Question

Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

What should be the speed of water if the rise in water level is to be attained in 1 hour?

Answer 1

Length of the pond, l = 50m, width of the pond, b = 44m

Water level is to rise by, h = 21 cm = ${\displaystyle \frac{21}{100}}$m

Volume of water in the pond = lbh = ${\displaystyle 50\times 44\times \frac{21}{100}}$m³ = 462 m³

Diameter of the pipe = 14 cm

Radius of the pipe, r = 7 cm = ${\displaystyle \frac{7}{100}}$m

Area of cross-section of pipe = πr²

= ${\displaystyle \frac{22}{7}\times \frac{7}{100}\times \frac{7}{100}}$

= ${\displaystyle \frac{154}{10000}}$m²

Rate at which the water is flowing through the pipe, h = 15 km/h = 15000 m/h

Volume of water flowing in 1 hour = Area of cross-section of pipe × height of water coming out of pipe

= ${\displaystyle (\frac{154}{10000}\times 15000)m^3}$

Time required to fill the pond = ${\displaystyle \frac{\text{Volume of the pond}}{\text{Volume of water flowing in 1 hour}}}$

= ${\displaystyle \frac{462\times 10000}{154\times 15000}}$

= 2 hours

Speed of water if the rise in water level is to be attained in 1 hour = 30km/h