熱力學蘇金佳老師考古題第二題
An oil pump is drawing 52kW of electric power while pumping oil with
ρ=830kg/m^3 at a rate of 0.15m^3/s. The inlet and outlet diameters of the
pipe are 10cm and 15cm, respectively. If the pressure rise of oil in
the pump is measured to be 380 kpa and the moter efficiency is 89%, determine
the mechanical efficiency of the pump.
已知
ρ=830 (kg/m^3)
P2-P1=380 (kpa)
dV/dt=0.15 (m^3/s)
可得
v=1/ρ=1/830
dm/dt=ρdV/dt=830*0.15
dV/dt=uA (u為速度) 進出流量相同
u1=0.15/(pi(0.1/2)^2)=19.09
u1=0.15/(pi(0.15/2)^2)=8.49
Δe=Δu+ΔPv+Δu^2/2
假設溫度不變 Δu=0
Δe=(P1-P2)v+(u1^2-u2^2)/2
=(380*1000/830)+(8.49^2-19.09^2)
=311.66 (J)
ΔE=dm/dt*Δe=830*0.15*311.66
52*1000*0.89*η=311.66
功*換成J*馬達效率*pump效率
η=0.84
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