Question

The volume flow rate of the water supplied by a well is 2.0×10−4m3/s.The well is 40.0 m deep. (a) What is the power output of the pump-in other words, at what rate does the well do work on the water? (b) Find the pressure difference the pump must maintain. (c) Can the pump be at the top of the well or must it be at the bottom? Explain.

Answer 1

a).
`P=78.4W`

b).
`P=392kPa`

c.) It must be at the bottom

Step-by-step explanation:

Given:

Volume flow
`V_f=2.0x10^(-4)m^3/s`

Well depp
`h=40.m`

a.

The power output of the pum

`W=F*d`

`F=m*g`

`m=p*V=1000kg/m^3*2.0x10^(-4)m^3}=0.2Kg`

`W=m*g*d=0.2kg*9.8m/s^2*40.0m=78.4kg*m^2/s^2`

`W=78.4J`

`P=(W)/(t)=(78.4J)/(1s)=78.4W`

b.

The pressure of difference the pum

Δ
`P=p*g*y'`

Δ
`P=1000kg/m^3*9.8m/s^2*40.0m=392x10^3Pa`

`P=392kPa`

c.

It must be at the bottom since the pressure difference is greater than atmospheric pressure, so it wouldn't be able to lift the water all the way