Respuesta :
Answer:
[tex]\eta = 91.7[/tex]%
Explanation:
Determine the initial velocity
[tex]v_1 = \frac{\dot v}{A_1}[/tex]
[tex] = \frac{0.1}{\pi}{4} 0.08^2[/tex]
= 19.89 m/s
final velocity
[tex]v_2 =\frac{\dot v}{A_2}[/tex]
[tex]= \frac{0.1}{\frac{\pi}{4} 0.12^2}[/tex]
=8.84 m/s
total mechanical energy is given as
[tex]E_{mech} = \dot m (P_2v_2 -P_1v_1) + \dot m \frac{v_2^2 - v_1^2}{2}[/tex]
[tex]\dot v = \dot m v[/tex] [tex]( v =v_1 =v_2)[/tex]
[tex]E_{mech} = \dot mv (P_2 -P_1) + \dot m \frac{v_2^2 - v_1^2}{2}[/tex]
[tex] = mv\Delta P + \dot m \frac{v_2^2 -v_1^2}{2}[/tex]
[tex]= \dot v \Delta P + \dot v \rho \frac{v_2^2 -v_1^2}{2}[/tex]
[tex] = 0.1\times 500 + 0.1\times 860\frac{8.84^2 -19.89^2}{2}\times \frac{1}{1000}[/tex]
[tex]E_{mech} = 36.34 W[/tex]
Shaft power
[tex]W = \eta_[motar} W_{elec}[/tex]
[tex]=0.9\times 44 =39.6[/tex]
mechanical efficiency
[tex]\eta{pump} =\frac{ E_{mech}}{W}[/tex]
[tex]=\frac{36.34}{39.6} = 0.917 = 91.7[/tex]%
