Question

A pump pulls 100kg water per minnute from a 15m deep well and provides 4m/sec velocity to it. The power of the pump is....
options are 1)2.6 kw 2)2.6 w 3)0.6 w 4)0.6 kw

Answer 1

Given:-

• $\sf{ Mass\:of\:water = 100kg }$

• $\sf{ Height\ of \ pipe = 15m}$

• $\sf{ Initial \ velocity \ of \ Pipe = 4m/s}$

To Find:-

• $\sf{Power\:of\:the\:Pump}$

Formulae used:-

• K.E = ½ × m × v²

• P.E = mgh

• $\sf{ Power = \dfrac{ Work\:Done}{ Time\:Taken }}$

Now,

→ Kinetic energy of Object = ½ × mv²

→ ½ × 100 × (4)²

→ 50 × 16

→ 800J

Again,

→ Potential energy of Object = mgh

→ 100 × 10 × 15

→ 1000 × 15

→ 15000J

Therefore,

→ Work Done = Potential energy + Kinetic energy

→ Work Done = (15000 + 800)J

→ Work Done = 15800J

Therefore,

→ $\sf{ Power = \dfrac{ Work\:Done}{ Time\:Taken }}$

→ $\sf{ Power = \dfrac{ 158000}{60}}$

→ $\sf{ Power = 263.33W}$

Hence, The power of Pump is 2.6KW.