Consider the Possibility of Extracting Power from a Flow of Water

Question

Examlex · Accepted Answer

The Answer is (a) Thermal energy is

E = \eta m C \Delta T

so the power is given by the flow as

P = \eta ( d m / d t ) C \Delta T

For a flow of

1000 \mathrm {~L} / \mathrm { s } = 1000 \mathrm {~kg} / \mathrm { s }

the power is

P = ( 0.85 ) imes ( 1000 \mathrm {~kg} / \mathrm { s } ) imes \left( 4180 \mathrm {~J} / \left( \mathrm { kg } \cdot { } ^ { \circ } \mathrm { C } ight) ight) imes \left( 200 ^ { \circ } \mathrm { C } - 40 ^ { \circ } \mathrm { C } ight) = 5.68 imes 10 ^ { 8 } \mathrm {~W}

(b) For an OTEC system where the flow is the flow of hot water to the evaporator the power is

P = \frac { d m } { d t } \frac { \eta C ( \Delta T ) ^ { 2 } } { 8 T _ { h } }

Substituting appropriate values gives

P = ( 1000 \mathrm {~kg} / \mathrm { s } ) imes ( 0.85 ) imes \left( 3930 \mathrm {~J} / \left( \mathrm { kg } \cdot { } ^ { \circ } \mathrm { C } ight) ight) imes \left( 24 ^ { \circ } \mathrm { C } - 4 ^ { \circ } \mathrm { C } ight) ^ { 2 } / \left( 8 imes \left( 24 ^ { \circ } \mathrm { C } + 273 ight) ight) = 5.62 imes 10 ^ { 5 } \mathrm {~W}

(c) The gravitational potential energy is

E = \eta m g h

So the power will be

P = \eta ( d m / d t ) g h

Substituting appropriate values gives

P = ( 0.85 ) imes ( 1000 \mathrm {~kg} / \mathrm { s } ) imes \left( 9.8 \mathrm {~m} / \mathrm { s } ^ { 2 } ight) imes ( 100 \mathrm {~m} ) = 8.33 imes 10 ^ { 5 } \mathrm {~W}

(d) The kinetic energy of flowing water is

E = ( 1 / 2 ) \eta m v ^ { 2 }

So the power is

P = ( 1 / 2 ) \eta ( d m / d t ) v ^ { 2 }

Substituting appropriate values

P = ( 0.5 ) imes ( 0.85 ) imes ( 1000 \mathrm {~kg} / \mathrm { s } ) imes ( 5 \mathrm {~m} / \mathrm { s } ) ^ { 2 } = 1.06 imes 10 ^ { 4 } \mathrm {~W}

In general, these results show that for typical conditions in different types of facilities utilizing flowing water that thermal energy provides greater generating capacity than mechanical energy and that the OTEC system suffers compared to other systems utilizing thermal energy because of its low efficiency.

Consider the Possibility of Extracting Power from a Flow of Water

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