30 mins, length = 5 km or 5000 m
Therefore, the length of the canal = 5000 m
Therefore, the volume of the canal = l × b × h
= 1.5 × 6 × 5000
= 45000 m3
Now to find the area that needs to be irrigated by 8 cm or 0.08 m of standing water, we will compare the volume of the field with that of the canal as the time for which the water is irrigated in the field and the time for which water is flowing out of the canal are same.
The volume of the canal = Volume of the field to be irrigated
or, 45000 = Area of the field to be irrigated × Height of the standing water
or, 45000 = Area of the field × 0.08
or, Area of the field = 45000/0.08 = 562500 m2
Therefore, the area of the field that needs to be irrigated is 56,2500 m2.