B) A pump is to raise 100 litre of water a height of 1.2 m in 10s. Calculate the power required assuming 1 litre of water has a mass of 1 kg?.

2 Answers

#\color{red}{117.72\ W#

Explanation:

Power (#P#) of the pump that lifts #Q=100# liters of water (density, #rho=1\ \text{kg/Ltr}#) at a vertical height #H=1.2\ m# in time #t=10# sec is given as follows

#P={\rho gQH}/t#

#={1 \cdot 9.81\cdot 100\cdot 1.2}/10#

#=117.72 \ W#

Jul 7, 2018

I get #117.6# watts.

Explanation:

The mass of the water here is:

#100color(red)cancelcolor(black)"L"*(1 \ "kg")/(color(red)cancelcolor(black)"L")=100 \ "kg"#

The weight of the water is therefore:

#100 \ "kg"*9.8 \ "m/s"^2=980 \ "kg m/s"^2=980 \ "N" \ (because 1 \ "N"-=1 \ "kg m/s"^2)#

Work done is given by the equation:

#W=F*d#

where:

  • #W# is the work done in joules

  • #F# is the force exerted in newtons

  • #d# is the distance moved in meters

So, we get:

#W=980 \ "N"*1.2 \ "m"#

#=1176 \ "J"#

Power here is given by the equation:

#P=W/t#

where:

  • #P# is the power in watts

  • #W# is the work done in joules

  • #t# is the time taken in seconds

So, we get:

#P=(1176 \ "J")/(10 \ "s")#

#=117.6 \ "W"#