Respuesta :
Answer:
[tex]P=22050\ W[/tex]
Explanation:
Given:
- width of the stream, [tex]w=3\ m[/tex]
- depth of the stream, [tex]d=0.5\ m[/tex]
- height of the waterfall, [tex]h=5\ m[/tex]
- velocity of flow, [tex]v=1.2\ m.s^{-1}[/tex]
- efficiency promised by the manufacturer, [tex]\eta=25\%[/tex]
Now the volume flow rate of the water through the fall:
[tex]\dot V=v\times w\times d[/tex]
[tex]\dot V=1.2\times 3\times 0.5[/tex]
[tex]\dot V=1.8\ m^3.s^{-1}[/tex]
Now we know the density of water is 1000 kilogram per cubic meter.
So, the mass flow rate:
[tex]\dot m=\dot V\times 1000[/tex]
[tex]\dot m=1.8\times 1000[/tex]
[tex]\dot m=1800\ kg.s^{-1}[/tex]
Hence potential energy delivered to the system per second:
[tex]\dot {PE}=\dot m\times g\times h[/tex]
[tex]\dot {PE}=1800\times 9.8\times 5[/tex]
[tex]\dot {PE}=88200\ J.s^{-1}[/tex]
Now the power generated according to efficiency:
[tex]P=\dot{PE}\times \eta[/tex]
[tex]P=88200\times 0.25[/tex]
[tex]P=22050\ W[/tex]
