Energy, Work, and Power http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...
7.1 Energy, Work, and Power
The energy equation involves energy, work, and power as well as machines that interact with flowing fluids.
These topics are introduced in this section.
When matter has energy, the matter can be used to do work. A fluid can have several forms of energy. For
example a fluid jet has kinetic energy, water behind a dam has gravitational potential energy, and hot steam has
thermal energy. Work is force acting through a distance when the force is parallel to the direction of motion. For
example, for the spray bottle shown in Fig. 7.1, work is done when a finger exerts a force that acts through a
distance as the trigger is depressed. Similarly, work is done when the piston exerts a pressure force that acts on
the liquid over a distance. Another example of work involves wind passing over the blades of a wind turbine as
shown in Figure 7.2. The wind exerts a force on the blades; this force produces a torque and work is given by
Figure 7.1 In a spray bottle, a piston pump does work on the fluid thereby increasing the energy in the
liquid.
Figure 7.2 When air passes across the rotor of a wind turbine, the air exerts forces that result in a net
torque. This torque does work on the blades.
A machine is any device that transmits or modifies energy, typically to perform or assist in a human task. In
fluid mechanics, a turbine is a machine that is used to extract energy from a flowing fluid.* Examples of turbines
include the horizontal-axis wind turbine shown in Fig. 7.2, the gas turbine, the Kaplan turbine, the Francis
turbine, and the Pelton wheel. Similarly, a pump is a machine that is used to provide energy to a flowing fluid.
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Energy, Work, and Power http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...
Examples of pumps include the piston pump shown in Fig. 7.1, the centrifugal pump, the diaphragm pump, and
the gear pump.
Work and energy both have the same primary dimensions, and the same units, and both characterize an amount
or quantity. For example, 1 calorie is the amount of thermal energy needed to raise the temperature of 1 gram of
water by 1°C. Other common units include the joule (J), newton-meter, kilowatt-hour (kWh), foot-pound-force
(ft-lbf), calorie (cal), and the British thermal unit (Btu).
Power, which expresses a rate of work or energy, is defined by
(7.1)
Equation 7.1 uses a derivative because power can vary with each instant in time. To derive an equation for
power, let the amount of work be given by the product of force and displacement " W = F " x:
(7.2a)
where V is velocity of a moving body. When a shaft is rotating (e.g., Fig. 7.2), the amount of work is given by
the product of torque and angular displacement " W = T "¸. In this case, the power equation is
(7.2b)
where É is the angular speed. Common units are radians per second (s-1), revolutions per minute (rpm), and
revolutions per second (rps).
Equations 7.2a and 7.2b may be combined to show the relationships between power associated with linear
motion and power associated with rotational motion:
(7.3)
Common units for power are the watt (W), horsepower (hp), and the ft-lbf/s. Other units are given in Table F.1.
Watts and horsepower are related by 1 kW = 1.34 hp. Similarly, 1 hp = 550 ft-lbf/s. It is useful to know some
typical values of power. A 60-watt light bulb uses 60 J/s of electrical energy. A well-conditioned athlete can
sustain a power output of about 300 W = 0.4 hp for one hour. A 1970 Volkswagen bug has an engine that is
rated at about 50 hp. The Bonneville Dam on the Columbia River 40 miles east of Portland, Oregon, has a rated
power of about 1080 MW.
Copyright © 2009 John Wiley & Sons, Inc. All rights reserved.
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