Question

How do the energies of a flowing fluid and a fluid at rest compare? Name the specific forms of energy associated with each case.

Short answer

Answer: A fluid at rest possesses only gravitational potential energy, which depends on the height of the fluid column. In contrast, a flowing fluid possesses three forms of energy: kinetic energy (associated with the motion of fluid particles), pressure energy (associated with the pressure exerted by the fluid), and gravitational potential energy (similar to a fluid at rest, depending on its height above a reference level).

Step-by-step solution

The energy of a fluid at rest

A fluid at rest (or a static fluid) only possesses potential energy and its associated energy form is known as gravitational potential energy. Gravitational potential energy depends on the height of the fluid column and can be calculated using the formula: \[PE = mgh\] Where, PE - Gravitational Potential Energy m - mass of the fluid g - acceleration due to gravity (approximately 9.81 m/s^2) h - height of the fluid column

The energy of a flowing fluid

A flowing fluid (also known as dynamic fluid) possesses three forms of energy: 1. Kinetic energy: This is the energy associated with the motion of the fluid particles. The kinetic energy of a moving fluid can be calculated using the formula: \[KE = \frac{1}{2}mv^2\] Where, KE - Kinetic Energy m - mass of the fluid v - velocity of the fluid 2. Pressure energy: This is the energy associated with the pressure exerted by the fluid on its surroundings. Pressure energy can be calculated using the formula: \[PE = PV\] Where, PE - Pressure Energy P - Pressure exerted by the fluid V - Volume of the fluid 3. Gravitational potential energy: As with a fluid at rest, a flowing fluid also has gravitational potential energy, depending on its height (h) above a reference level. The formula is the same as described for a fluid at rest: \[PE = mgh\] The combination of these three energy forms in flowing fluids is described by the Bernoulli's Equation when considering a steady, incompressible, and non-viscous flow of a fluid. In conclusion, the energy of a fluid at rest is solely dependent on its gravitational potential energy, while a flowing fluid possesses kinetic energy, pressure energy, and gravitational potential energy.