To identify the type of flow, compute NR. Thus, D = 8 in (203.2 mm); L = 220 ft (6705.6
cm); v = 0.002 ft^2 /s (1.858 cm^2 /s); Q = 340/449 = 0.757, converting from gallons per
minute to cubic feet per second. Then V= QIA = 0.757/0.349 = 2.17 ft/s (66.142 cm/s). And
NR = 0.667(2.17)/0.002 = 724. Therefore, the flow is laminar because NR is less than 2100.
- Express all losses in terms of the velocity head
By Eq. 196, hF = (64/724)(220/0.667)F^2 /(2g) = 29.2 V^2 IVg). Where LID > 500, the fol-
lowing may be regarded as negligible in comparison with the loss due to friction: loss at
pipe entrance, losses at elbows, velocity head at the discharge, etc. In this instance, in-
clude the secondary items. The loss at the pipe entrance is hE = 0.5 V
2
IQg). The total loss
is/*L = 29.7F^2 /(2g). - Find the elevation of 1 by applying Eq. 9
Thus, Z 1 = Ff/(2g) + hL = 30.7F|/(2g) = 30.7(2.17)
2
/64.4 = 2.24 ft (68.275 cm).
TURBULENT FLOW IN PIPE-APPLICATION
OF DARCY-WEISBACH FORMULA
Water is pumped at the rate of 3 ft^3 /s (85.0 L/s) through an 8-in (203.2-mm) fairly smooth
pipe 2600 ft (792.48 m) long to a reservoir where the water surface is 180 ft (50.86 m)
higher than the pump. Determine the gage pressure at the pump discharge.
Calculation Procedure:- Compute hF
Turbulent flow in a pipe flowing full may be investigated by applying the Darcy-
Weisbach formula for friction head
fLV
2
h
?=^(20)
where/is a friction factor. However, since the friction head does not vary precisely in the
manner implied by this equation, / is dependent on D and V 9 as well as the degree of
roughness of the pipe. Values of/associated with a given set of values of the independent
quantities may be obtained from Fig. 8.
Accurate equations for hF are the following:
Extremely smooth pipes:
0.301,K^1 -^75
hF= 100QD'-* ^^Fairly smooth pipes:
0.38ZF^186
*'
=
100QD5T
(2lb}Rough pipes:
0.5OL K^1 -^95
hp= 100QD'-* (21C)