Optimal
Diameter and
Pressure Loss
Diameter & Pressure Loss
Flow of fluids
in Piping
Systems
Properties of
Fluids
Pressure Loss
Energy
Conservation
Flow
Calculation
• Mass
Conservation
Diameter
Calculation
Optimal Diameter
and Pressure Loss
Determining the
diameter of a tube
/ pipe is most often
a hydraulics
problem
Fluid
Mechanics
Fluids through Pipes
A fluid flowing through a pipe will always carry an
amount of energy loss.
The resistance is of two types:
• a) External, friction between the fluid against
the pipe walls.
• b) Internal, friction between the fluid
molecules themselves.
The energy lost is called "head loss" or "pressure loss”, results in a gradual decrease in the pressure
of the fluid, dropping from one point to another in the flow direction.
Thus, the only fluid energy variation between the end points of the pipeline is the produced by
pressure loss.
Flowing Fluids through pipes
Reynolds
Number
Diameter and Pressure
Loss
Flow regimes:
Laminar: mean velocity of the stream is small,
filaments will be seen as straight lines (fig. A)
Critical: when V ↑, there is a point where the
filaments begin to curl, breaking up abruptly
Turbulent: at higher velocities than the critical, the
filaments disperse indeterminately throughout the
stream (fig. B)
Reynolds
number
Depends on the diameter
of the pipe, the fluid
density, the fluid viscosity
and flow velocity.
It is dimensionless.
Ratio of the dynamic forces
of the fluid mass with
respect to the deformation
stresses caused by
viscosity.
Reynolds
Number
Energy Conservation
The energy conservation law states that energy
cannot be created or destroyed can only be
transformed from one form to another. For
example, when electrical energy is transformed
into heat energy in a heater
Bernoulli’s
Equation
Pressure Loss
The flow of fluids in pipes is always accompanied by
friction produced between the particles themselves and
between the fluid and the pipe wall. In other words,
energy loss, it means that there is a pressure loss in the
direction of the flow.
Fluid's Flow
general
Equation - Darcy
Flow of fluids in pipes is
always accompanied by
friction, in other words,
energy loss and pressure
loss.
Darcy's Equation
Darcy's equation determines the pressure loss
between two sections of a pipeline.
Valid for both laminar and turbulent flow of any
fluid in a pipe.
With the applicable restrictions, Darcy's equation
can be used with compressible fluids (vapours
and gases).
Friction Factor
Laminar Flow (R< 2000):
Turbulent flow (R > 4000): Depends on E/d
(roughness/diameter). 1o Equation for
turbulent flow:
Colebrook año 1937
Diameter Calculation
As known:
Moreover, the Pressure Loss is a function of the velocity of the
system:
Recommended
Velocity
Wrap Up
• Explored fluid mechanics for industrial
piping design.
• Covered fluid properties,
laminar/turbulent flow, energy
conservation, and pressure loss.
• Highlighted challenges like
external/internal resistance and the
Reynolds number.
• Discussed energy conservation laws,
Bernoulli's principle, and Darcy's
equation for pressure loss.
• Emphasized Crane's method for
quantifying energy loss in piping design.
• Encouraged deeper exploration and
consideration of variables in piping
design.