9-1 CHAPTER 9 Mass and Mass-Related Parameters © 2011 Cengage Learning Engineering. All Rights Reserved.

9-2 Outline In this chapter we will introduce the concept of mass in terms of a quantitative measure of the amount of atoms and molecules possessed by a substance define mass-related engineering quantities  density, specific gravity, mass moment of inertia, momentum, mass flow rate discuss conservation of mass © 2011 Cengage Learning Engineering. All Rights Reserved.

9-3 Why Is the Concept of Mass Important? It provides a quantitative measure of the amount of atoms and molecules possessed by a substance It provides a measure of resistance to translation motion It is important in determining the momentum of moving objects It is important in describing material properties such as density and specific gravity © 2011 Cengage Learning Engineering. All Rights Reserved.

9-4 What Is Mass? Provides a quantitative measure of how many molecules or atoms are in a given object A physical variable that provides a measure of how light or heavy things are © 2011 Cengage Learning Engineering. All Rights Reserved.

9-5 Mass – A Physical Variable All objects and living things are made of matters Matter is made of atoms or chemical elements Atoms are made of smaller particles called electrons, protons, and neutrons Atoms are the basic building block of all matter Matter can exist in 4 states, depending on its own and surrounding conditions – solid, liquid, gaseous, or plasma © 2011 Cengage Learning Engineering. All Rights Reserved.

9-6 heavy light massive tiny In the earlier days, we did not fully understand the concept of gravity. Hence, there was no clear distinction between mass and weight How Do We Describe Mass? descriptive but not exact © 2011 Cengage Learning Engineering. All Rights Reserved.

9-7 How Do We Describe Mass? © 2011 Cengage Learning Engineering. All Rights Reserved.

9-8 How do we describe mass? The gravitational pull on the moon is about 1/6 th of that on the earth. If your mass on the earth is 100 kg, what is your mass on the moon? © 2011 Cengage Learning Engineering. All Rights Reserved.

9-9 Mass Base SI Unit – kilogram (kg) kilogram (kg) – a unit of mass in SI; it is equal to the mass of the international prototype of the kilogram Mass provides a quantitative measure of how many molecules or atoms are in a given object © 2011 Cengage Learning Engineering. All Rights Reserved.

9-10 Other Mass Units pound mass (lb m ) slug (which system of units is this?) © 2011 Cengage Learning Engineering. All Rights Reserved.

9-11 Measurement of Mass In practice, mass of an object is measured indirectly through its weight Weight of an object on earth is the force that is exerted on the mass due to gravitational pull of the earth © 2011 Cengage Learning Engineering. All Rights Reserved.

9-12 Density – ratio of the mass of an object to the volume that it occupies Specific volume – inverse of density Mass-Related Parameters © 2011 Cengage Learning Engineering. All Rights Reserved.

9-13 Specific gravity – compares the density of a material to the density of water Specific weight – another way to measure how truly heavy or light a material is for a given volume Mass-Related Parameters © 2011 Cengage Learning Engineering. All Rights Reserved.

9-14 Density, Specific Gravity, and Specific Weight of Some Solid Materials Values shown are at room temperature or at the specified temperature © 2011 Cengage Learning Engineering. All Rights Reserved.

9-15 Density, Specific Gravity, and Specific Weight of Some Fluids Values shown are at room temperature or at the specified temperature © 2011 Cengage Learning Engineering. All Rights Reserved.

9-16 Mass Flow Rate Mass flow rate tells engineers how much material is being used or moved over a period of time so that they can replenish the supply of material Engineers use flowmeters to measure volume or mass flow rate © 2011 Cengage Learning Engineering. All Rights Reserved.

9-17 Mass Flow Rate Mass flow rate – amount of mass that flows through something per unit of time Units: kg/s, kg/min, kg/h, slugs/s, lb m /s © 2011 Cengage Learning Engineering. All Rights Reserved.

9-18 Mass Flow Rate and Volume Flow Rate © 2011 Cengage Learning Engineering. All Rights Reserved.

9-19 Mass Moment of Inertia Mass moment of inertia provides a measure of how hard it is to rotate something with respect to a center of rotation  The further away the mass is located from the center of rotation, the harder it is to rotate the mass about the given center of rotation © 2011 Cengage Learning Engineering. All Rights Reserved.

9-20 Mass Moment of Inertia For a single particle m, located at a distance r from the axis of rotation z-z, the mass moment of inertia is defined by © 2011 Cengage Learning Engineering. All Rights Reserved.

9-21 Mass Moment of Inertia For a system of 3 mass particles shown, the mass moment of inertia about the z-z axis is In general the mass moment of inertia about the z-z axis of a continuous body is determined from © 2011 Cengage Learning Engineering. All Rights Reserved.

9-22 Mass Moment of Inertia of Some Typical Objects disk circular cylinder sphere thin rectangular plate © 2011 Cengage Learning Engineering. All Rights Reserved.

9-23 Example 9.1 – Mass Moment of Inertia Given: a 2-m long steel shaft with a diameter (d) of 10 cm; density of steel = 7860 kg/m 3 Find: mass moment of inertia Solution: Moment of inertia of the shaft about the longitudinal axis becomes, © 2011 Cengage Learning Engineering. All Rights Reserved.

9-24 Momentum © 2011 Cengage Learning Engineering. All Rights Reserved.

9-25 Momentum – a physical variable that is defined as the product of mass and velocity Momentum’s direction is the same as the direction of the velocity vector or the direction of the moving object Momentum © 2011 Cengage Learning Engineering. All Rights Reserved.

9-26 Momentum How can a small pebble break my wind shield? © 2011 Cengage Learning Engineering. All Rights Reserved.

9-27 Example 9.2 – Linear Momentum Given: a person with a mass of 80 kg and running at a speed of 3 m/s; a car with a mass of 2000 kg and moving at a speed of 30 m/s in the same direction as the person Find: the linear momentum of the person and the car Solution: © 2011 Cengage Learning Engineering. All Rights Reserved.

Momentum Engineering Fundamentals, By Saeed Moaveni, Fourth Edition, Copyrighted

Momentum Engineering Fundamentals, By Saeed Moaveni, Fourth Edition, Copyrighted

Momentum Engineering Fundamentals, By Saeed Moaveni, Fourth Edition, Copyrighted

Momentum Engineering Fundamentals, By Saeed Moaveni, Fourth Edition, Copyrighted

The rate at which a fluid enters a 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 = the tub 9-32 Conservation of Mass – Keeping Track of Mass © 2011 Cengage Learning Engineering. All Rights Reserved.

9-33 Conservation of Mass – Keeping Track of Mass The concept of conservation of mass can also be applied to a concept called queuing  a broad area in mathematics, operation research, engineering management, and traffic management  a study of people waiting in service lines products waiting in assembly lines digital information waiting to move through computer networks © 2011 Cengage Learning Engineering. All Rights Reserved.

9-34 Conservation of Mass – Keeping Track of Mass © 2011 Cengage Learning Engineering. All Rights Reserved.

outlet. Tank B has an outlet that discharges the water at 1 kg/s. Assume density of water is 1000 kg/m 3. Find: the amount of water stored in each tank after 5 minutes; how long will it take to fill the tanks completely if the volume of each tank is 12 m 3 ? 9-35 Example 9.3 – Conservation of Mass Given: two identical size tanks A and B are filled with water at a rate of 2 kg/s. Tank A has no © 2011 Cengage Learning Engineering. All Rights Reserved.

9-36 Example 9.3 – Conservation of Mass (rate at which fluid enters a control volume) - (rate at which fluid leaves the control volume) = (rate of accumulation or depletion of the mass of fluid within the given control volume) Solution: Using the conservation of mass, Tank A: no water leaves the tank © 2011 Cengage Learning Engineering. All Rights Reserved.

9-37 Example 9.3 – Conservation of Mass Solution (continued): Time to fill tank A: © 2011 Cengage Learning Engineering. All Rights Reserved.

9-38 Example 9.3 – Conservation of Mass Solution (continued): Tank B: water leaves the tank at the rate of 1 kg/s: Time to fill tank B: © 2011 Cengage Learning Engineering. All Rights Reserved.

Given: The gasoline consumption of a car is 15 km/liter when the car is moving at a speed of 90 km/h. The specific gravity of gasoline is Find: The amount of gasoline, in kg, burned every hour if there were one million of these cars on the road? Solution: First, we will use Equation (9.2) to compute the density of gasoline Example 9.4 – Mass Flow Rate © 2011 Cengage Learning Engineering. All Rights Reserved.

9-40 Example 9.4 – Mass Flow Rate Solution (continued): The volume-flow rate of fluid for a single car is determined from: Next, we will use Equation (9.6) to calculate the mass-flow rate of the fuel per car For one million cars 4,320,000 kg of gasoline is burned each hour! © 2011 Cengage Learning Engineering. All Rights Reserved.

9-41 Summary You should have a good understanding of mass and its important role in engineering applications and analysis. You should know that in engineering to show how light or heavy materials are, we use properties such as density, specific volume, specific weight, and specific gravity. You should also know the definition of these properties. © 2011 Cengage Learning Engineering. All Rights Reserved.

9-42 Summary You should have a good understanding of mass flow rate and its relationship to volume flow rate. You should realize that mass provides a measure of resistance to translational motion. You should also know the role the distribution of mass plays in rotational motion in terms of mass moment of inertia © 2011 Cengage Learning Engineering. All Rights Reserved.

9-43 Summary You should know how we define momentum for a moving object. You should know how to use the conservation of mass to keep track of mass entering, leaving, accumulating, or depleting for a control volume © 2011 Cengage Learning Engineering. All Rights Reserved.