CIVIL ENGINEERING FORMULAS

300 CHAPTER TWELVE

For true models, Sr1,RrLr. Hence,

(12.15)

In models of rivers and channels, it is necessary for the flow to be turbulent. The
U.S. Waterways Experiment Station has determined that flow is turbulent if

(12.16)

whereVmean velocity, ft/s (m/s)
Rhydraulic radius, ft (m)
kinematic viscosity, ft^2 /s (m^2 /s)

If the model is to be a true model, it may have to be uneconomically large for
the flow to be turbulent.

FLUID FLOW IN PIPES

Laminar Flow

In laminar flow, fluid particles move in parallel layers in one direction. The
parabolic velocity distribution in laminar flow, shown in Fig. 12.5, creates a
shearing stress !dV/dy, where dV/dyis the rate of change of velocity with
depth, and is the coefficient of viscosity. As this shearing stress increases, the
viscous forces become unable to damp out disturbances, and turbulent flow
results. The region of change is dependent on the fluid velocity, density, viscosity,
and the size of the conduit.
A dimensionless parameter called the Reynolds number has been found to
be a reliable criterion for the determination of laminar or turbulent flow. It is
the ratio of inertial forces/viscous forces, and is given by

R (12.17)

VD





VD

VR

 4000

Vr

L2/3r

nr

Vmax

FIGURE 12.5 Velocity distribution for laminar flow in

a circular pipe is parabolic. Maximum velocity is twice

the average velocity.