Answer:
mechanical efficiency = 54%
Explanation:
given data
power We = 44 kW
density = 860 kg/m³
rate of flow = 0.07 m³/s
inlet diameter d1 = 8 cm
outlet diameter d2 = 12 cm
pressure = 500 kPa
efficiency η = 90%
to find out
mechanical efficiency
solution
we get here shaft power is here
shaft power = efficiency × electric power
shaft power = 0.9 × 44 = 39.6
and
now we get DEmech that is
DE(mech)= m g h + [tex]\frac{m}{2}[/tex] (v² - u ²) .....................1
that is we can write as
DEmech = ρVgh +[tex]\frac{\rho V}{2} [(\frac{V}{\pi r2^2})^2- (\frac{V}{\pi r2^2})^2 ][/tex]
= VDP + [tex]\frac{\rho V^3}{2\pi ^2}[/tex] × [tex](\frac{1}{\pi r2^2} - \frac{1}{\pi r1^2})^4[/tex]
Plugging in values we now have DEmech that is
DEmech = (0.07m^3/s × 500kPa) + [tex]\frac{860*0.1^3}{2\pi ^2} *( \frac{1}{0.06^4} -\frac{1}{0.04^4} )[/tex]
solve we get
DEmech = 21342 W
DEmech = 21.3 kW
mechanical efficiency is
mechanical efficiency = [tex]\frac{21.3}{39.6}[/tex]
mechanical efficiency = 0.54
mechanical efficiency = 54%
