Chapter 9: Mass and mass-related parameters 서강대학교 전자공학과

Mass as fundamental dimension Atoms are the basic building block of all matter. Atoms are made up of even smaller particles: electrons, protons, and neutrons. Periodic table 2

Mass as fundamental dimension Atoms are combined to create molecules. Water : H2O A glass of water is made up of billions and billions of homogeneous water molecules. Molecules are the smallest portion of a given matter that possesses its characteristic properties. Four states of matter: solid, liquid, gaseous, plasma. Mass provides a quantitative measure of how many molecules or atoms are in a given object. The matter may change its phase, but its mass remains constant. 3

Mass as fundamental dimension Mass moment of inertia A measure of how hard it is to rotate something with respect to center of rotation Momentum A measure of how difficult it is to stop the object. Mass plays an important role in storing thermal energy. The more massive something is, the more thermal energy can be stored within it. water is better at storing thermal energy than air is. 4

Measurement of mass The mass of an object is measured indirectly by using how much something weights. Weight of an object: the force that is exerted on the mass due to the gravitational pull of the earth. spring scale – measuring the deflection of the spring the difference between weight and mass 5

Density, specific volume, and specific gravity The ratio of the mass to the volume that it occupies. Specific volume (commonly in thermodynamics) The inverse of density Specific gravity To represent the heaviness of some material 6

Density, specific volume, and specific gravity Specific weight To measure how truly heavy or light a material is for a given volume. 7

Mass flow rate Mass flow rate Mass and volume flow measurements It tells how much material is being used or moved over a period of time. Mass and volume flow measurements Gasoline service station the amount of domestic water used. The relationship between the mass flow rate and the volume flow rate. 8

Mass momentum of Inertia How hard it is to rotate something wrt center of rotation 9

Mass momentum of Inertia 10

Momentum The product of mass and velocity A direction is associated with momentum. The term is commonly abused by sports casters? A bullet – small mass, but high velocity 11

Conservation of mass The rate at which water comes to the tub is equal to the rate at which the water leaves the tub plus the time rate of accumulation of the mass of water within the tub. 12

Conservation of mass The rate at which the fluid enters the control volume minus the rate at which the fluid leaves the control volume should be equal to the rate of accumulation or depletion of the mass of fluid within the given control volume. A study of queues People waiting in service lines Products waiting in assembly lines Digital information waiting to move through computer networks 13

Example 9.3 How much water is stored after 5 min in each of the takes shown in Figure 9.5? How long will it take to fill the tanks completely provided that the volume of each tank is 12 m3? Assume the density of water is 1000 kg/m3. 14

Example 9.3 In Fig. 9.5(a) In Fig. 9.5(b) 1) 2 kg/s – 0 = changes of mass inside the control volume / change in time changes of mass inside the control volume = 2 kg/s * 5 min * 60 s/min = 600 kg 2) mass = (density) (volume) = 1000 kg/m3 * 12 m3 = 12000 kg 3) time required to fill the tank = 12000 kg / 2 (kg/s) = 6000 s = 100 min In Fig. 9.5(b) 1) 2 kg/s – 1 kg/s= changes of mass inside the control volume / change in time changes of mass inside the control volume = 1 kg/s * 5 min * 60 s/min = 300 kg 3) time required to fill the tank = 12000 kg / 1 (kg/s) = 12000 s = 200 min 15