Question

An inventor has developed a machine that extracts energy from water and other effluents drained from apartments in a building. The machine essentially consists of a hydraulic turbine placed in the basement (level zero), through which the effluents pass before being dumped into the sewage system.
(a) If the average height of an apartment relative to the location of the turbine is 30 meters and the average flow from each apartment (assume it to be water) is 100 liters per day, calculate the average power produced by the contraption if there are 100 apartments in the building. Assume ambient state to be 300 K, 1 bar.

Answer 1

Answer:

34.06 W.

Explanation:

Assumptions : ideal turbine " no loss of work", no pipe or friction losses, all the available energy of water in converted to useful power.

(A) total volume of water per day in cubic meters:

1 cubic meters=1000 L

average flow from each apartment*total apartments/1000= (100/1000)*100

                                                                                                =10 m^3

total mass of water m= density*volume=1000*10=10000 kg

total energy of water at 30 m height= m*g*h= 10000*9.81*30=2943000 J

if all the available energy is converted to power.

power produced per day=total energy of water / time

time in seconds=24*3600=86400 s

power produced in a day=2943000/86400= 34.06 W

Answer 2

Answer:

34.06 W

Explanation:

Assuming ideal conditions which are assuming no fiction or pipe loss is made along the line of extraction of water

Energy of water at ideal condition ( Eₐ ) = 1000 kg/m³

height given = 30 meters

quantity of water = 100 Liters

to calculate the quantity of water in M³/s ( cubic per second )

= $\frac{100*10^{-3} }{24*3600}$ = 1.157 * $10^{-6}$

power produced by water ( Pw) = energy of water * quantity of water in m^3/s

  = 1.157 * $10^{-6}$  * $10^{3}$ = 1.157 *$10^{-3}$

since it is an ideal condition all the power produced by water is converted to power produced by the contraception

Pc = ( Pw * g * h ) * n

H = height = 30

g = 9.81

n = number of apartments = 100

Pc =( 1.157 * $10^{-3}$  * 9.81 * 30) *100   = 34.06 W