Question

27. Water in a canal, 30 dm wide and 12 dm deep, is flowing with a velocity
of 20 km per hour. How much area will it irrigate in 30min , if 9 cm of standing
water is desired?​

Answer 1

Given,

Depth(d) = 12dm = 1.2m

Width(w) = 30dm = 3m

Velocity of water (v) = 20km/h = 20,000 m/h

time (t) = 30minute = 0.5 hour

⇒ The volume of water = w × d × length

Here length becomes speed × time = v × t

Volume of water = w × d × v × t

1.2 × 3 × 20000 × 0.5

= 36000 m3

Now,

Let the area irrigated be x

And Desired standing water = 9cm = 0.09m

Since volume of water will be same

⇒ 36000 = x × 0.09

⇒ x = 400000

So, area irrigated by the canal is 400000 m2

Answer 2

AnswEr:

Water in a canal forms a cuboid of breadth

$\tt = 12 \: dm \\ \\ \tt = \frac{12}{10} \\ \\ \tt = 1.2m$

Height = 30 dm = 30 / 10 = 3 m

and , Length = Distance covered by water in 30 minutes

= Velocity of water * time

$\tt = 20000 \times \frac{30}{60} \: m \\ \\ \tt = 10000 \: m$

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$\therefore$ Volume of water flown in 30 minutes

= lbh

$\tt = (1.2 \times 3 \times 10000) \: {m}^{3} \\ \\ \tt = 36000 \: {m}^{3}$

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Suppose area irrigated be A m². Then,

$\tt \: a \times \frac{9}{100} = volume \\ \\ \tt = a \times \frac{9}{100} \times 36000 \\ \\ \implies \tt = a = 400000 \: {m}^{2}$

Hence, area irrigated 400000 m²

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