Jamil Ghojel - Fundamentals of Heat Engines

Fluid mechanics deals with the behaviour of a fluid – liquid, gas, or vapour – in quiescent state and in a state of motion. Fluids are substances that cannot preserve a shape of their own. In heat engine processes, the fluids used are predominantly in gas form and include air at various degrees of compression and products of combustion at elevated pressures and temperatures. Understanding the principles of fluid mechanics will help students to better handle the processes in the reciprocating and gas turbine engines.

Mass is a measure of inertia and quantity of the body of matter (fluid), m ( kg ).

Weight is the force with which a body of the fluid is attracted towards the earth by gravity:

Density is the amount of mass per unit volume:

Specific weight is the weight of a unit volume of a substance:

Specific gravity is

where subscripts f and w are for fluid and water, respectively.

Pressure is the force exerted by a fluid on a unit area of its surroundings:

Pressure acts perpendicular to the walls of the container surrounding the fluid. A column of fluid of height h m having a cross sectional area of A m 2and density ρ kg / m 3will exert a pressure of

Compressibility is the change in volume of a substance when subjected to a change in pressure exerted on it. The usual parameter used to measure compressibility of liquids is the bulk modulus of elasticity E :

The compressibility of a gas at constant temperature is defined as

For a perfect gas:

Generally, the shearing stress τ developed in a moving fluid between a stationary surface and a moving fluid body is proportional to the velocity gradient Δv / Δy , and the constant of proportionality is the dynamic viscosity μ :

Fluids such as water, oil, gasoline, alcohol, kerosene, benzene, and glycerine behave in accordance with this equation and are known as Newtonian fluids. Fluids that behave otherwise (viscosity changes with stress) are known as non‐Newtonian fluids.

The previous equation can be rewritten in terms of the viscosity as

The units of μ can be developed as follows:

The ratio of dynamic viscosity to density of the fluid is the kinematic viscosity ν :

Viscosity of liquids decreases with increasing temperature, and that of gases increases with increasing temperature.

If a fluid body with cross‐sectional area A is flowing at velocity C , its volumetric flow rate Q is given by

(1.25)

And the mass flow rate is given by

(1.26)

Consider now the flow of this fluid through the control volume shown in Figure 1.6. The mass flow equations at inlet 1 and exit 2 are given by

Figure 1.6Fluid flow through a control volume.

The continuity equation or equation of conservation of mass for this flow is obtained by equating the mass flow rates at sections 1 and 2, , or

(1.27)

The total energy (in units of N . m ) for an element of fluid of mass m at sections 1 and 2 of the control volume shown in Figure 1.6is given by

where

mp/ρ : flow energy required to move fluid element m against pressure p

mC2/2 : kinetic energy of element m travelling at velocity C

mgz : potential energy of the element due to its elevation z relative to a reference level