Question

a cylindrical reservoir is 21m in diameter. water is passed into it at 420 litres per min find rise of water level in the reservoir per hour ​

Answer 1

Answer: ≈ 7.3 cm

Diameter of cylindrical reservoir, d = 21m

∴ Radius = Diameter/2 = 21/2 m

Now, The volume of water passed into the reservoir per minute is 420 litres.

Convert the volume into m³ because we have to find the rise of water level in the reservoir per hour.

We know,

• 1 litre = 0.001 m³

Hence, 0.42 m³ per min is the rate of passing of water into the reservoir. Let's find the volume of water passes into the reservoir per hour.

⇒ 1 minute ➞ 0.42 m³

As, 1 hour = 60 minutes, hence multiply both sides by 60 to get the volume of water passes into the reservoir per hour.

⇒ 1 × 60 minutes ➞ 0.42 × 60 m³

⇒ 1 hour ➞ 25.2 m³

Now, Let's find the rise of water level. As the reservoir is in the shape of a cylinder hence the volume of the reservoir in one hour after being empty is 25.2 m³ which is given by the formula,

• Volume = πr²h = 25.2

⇒ πr²h = 25.2

⇒ 22/7 × 21/2 × 21/2 × h = 25.2

⇒ 11 × 3 × 21/2 × h = 25.2

⇒ h = 25.2 × 2 / (33 × 21)

⇒ h = 50.4 / 33 × 21

⇒ h = 2.4 / 33

⇒ h ≈ 0.073 m or 7.3 cm

Hence, the rise in water level of the reservoir per hour is approx. 7.3 cm.

Answer 2

Given :-

Diameter = 21 m

Water passed = 420 l

To Find :-

Water level

Solution :-

Water passed in 1 hour = Water passed in 1 min × 60

Water passed in 1 hour = 420/1000 × 60

Water passed in 1 hour = 42/10 × 6

Water passed in 1 hour = 42/5 × 3

Water passed in 1 hour = 25.2 m³

Now

We know that

R = D/2

R = 21/2 m

Volume = πr²h

25.2 = 22/7 × (21/2)² × h

25.2 = 22/7 × 441/4 × h

25.2 = 11/7 × 441/2 × h

25.2 = 11 × 63/2 × h

25.2 × 2 = 11 × 63h

50.4 = 693h

50.4/693 = h

0.72 = h