In this lesson, we will discuss how to calculate
major losses in non-circular ducts.
Not all conduits used to transport fluids
are circular.
For example, many ducts used for heating,
ventilation, and air conditioning in buildings
have a rectangular cross section.
Regardless of the shape, you can still use
the Darcy-Weisbach equation to calculate the
major losses.
However, the pipe diameter D is replaced by
the hydraulic diameter Dh.
The hydraulic diameter is equal to four times
the cross sectional area of the flow A, divided
by the wetted perimeter l.
If we examine the cross section of a duct
that is filled with an orange fluid, the wetted
perimeter is the length of the wall that is
exposed to the fluid.
Since the duct is completely filled, l is
the entire perimeter of the duct.
A is the region shaded in orange, which encompasses
the entire duct cross sectional area.
If the flow is fully-developed and laminar,
the friction factor is a constant C divided
by the Reynolds number.
The Reynolds number uses the hydraulic diameter,
and the constant is related to the shape of
the duct.
For circular ducts this constant is 64.
If the flow is fully-developed and turbulent,
the friction factor will be a function of
both the Reynolds number and relative roughness,
where both parameters use the hydraulic diameter.
You may use the Colebrook equation or Moody
chart to estimate the friction factor for
non-circular ducts.
However, keep in mind that the Colebrook equation
and Moody chart were based on experiments
that used circular pipes, so some additional
error will be introduced into your calculations
if you use them to calculate the friction
factor for non-circular ducts.
