Merc thermal fluids_05_fluidmechanics_0119

Fluid Mechanics
© 2019 Kaplan, Inc.
Fluid Mechanics
Mechanical PE Thermal & Fluids Systems Exam Prep Course

Fluid Mechanics
Topics
• Introduction
• Fluid Properties (MERM Chapter 14)
• Fluid Statics (MERM Chapter 15)
• Fluid Flow Parameters (MERM Chapter 16)
• Fluid Dynamics (MERM Chapter 17)
2

Fluid Mechanics
Fluid Mechanics
• Fluid Mechanics
• The study of liquids and gasses at rest (statics) and in motion (dynamics)
• Liquids and gases can both be categorized as fluids
• Aerodynamics (gases in motion)
• Hydrodynamics (liquids in motion)
3

Fluid Mechanics
Assumptions
Fluid mechanics assumes that every fluid obeys the following:
• Conservation of mass
• Conservation of momentum
• It is often useful to assume a fluid is incompressible - that is, the density of the fluid
does not change
• Liquids can often be modeled as incompressible fluids, whereas gases cannot.
• Similarly, it can sometimes be assumed that the viscosity of the fluid is zero (the fluid is
inviscous).
• Gases can often be assumed to be inviscous.
• If a fluid isn't inviscous, and its flow is contained in some way (e.g. in a pipe), then the
flow at the boundary must have zero velocity
4

Fluid Mechanics
Ideal Fluids
• Steady:
• velocity, density and pressure do not change with time; no turbulence
• Incompressible:
• constant density
• Nonviscous:
• no internal friction between adjacent layers
• Irrotational:
• no particle rotation about center of mass
5

Fluid Mechanics
Fluid Properties
• Density - mass per unit volume, units of
lbm/ft3
• Specific Volume
• Viscosity - is a measure of that fluid’s
resistance to flow when acted upon by an
external force such as a pressure
differential or gravity
• Specific Weight - to simplify some calcs,
units of lbf/ft3
• Specific Gravity - dimensionless ratio of a
fluid’s density to some standard reference
density. For liquids and solids, the
reference is the density of pure water.
cg
g
ργ =
M
V
v ==
ρ
1
V
M
=ρ
6

Fluid Mechanics
Speed of Sound
The speed of sound (acoustical velocity or
sonic velocity), a, in a fluid is a function of
its bulk modulus, E, (or, equivalently, of its
compressibility).
In an ideal gas, the speed of sound is a
function of temperature only:
Mach Number:
Example:
What is the speed of sound in air at a
temperature of 339K?
The heat capacity ratio is k = 1.4.
2
2
m
(1.4) 286.7 (339K) 369 m/s
K
a kRT
s
 
= = = 
⋅ 
7

Fluid Mechanics
Compressible vs. Incompressible Flow
• A flow is classified as incompressible if the density remains nearly constant.
• Liquid flows are typically incompressible.
• Gas flows are often compressible, especially for high speeds.
• Mach number, Ma = V/a is a good indicator of whether or not compressibility effects
are important.
• Ma < 0.3 : Incompressible
• Ma < 1 : Subsonic
• Ma = 1 : Sonic
• Ma > 1 : Supersonic
• Ma >> 1 : Hypersonic
8

Fluid Mechanics
Fluid Statics
• Fluid Statics deals with problems associated with fluids at rest
• In fluid statics, there is no relative motion between adjacent fluid layers.
• Therefore, there is no shear stress in the fluid trying to deform it
• The only stress in fluid statics is normal stress
• Normal stress is due to pressure
• Variation of pressure is due only to the weight of the fluid → fluid statics is only
relevant in presence of gravity fields.
• Applications: Floating or submerged bodies, water dams and gates, liquid storage
tanks, etc.
9

Fluid Mechanics
Hydrostatic Pressure
• Pressure at any point in a fluid is the same in all directions
• Pressure has a magnitude, but not a specific direction, and thus it is a scalar quantity
• Hydrostatic pressure is the pressure a fluid exerts on an immersed object or container
walls
• Pressure is independent of an object’s
area of the object
• Pressure varies linearly with depth
10

Fluid Mechanics
Variation of Pressure with Depth
• In the presence of a gravitational field, pressure increases
with depth because more fluid rests on deeper layers.
• To obtain a relation for the variation of pressure with depth,
consider rectangular element
• Force balance in z-direction gives
• Dividing by Δx and rearranging gives
• ∆ z = h is called the pressure head (hydrostatic head)
2 1
0
0
z zF ma
P x P x g x zρ
= =
∆ − ∆ − ∆ ∆ =
∑
2 1 sP P P g z zρ γ∆ = − = ∆ = ∆
11

Fluid Mechanics
The Manometer
• An elevation change of Δz in a fluid at rest
corresponds to ΔP/ρg.
• A device based on this is called a manometer.
• A manometer consists of a U-tube containing
one or more fluids such as mercury, water,
alcohol, or oil.
• Heavy fluids such as mercury are used if large
pressure differences are anticipated.
12

Fluid Mechanics
Pressure on a Horizontal Plane Surface
• The pressure on a horizontal plane surface is uniform over the surface because the
depth of the fluid is uniform
• The resultant of the pressure distribution acts through the center of pressure of the
surface, which corresponds to the centroid of the surface
13

Fluid Mechanics
Hydrostatic Forces on Plane Surfaces
• On a plane surface, the hydrostatic
forces form a system of parallel
forces
• For many applications, magnitude
and location of application, which is
called center of pressure, must be
determined
14

Fluid Mechanics
Center of Pressure
• Line of action of resultant force does
not pass through the centroid of the
surface. In general, it lies underneath
where the pressure is higher.
• Vertical location of center of pressure is
determined by equation the moment of
the resultant force to the moment of
the distributed pressure force.
• IC is tabulated for simple geometries.
Special cases: vertical surfaces
15

Fluid Mechanics
Pascal’s Law
• Two points at the same elevation in a
continuous fluid at rest are at the same
pressure, called Pascal’s law,
• Pressure applied to a confined fluid
increases the pressure throughout by
the same amount.
• Ratio Ar/Ap is called ideal mechanical
advantage
A hydraulic ram (hydraulic jack, hydraulic press)
16

Fluid Mechanics
Buoyancy and Stability
• Buoyancy is due to the fluid displaced by a body.
• Buoyant force always acts to counteract an object’s weight (i.e., buoyancy acts against
gravity). The magnitude of the buoyant force is predicted from Archimedes’ principle.
• Archimedes principle: The buoyant force acting on a body immersed in a fluid is equal
to the weight of the fluid displaced by the body, and it acts upward through the
centroid of the displaced volume.
17

Fluid Mechanics
Buoyancy and Stability
• Buoyancy force FB is equal only to the displaced volume ρfgVdisplaced
• Three scenarios possible
1. ρbody < ρfluid: floating body
2. ρbody = ρfluid : neutrally buoyant
3. ρbody > ρfluid : sinking body
18

Fluid Mechanics
Fluid Dynamics
• The two types of fluid mechanics problems are solved in one of two ways:
• When fluid energy is involved, solve by an energy solution.
or
• When fluid forces are involved, solve by impulse-momentum.
19

Fluid Mechanics
Use the Bernoulli equation – energy conservation equation.
In terms of energy per unit mass: In terms of head:
Fluid Energy
Continuity holds between any two positions in a closed conduit.
Use the continuity equation.
20

Fluid Mechanics
Example
21

Fluid Mechanics
Example: Solution
22

Fluid Mechanics
The Bernoulli Equation
• Without the consideration of any losses, two points on the same streamline satisfy
where (all per unit mass)
P/r is flow energy
V2/2 is kinetic energy
gz is potential energy
• The Bernoulli equation can be viewed as an expression of mechanical energy balance.
2 2
1 1 2 2
1 2
1 22 2
P V P V
z z
g g g gρ ρ
+ + = + +
23

Fluid Mechanics
Static and Dynamic Pressure
The sum of the static, dynamic, and hydrostatic
pressures is called the total pressure (a constant
along a streamline).
The sum of the static and dynamic pressures is
called the stagnation pressure.
24

Fluid Mechanics
Energy Grade Line (EGL)
25

Fluid Mechanics
Conservation of Mass
26

Fluid Mechanics
Head Losses
• There are two types of head losses:
• friction losses, and
• minor losses
• For friction losses, use one of two equations.
• Darcy equation, or
• Hazen-Williams equation
• Minor losses (changes in direction, flow area, etc.)
• Usually, can be calculated using loss coefficients (K) but can also be determined using
equivalent lengths.
27

Fluid Mechanics
Friction Losses – Darcy Equation
• The Darcy equation is
• Can be used for both laminar and turbulent flow.
• To find f, use the Moody diagram. Enter the diagram with the Reynolds number and
the ratio of surface roughness to diameter (See MERM Appendix 17.A and Table 17.2).
28

Fluid Mechanics
Friction Losses – Reynolds Number
• The Reynolds number is the ratio of inertia force to viscous force in a fluid.
• Note that kinematic viscosity is usually given in the problem statement, but tabular
values are available in MERM appendices.
29

Fluid Mechanics
Moody Diagram
30

Fluid Mechanics
Friction Losses – Hazen-Williams
The Hazen-Williams equation is
For C, use MERM Appendix 17.A.
Advantage: C does not depend on the Re number
The Hazen-Williams equation should be used only for turbulent flow.
31

Fluid Mechanics
Example
32

Fluid Mechanics
Example: Solution
33

Fluid Mechanics
Example
34

Fluid Mechanics
Example: Solution
35

Fluid Mechanics
Minor Losses
The loss coefficient is defined by:
K is usually given, or K can be calculated for certain changes as:
36

Fluid Mechanics
Minor Losses
37

Fluid Mechanics
Minor Losses
• For equivalent lengths, determine the additional length of pipe whose friction losses
equal the minor loss under consideration, then add that to the actual length and
compute head loss as usual.
• Equivalent lengths are in MERM13 Appendix 17.D on page A-54.
38

Fluid Mechanics
Example
39

Fluid Mechanics
Example: Solution
40

Fluid Mechanics
Multiple Pipe Systems
There are two types of multiple pipe systems.
• Series, and
• Parallel
41

Fluid Mechanics
Series Pipe Systems
A series pipe system consists of two or more pipes of differing diameters placed in
sequence. There is one basic principle and two cases of knowns vs. unknowns.
If the flow rate or velocity in any part of the system is known, we use continuity to solve.
If neither the velocity nor the flow quantity are known, a trial-and-error method as
described in MERM Ch.17, Sec. 28 must be conducted.
42

Fluid Mechanics
Parallel Pipe Systems
A parallel pipe system consists of two or more pipes sharing a common source.
There are three basic principles:
1. Head loss in each branch is the same
2. Head loss between two junctions is the same as the head loss in each branch
3. The total flow rate:
43

Fluid Mechanics
Example
44

Fluid Mechanics
Example: Solution
45

Fluid Mechanics
Impulse-Momentum Principle
• The impulse applied to a body is equal to the change in momentum
• This equation calculates the constant force required to accelerate or retard a fluid
stream. This would occur when fluid enters a reduced or enlarged flow area. If the flow
area decreases, for example, the fluid will be accelerated by a wall force up to the new
velocity.
• MERM Ch.17, Sec. 38
46

Fluid Mechanics
Confined Streams in Pipe Bends
• Since the fluid is confined, the forces due to static pressure must be included in the
analysis. (The effects of gravity and friction are neglected.)
47

Fluid Mechanics
Impulse Turbine
• The maximum power possible is the kinetic
energy in the flow.
• The max power transferred to the turbine is
the component in the direction of the flow.
48

Fluid Mechanics
Pumps
• Pumps add hydraulic head to a system.
• It is usually necessary to compute the following:
• head required of the pump
• Corresponding flow rate Q (if system curve is given - otherwise the system curve
must be derived)
• pump power requirements
49

Fluid Mechanics
Turbomachinery
• Pumps – add energy to a flow
Positive Displacement– force fluid along through volume changes
• Dynamic – add momentum to the fluid with fast moving blades
─ Centrifugal – radial exit flow
─ Axial – axial exit flow
• Turbines – extract energy from a flow
• Reaction – dynamic devices which admit high energy fluid and extract its momentum
• Impulse – converts high head to high velocity which impacts blades
50

Fluid Mechanics
Fluid Mechanics - Other Topics
• Viscosity Conversions
• Surface Tension and Capillary Action
• Multifluid Barometers
• Forces on Inclined and Curved Surfaces
• Pipes, Valves
• Discharge From Tanks
• Flow Measuring Devices
• Open Jets, Lift, Drag
MERM Chapter 14
MERM Chapter 17
MERM Chapter 16
MERM Chapter 15
51

Fluid Mechanics
Questions?
52

Merc thermal fluids_05_fluidmechanics_0119

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