Water behind a dam enters an intake pipe at a pressure of 1.05 bar and velocity

Question

Water behind a dam enters an intake pipe at a pressure of 1.05 bar and velocity of 1 m/s, flow through a hydraulic turbine-generator, and exits at a point 100                    m below the intake at 1 bar, 15 degrees C, 10 m/s. the diameter of the exit pipe is 1.2 m and the local acceleration of gravity is 9.8 m/s^2. Evaluating the                    electricity generated at 8 cents per kWh, determine the value of the power produced, in $/day, for operation at steady state and in the absence of internal                    irreversibilities.

Explanation / Answer

initial energy of system per unit volume = Pressure + (0.5*density*velocity^2) + denstiy*g*height

= 1.05*10^5 + (0.5 * 1000* 1^2 ) + 100*9.8*1000 = 1085500 J / m^3

Final energy of system per unit volume

= 1 *10^5 + (0.5 * 1000* 10^2 ) + 0*9.8*1000 = 150000 J / m^3

so... difference in energy = initial - final = 1085500 - 150000 = 935500 J/m^3

volumetric flow rate = area of coss section of pipe * velocity = (pi*0.6^2) * 10 = 11.3097 m^3 / sec

so.... power = difference in energy * volumetric flow rater = 935500* 11.3097 = 10580255.739 W = 10580.2557 KW

so... energy produced in one day = 10580.2557 * 24 = 253926.13773 KWh

so... value of power = 253926.13773 * 0.08 = 20314.091 $ / day

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