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

Answer:

4.29%

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 = $(1-n_p)\times100$

where,

$n_p\frac{W_{actual}}{W_{theoretical}}$

also,

$W_{actual}=\frac{g\Delta z}{1000}$

Where, g is the acceleration due to the gravity

on substituting the values, we get

$W_{actual}=\frac{9.81\times800}{1000}$

or

$W_{actual}=7.848\ KJ/kg$

or

$W_{actual}=7848\ J/kg$

Therefore,

The percent irreversibility = $(1-n_p)\times100$

on substituting the values, we get

The percent irreversibility = $(1-\frac{7848}{8,200})\times100$

or

The percent irreversibility = 4.29%