Flow of fluid past a cylinder (A) laminar and (B) turbulent.
CALCULATION OF THE PRESSURE DROP IN A PIPE DUE TO FRICTION
If
the volumetric flow rate of a liquid of density ρ and viscosity η through a pipe of
diameter d is Q, the derivation of the mean velocity, u, from the flow rate and pipe area completes the data required for
calculating Re.
FIGURE 2.11 Flow of fluid past a cylinder
(A) laminar and (B) turbulent.
If the pipe roughness factor
is known, the equivalent value of R/ρu2 can be determined from
Figure 2.10, and the shear stress at the pipe wall can be calculated. The total
frictional force opposing motion is the product of R and the surface area of
the pipe, πdl, where l is the
length of the pipe. If the unknown pressure drop across the pipe is DP, the force driving through the
pipe is ΔP · πd2/4. Equating pressure
force and frictional force gives
Division
by ρg gives the pressure loss as a friction head. This form is
used in equations (2.7) and (2.8).
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