Question

A pump collects water (rho = 1000 kg/m^3) from the top of one reservoir and pumps it uphill to the top of another reservoir with an elevation change of Δz = 800 m. The work per unit mass delivered by an electric motor to the shaft of the pump is Wp = 8,200 J/kg. Determine the percent irreversibility associated with the pump.

Answer 1

4.29%

Step-by-step explanation:

Given:

Density of water, ρ = 1000 kg/m³

elevation change of Δz = 800 m

work per unit mass delivered, Wp = 8,200 J/kg

Now,

The percent irreversibility =
`(1-n_p)*100`

where,

`n_p(W_(actual))/(W_(theoretical))`

also,

`W_(actual)=(g\Delta z)/(1000)`

Where, g is the acceleration due to the gravity

on substituting the values, we get

`W_(actual)=(9.81*800)/(1000)`

or

`W_(actual)=7.848\ KJ/kg`

or

`W_(actual)=7848\ J/kg`

Therefore,

The percent irreversibility =
`(1-n_p)*100`

on substituting the values, we get

The percent irreversibility =
`(1-(7848)/(8,200))*100`

or

The percent irreversibility = 4.29%