Question

7. A rectangular water-tank measuring 80 cm x
60 cm x 60 cm is filled from a pipe of cross-
sectional area 1.5 cm², the water emerging at
3.2 m/s. How long does it take to fill the
tank?​

Answer 1

Step-by-step explanation:

Given : A rectangular water-tank measuring 80 cm x  60 cm x 60 cm is filled from a pipe of cross- sectional area 1.5 cm, the water emerging at 3.2 m/s.

To find : How long does it take to fill the  tank?

Solution :

A rectangular water-tank measuring 80 cm x  60 cm x 60 cm.

The volume of the tank is

Volume = L × B × H

= 80×60×60 cm^3

= 288000 cm^3

A pipe of cross- sectional area 1.5 cm, the water emerging at  3.2 m/s.

Converting m/s into cm/s,

1 m/s = 100 cm/s

3.2 m/s = 320 cm/s

Let the time taken to fill tank be 't'.

The volume of flow rate is

i.e.

Volume = 320 × 1.5 × t

288000 cm^3 = 320 × 1.5 × t

t = 28800 / 320 ×1.5

t = 600 seconds

Therefore, time taken by pipe to fill a tank is 600 seconds.

600sec = 10 min

Hope it will help you

Answer 2

Volume of rectangular tank =80×60×60cm³

=288000cm³

One litre =1000cm³

Volume of water flowing in per sec =

$1.5c {m}^{2} ×3.2 \frac{m}{s} =1.5c {m}^{2} × \frac{(3.2×100)cm}{s} =480 \frac{ {cm}^{3} }{s}$

Vol. of water flowing in 1 min=480×60=28800cm³

Hence,

28800cm³ can be filled in 1 min

28800cm³ can be filled in

$( \frac{1}{28800} \times 28800)min=10 min$