South valley University
Faculty of Engineering
Mechanical Power Engineering Dep.
Fluid Mechanics 2
Course Code MPEG222
Second Semester
Fall 2016/2017
By
Dr. Eng./Ahmed Abdelhady
Mobile: 01118501269
Email: a_abdelhady80@eng.sve.edu.eg
Lecture No. 3
Hydraulic Grade Line (HGL)
and Energy Grade Line (EGL)
• P/ρg is the pressure head
• V2/2g is the velocity head
• z is the elevation head
Hydraulic Grade Line (HGL)
and Energy Grade Line (EGL)
Applications of the Bernoulli Equation
Flow Rate and Velocity Measurement
Direct Methods
Obstruction
Methods
Flow Rate and Velocity Measurement
Direct Methods
Stopwatch and
Scaled Tank
Flow Rate and Velocity Measurement
Direct Methods
Pitot and Pitot-Static Probes
Flow Rate and Velocity Measurement
Pitot-Static Probes
Flow Rate and Velocity Measurement
Obstruction Methods
Orifice
Venturi
Flow Nozzle
Flow Rate and Velocity Measurement
Obstruction Methods
Flow Rate and Velocity Measurement
Positive Displacement Flowmeters
Turbine Flowmeters
Flow Rate and Velocity Measurement
Positive Displacement Flowmeters
Paddlewheel Flowmeters
Flow Rate and Velocity Measurement
Variable-Area Flowmeters (Rotameters)
Viscous Flow in Pipes
Basic equations
1- Continuity equation:
Viscous Flow in Pipes
Basic equations
2- Energy Equation:
The kinetic energy coefficients α1 and α2 compensate for
the fact that the velocity profile across the pipe is not
uniform. For uniform velocity profiles α=1, whereas for
any non-uniform profile α>1,
Laminar and Turbulent Flow
We can verify the existence of these laminar, transitional, and
turbulent flow regimes by injecting some dye streaks into the
flow in a glass pipe, as the British engineer Osborne Reynolds
(1842–1912) did over a century ago.
Laminar and Turbulent Flow
Time dependence of fluid velocity at A point.
Reynolds Number
Where:
Vavg = average flow velocity (m/s)
D = characteristic length of the geometry (diameter in
this case, in m)
= kinematic viscosity of the fluid (m2/s)
hydraulic diameter
The Entrance Region
Entrance region, developing flow, and fully developed flow in a pipe system.
Entry Lengths
In many pipe flows of practical engineering interest, the
entrance effects become insignificant beyond a pipe
length of 10 diameters
Classifications of Flow Losses
Major LOSSES
Darcy friction factor
For Laminar Flow
For Turbulent Flow
Colebrook Eq.
The Moody Chart
Recommended Roughness
Values for Commercial Ducts
MINOR LOSSES
Sources of Minor Losses
The head loss at the inlet and Exit of a pipe
Sharp-Edge
Round-Edge
Sources of Minor Losses
Sudden Expansion
(based on the velocity in the smaller-diameter pipe)
Sources of Minor Losses
Sudden Contraction
Sources of Minor Losses
Flow-Turning or (Bends-Elbows)
Round-Elbow
Sharp-Turn
90o Elbow
Sources of Minor Losses
Flow-Control Devices (Valves)
Energy Analysis of Steady Flows
For Steady-State Flow
For Specific Energy
Energy Analysis of Steady Flows
Using the definition of enthalpy
Energy Analysis of Steady Flows
Example
Example
Water flows from the basement to the second floor
through the 2 cm diameter copper pipe (ε = 0.00016 cm)
at a rate of Q = 0.8 l/s and exits through a faucet of
diameter 1.3 cm as shown in figure. Determine the
pressure at point 1 if :
a) viscous effects are neglected,
b) the only losses included are major losses
c) all losses are included
Example
Solution
Solution
Solution
Solution
Pipes in Series and in Parallel
Pipes in Series
For pipes in series, the flow rate is the same in each pipe, and
the total head loss is the sum of the head losses in individual
pipes
Equivalent velocity method
Pipes in Series and in Parallel
Equivalent length method
For two pipes to be equivalent
Pipes in Series and in Parallel
Pipes in Parallel
For a system of two parallel pipes 1 and 2 between junctions A
and B with negligible minor losses, this can be expressed as:
Flow Between Reservoirs
Flow Between Reservoirs