Handbook of Civil Engineering Calculations

3. Evaluate V 3 by applying Eq. 9; then determine Q
   Thus, V\l(2g) +pjw = Vll(2g) + P3lw + Z 3 + (
   1
   Xi 5 )F 2 V^g) + (
   1
   Xi 0 )F 3 V^g), or O + 4 + O =
   Ki/(2g) - 14.6 + 13 + [F 3 V^g)](^1 Xi 5 x °-^342 = '/«>); *3 =^18 -° ft/s (548.64 cm/s); then g 3 =
   ^ 3 F 3 = 0.785(1.75)
   2
   (18.0) = 43.3 ft
   3
   /s (1225.92 L/s).

POWER OFA FLOWING LIQUID

A pump is discharging 8 fWs (226.5 L/s) of water. Gages attached immediately upstream
and downstream of the pump indicate a pressure differential of 36 lb/in
2
(248.2 kPa). If
the pump efficiency is 85 percent, what is the horsepower output and input?

Calculation Procedure:

1. Evaluate the increase in head of the liquid
   Power is the rate of performing work, or the amount of work performed in a unit time. If
   the fluid flows with a specific energy H 9 the total energy of the fluid discharged in a unit
   time is QwH. This expression thus represents the work that the flowing fluid can perform
   in a unit time and therefore the power associated with this discharge. Since 1 hp = 550
   ft-lb/s,

QwH

lhp= ^- (16)

In this situation, the power developed by the pump is desired. Therefore, H must be

equated to the specific energy added by the pump.

To evaluate the increase in head, consider the differences of the two sections being

considered. Since both sections have the same velocity and elevation, only their pressure

heads differ. Thus,^ 2 /"

7

-Pi/w = 36(144)762.4 = 83.1 ft (2532.89 cm).

2. Compute the horsepower output and input
   Thus, hpout = 8(62.4)(83.1)/550 = 75.4 hp; hpin = 75.4/0.85 = 88.7 hp.

DISCHARGE OVER A SHARP-EDGED WEIR

Compute the discharge over a sharp-edged rectangular weir 4 ft (121.9 cm) high and 10 ft

(304.8 cm) long, with two end contractions, if the water in the canal behind the weir is 4 ft

9 in (144.78 cm) high. Disregard the velocity of approach.

Calculation Procedure:

1. Adopt a standard relation for this weir
   The discharge over a sharp-edged rectangular weir without end contractions in which the
   velocity of approach is negligible is given by the Francis formula as

Q = 3.33bh^1 -^5 (lid)