The owner of a cabin that is located on a small stream is thinking of placing a dam across the stream to create a possible drop of 120 cm. The stream is measured to have approximate
Dimensions of 180 cm by 10 cm and a leaf on the water's surface is observed to travel 10 m in
8 s) If an 80% efficient turbine is used, how much power can the owner expect to generate?
A) 1 kW
B) 2 kW
C) 3 kW
D) 4 kW

Question

Quizplus · Accepted Answer

$2 \mathrm {~kW}$
$\text {The flow rate is calculated, based on the estimates with the assumption of uniform }$$\text {flow, to be}$
$$Q = A V = ( 1.8 \times 0.1 ) \times \frac { 10 } { 8 } = 0.225 \mathrm {~m} ^ { 3 } / \mathrm { s }$$
$\text {The energy equation, Eq. 4.5.24, with $p _ { 1 } = p _ { 2 } = 0$ and negligible kinetic energy }$$\text {change, provides}$
$$\frac { V ^ { 2 } } { 2 g } + \frac { p / } { \gamma \gamma } + 1.2 = H _ { T } + \frac { V ^ { 2 } } { p g } + \frac { p z } { \gamma \gamma } + \not / 2 \text { or } H _ { T } = 1.2 \mathrm {~m}$$
$\text {Equation (4.5.25) predicts that the energy output may be}$
$$\dot { W } _ { T } = \gamma Q _ { T } \eta _ { T } = 9810 \times 0.225 \times 1.2 \times 0.8 = \underline { 2120 \mathrm {~W} }$$

The Owner of a Cabin That Is Located on a Small