Question

water is flowing through a cylindrical pipe of internal diameter 2 cm into a cylindrical tank of base radius 40 cm at the rate of 0.4 M per second determine the rise in level of water in the tank in half an hour

Answer 1

radius of cylindrical pipe , r = 1cm
radius of cylindrical tank , R = 40cm

water is flowing through a cylinderical pipe into cylindrical tank at the rate of 0.4m/s or 40cm/s.

length of water through pipe , l= rate × time taken
= 40cm/s × 1/2 hr
= 40cm/s × 30 × 60
= 40 × 1800 cm
= 72000 cm

now, volume of water flows through pipe = volume of water rise in cylindrical tank

or, πr² × l = πR² × h

or, (1cm)² × 72000 cm = (40cm)² × h

or, 72000cm³ = 1600 cm² × h

or, h = 720/16 cm = 45cm

hence, 45cm rise in the level of water in the rank in half an hour.

Answer 2

Step-by-step explanation:

For pipe, r = 1cm

Length of water flowing in 1 sec, h = 0.7m = 7cm

Cylindrical Tank, R = 40 cm, rise in water level = H

Volume of water flowing in 1 sec = πr2h = π x 1 x 1 x 70

= 70π

Volume of water flowing in 60 sec = 70π x 60

Volume of water flowing in 30 minutes = 70π x 60 x 30

Volume of water in Tank = πr2H = π x 40 x 40 x H

Volume of water in Tank = Volume of water flowing in 30 minutes

π x 40 x 40 x H = 70π x 60 x 30

H = 78.75cm