# Thermal & Fluids - Fluid Mechanics

### Principles - Fluid Mechanics - 6 of 80 Problems

The fluid mechanics principles section accounts for 6 questions. These questions can cover any of the topics below. Fluid properties describe the density, viscosity, kinematic viscosity, specific gravity and much more. Other properties are described in other sections of this book. In order to be prepared for questions on Fluid properties you need to understand what these properties describe, its units and where to find the properties of common fluids. Finally in this section you need to understand the difference between compressible and incompressible flow and when you can use compressible equations versus incompressible equations. The majority of the exam, which basically includes all sections in this book except for the compressible flow section, will assume incompressible flow.

### Fluid Properties

During the exam you will need to be able to find and use fluid properties to complete many problems. You should be very familiar with your resources and where to find these fluid properties. As you go through these descriptions of the important fluid properties, look through your Mechanical Engineering Reference Manual and your Schaum’s Thermodynamic Fluid Mechanics. Tag the appendices that contain these properties and recognize the units. The key is to not waste time looking for fluid properties and to not make mistakes when solving a problem due to incorrect units.

• #### Density:

The density of a substance is its mass per unit volume, basically how heavy is something in one cubic foot or one cubic meter. The density of a fluid is measured as a weight per unit volume. Specific volume is the inverse of density and is measures as a volume per unit mass.
• #### Viscosity:

The viscosity of a fluid describes the fluids resistance to flow. Viscosity is measured in cP or centipoises and is represented by the variable, µ or mu. Viscosity is measured with a device called a viscometer. There are many different types of viscometers, but each typically has the fluid moving past/through an object or it has the object moving through the fluid. The time of travel will vary based on the viscosity of the fluid. For example, water has a viscosity of ~1.00 cP (centipoises) at 68° F, while syrup has a viscosity of ~1400 cP and air has a viscosity of ~.01827 cP.

There are two types of viscosities, dynamic (absolute) viscosity and kinematic viscosity. The previously discussed viscosity µ is dynamic viscosity. Kinematic viscosity describes the ratio of the fluids resistance to flow (dynamic viscosity) to the fluids density. Kinematic viscosity is indicated by the symbol, v or nu.
Kinematic viscosity has the units ft^2/s as shown above. Viscosities of water have been included below for your convenience.
• #### Specific Gravity:

Specific gravity is the term used to describe the ratio between a fluid’s density compared to the density of water. Water has a specific gravity of 1.0.

### Compressible Flow

In reality, all fluids are compressible to some extent. A compressible fluid is defined as a fluid that changes in density when the fluid changes in pressure or temperature. On the exam and in practice, a distinction is made between compressible and incompressible fluids because it makes calculations simpler. The majority of the calculations on the exam will be for incompressible flow. The only exceptions will be when the exam clearly indicates or when the Mach number or nozzle type questions arise.

#### A Compressible Fluid

A compressible fluid will reduce its volume in the presence of an external pressure. The quantitative measurement of the compressibility is taken as the relative volume change of the liquid in response for a pressure change.

There are two types of compressibility that you should know for the exam. Compressibility is defined in two forms. The adiabatic compressibility describes the compressibility of the system when the temperature of the system is constant. This is denoted by βV. The isothermal compressibility refers to the compressibility measured under no energy transfer between the system and the surroundings. This is denoted by βS. Since an adiabatic process is also isentropic, this process is a constant entropy process.

#### Mach Number

Mach number is the ratio of speed to sound. It is a value between 0 and infinity. Transonic, subsonic, supersonic, hypersonic, hypervelosity...see book for full text

#### Nozzles

Nozzles are used to create changes in velocities and pressures of a moving fluid. A nozzle in its simplest form increases the velocity of a fluid by reducing the area, which also increases the fluids pressure.

The nozzle is an important part of the exam and if you can understand what the fluid is doing through the nozzle, then you will be in a good position to get these types of questions correct...see book for full text

#### Diffusers

Diffusers are the opposite of nozzles. Diffusers decrease the pressure of the fluid by reducing the velocity...see book for full text

#### Bulk Modulus

The term Bulk Modulus is a property of a fluid that describes the compressibility of the fluid. Bulk modulus, β, is defined in the equation below...see book for full text

### Incompressible Fluids

As previously discussed, incompressible fluids do not occur in the real world. Incompressible fluids were created to describe a range of fluids, in order to make calculations simpler. The calculations are simpler because incompressible fluids are assumed. An incompressible fluid is a fluid that does not change the volume of the fluid due to external pressure. Most of the basic calculations done in fluid dynamics are done assuming the fluid is incompressible. The approximation of incompressibility is acceptable for most of the liquids as their compressibility is very low. However, the compressibility of gases is high, so gases cannot be approximated as incompressible fluids. The compressibility of an incompressible fluid is always zero.

The following incompressible fluids topics are discussed in the book in more detail.