- #1
campblor
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I have this problem and have been pulling what's left of my hair out:
The Wivenhoe hydroelectric power station requires water to be pumped from Wivenhoe Dam to
Splityard Creek Dam, using two pumps (each consuming 250 MW of power at 98% efficiency) to
elevate the water approximately 70 m. At full power, Splityard Creek Dam can be filled from empty
to its capacity of 28 700 ML in 14 hours. The water being supplied is stationary at 4 atm and 10°C; it
is released at 1 atm through a pipe of 20 m diameter.
Assume that there will be no net heat transfer to the water. What is the maximum
temperature at which the water will exit?
Values that I'm using
State 1:
P1 = 405.3kPa T1 = 10C; h1=42.022kj/kg
KE1 = 0 ; PE1 = 0
State 2:
P2 = 101.325kPa
Ive got a volume flow rate of 569.4x103 L/s hence a mass flow rate of 569.4x103 kg/s
and doing some algebra from Mass flow rate = (density)*(Velocity)*(Cross-sectional Area) v = 1.8m/s
and A = 314.16m2
Win = 2x(250MW x 0.98) = 490,000kWFrom the 1st Law using
Win+m(h1+P1/p)=m(h2+P2/p+V^2/2+gz2).
my idea is to use the 1st law to find h2 and use that with the Pressure at state 2 get the temp.
but it give me a value of -643.71kJ/kg
There must be something I'm missing or completely off track..
any asssistance would be greatly appreciated
The Wivenhoe hydroelectric power station requires water to be pumped from Wivenhoe Dam to
Splityard Creek Dam, using two pumps (each consuming 250 MW of power at 98% efficiency) to
elevate the water approximately 70 m. At full power, Splityard Creek Dam can be filled from empty
to its capacity of 28 700 ML in 14 hours. The water being supplied is stationary at 4 atm and 10°C; it
is released at 1 atm through a pipe of 20 m diameter.
Assume that there will be no net heat transfer to the water. What is the maximum
temperature at which the water will exit?
Values that I'm using
State 1:
P1 = 405.3kPa T1 = 10C; h1=42.022kj/kg
KE1 = 0 ; PE1 = 0
State 2:
P2 = 101.325kPa
Ive got a volume flow rate of 569.4x103 L/s hence a mass flow rate of 569.4x103 kg/s
and doing some algebra from Mass flow rate = (density)*(Velocity)*(Cross-sectional Area) v = 1.8m/s
and A = 314.16m2
Win = 2x(250MW x 0.98) = 490,000kWFrom the 1st Law using
Win+m(h1+P1/p)=m(h2+P2/p+V^2/2+gz2).
my idea is to use the 1st law to find h2 and use that with the Pressure at state 2 get the temp.
but it give me a value of -643.71kJ/kg
There must be something I'm missing or completely off track..
any asssistance would be greatly appreciated