12.3 The Most General Applications of Bernoulli’s Equation

A horizontally oriented pipe has a diameter of 5.6 cm and is filled with water. The pipe draws water from a reservoir that is initially at rest. A manually operated plunger provides a force of 440 N in the pipe. Assuming that the other end of the pipe is open to the air, with what speed does the water emerge from the pipe?

1. 12 m/s
2. 19 m/s
3. 150 m/s
4. 190 m/s

A large container of water is open to the air, and it develops a hole of area 10 cm² at a point 5 m below the surface of the water. What is the flow rate (m³⁄s) of the water emerging from this hole?

1. 99 m³⁄s
2. 9.9 m³⁄s
3. 0.099 m³⁄s
4. 0.0099 m³⁄s

Hoover Dam on the Colorado River is the highest dam in the United States at 221 m, with a maximum output of 1300 MW. The dam generates electricity with water taken from a depth of 150 m and an average flow rate of $\text{650} \text{m}^{3} /\text{s}$. (a) Calculate the power in this flow. (b) What is the ratio of this power to the facility’s average of 680 MW?

The left ventricle of a resting adult’s heart pumps blood at a flow rate of $\text{83} . 0 \text{cm}^{3} /\text{s}$, increasing its pressure by 110 mm Hg, its speed from zero to 30.0 cm/s, and its height by 5.00 cm. (All numbers are averaged over the entire heartbeat.) Calculate the total power output of the left ventricle. Note that most of the power is used to increase blood pressure.