Question

#Quality Question
@Rate and Volumes

Water flows through a circular pipe whose internal diameter is 2 cm at the rate of 6 m/sec into a cylindrical tank, the radius of whose base is 60 cm. Find the rise in the level in water in 30 minutes.​

Answer 1

༒ Answer ➽ 3m

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༒ Given :-

Internal Diameter of pipe = 2cm

So,

Radius of pipe will be

$\sf r = 1cm = \dfrac{1}{100} m$

Flow of the water from pipe = 6 m/s.

Radius of base of cylindrical tank = 60 cm

i.e.

$\sf R = \dfrac{60}{100} m$

Time = 30 min.

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༒ To Calculate :-

Height of Water in tank after 30 min.

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༒ Solution :-

We have,

$\sf r = \dfrac{1}{100} m$

Flow of the water = 6 m/s

So,

Volume of water flows from pipe in 1 sec

$\sf = \pi \times ( \dfrac{1}{100} {)}^{2} \times6 \: \: {m}^3$

Hence,

Volume of water flows from pipe in 30 min

$\sf = \pi \times ( \frac{1}{100} {)}^{2} \times6 \times (30 \times 60) \: \: {m}^{3} \\ \\ = \sf\pi \times ( \frac{1}{100} {)}^{2} \times10800 \: \: {m}^{3}$

Let,

height of water in Tank after 30 min = h

According to the Given Condition,

After 30 min

Volume of cylindrical tank = Volume of water flows from pipe

i.e.

$\sf\pi {R}^{2} h = \pi \times ( \frac{1}{100} {)}^{2} \times10800\: \: {m}^{3} \\ \\ \sf \cancel{\pi} \times ( \frac{60}{100} {)}^{2} \times h = \cancel{ \pi }\times ( \frac{1}{100} {)}^{2} \times10800 \\ \\ \sf h \times \frac{3600}{ \cancel{10000}} = \frac{10800}{ \cancel{10000} } \\ \\ \implies \Large \purple{ \bf \underline{\boxed{ \bf h = 3m}}}$

Hence,

Rise in Water level after 30 min = 3m

$\Large \red{\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer.}}$

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Answer 2

Given :-

Water flows through a circular pipe whose internal diameter is 2 cm at the rate of 6 m/sec into a cylindrical tank, the radius of whose base is 60 cm.

To Find :-

Rise in the level in water in 30 minutes.​

Solution :-

Radius = D/2

Radius = 2/2

Radius = 1 cm

Now

1 cm = 1/100 m

Volume = πr²h

Volume = π × (1/100)² × 6

Now

1 min = 60 sec

30 min = 30 × 60 = 1800 sec

Now

Volume = π × (1/100 × 100) × 6 × 1800

Radius of tank = 60 cm = 60/100 cm

Volume of tank = πr²h

Volume = π × (60/100)² × h

According to the question

π × (60/100)² × h = π × (1/100)² × 6 × 1800

3600/100 × 100 × h = 1/100 × 100 × 10800

3600h = 10800

h = 10800/3600

h = 3 m