CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 301

whereVfluid velocity, ft/s (m/s)
Dpipe diameter, ft (m)
density of fluid, lbs^2 /ft^4 (kgs^2 /m^4 ) (specific weight divided by g,
32.2 ft/s^2 )
viscosity of fluid lbs/ft^2 (kgs/m^2 )
/kinematic viscosity, ft^2 /s (m^2 /s)

For a Reynolds number less than 2000, flow is laminar in circular pipes. When
the Reynolds number is greater than 2000, laminar flow is unstable; a distur-
bance is probably magnified, causing the flow to become turbulent.
In laminar flow, the following equation for head loss due to friction can be
developed by considering the forces acting on a cylinder of fluid in a pipe:

(12.18)

wherehfhead loss due to friction, ft (m)
Llength of pipe section considered, ft (m)
gacceleration due to gravity, 32.2 ft/s^2 (9.81 m/s^2 )
wspecific weight of fluid, lb/ft^3 (kg/m^3 )

Substitution of the Reynolds number yields

(12.19)

For laminar flow, the preceding equation is identical to the Darcy–Weisbach
formula because, in laminar flow, the friction f64/R. Equation (12.18) is
known as the Poiseuille equation.

Turbulent Flow

In turbulent flow, the inertial forces are so great that viscous forces cannot
dampen out disturbances caused primarily by the surface roughness. These dis-
turbances create eddies, which have both a rotational and translational velocity.
The translation of these eddies is a mixing action that affects an interchange of
momentum across the cross section of the conduit. As a result, the velocity dis-
tribution is more uniform, as shown in Fig. 12.6. Experimentation in turbulent
flow has shown that

The head loss varies directly as the length of the pipe.

The head loss varies almost as the square of the velocity.

The head loss varies almost inversely as the diameter.

The head loss depends on the surface roughness of the pipe wall.

The head loss depends on the fluid density and viscosity.

The head loss is independent of the pressure.

hf

64

R

L

D

V^2

2 g

hf

32 LV

D^2 g



32 LV

D^2 w