Handbook of Civil Engineering Calculations

where b = length of crest and h = head on weir, i.e., the difference between the elevation

of the crest and that of the water surface upstream of the weir.

2. Modify the Francis equation for end contractions
   With two end contractions, the discharge of the weir is

g = 3.33(6-0.2/0/*^15 (Ub)

Substituting the given values yields Q = 3.33(10 - 0.2 x 0.7S)OJS

1

• 5
  = 21.3 ftVs (603.05
  L/s).

LAMINAR FLOW IN A PIPE

A tank containing crude oil discharges 340 gal/min (21.4 L/s) through a steel pipe 220 ft
(67.1 m) long and 8 in (203.2 mm) in diameter. The kinematic viscosity of the oil is 0.002
ft
2
/s (1.858 cm
2
/s). Compute the difference in elevation between the liquid surface in the
tank and the pipe outlet.

Calculation Procedure:

1. Identify the type of flow in the pipe
   To investigate the discharge in a pipe, it is necessary to distinguish between two types of
   fluid flow—laminar and turbulent. Laminar (or viscous) flow is characterized by the tele-
   scopic sliding of one circular layer of fluid past the adjacent layer, each fluid particle tra-
   versing a straight line. The velocity of the fluid flow varies parabolically from zero at the
   pipe wall to its maximum value at the pipe center, where it equals twice the mean veloci-
   ty.
   Turbulent flow is characterized by the formation of eddy currents, with each fluid par-
   ticle traversing a sinuous path.
   In any pipe the type of flow is ascertained by applying a dimensionless index termed
   the Reynolds number, defined as

DV

NR=— (18)

Flow is considered laminar if NR < 2100 and turbulent is NR > 3000.
In laminar flow the head loss due to friction is

h 32LvV

*=-&r (

19

«)

or

*-(NoNo

Let 1 denote a point on the liquid surface and 2 a point at the pipe outlet. The elevation of
2 will be taken as datum.