230 
Journal of Agricultural Research 
Vol. XXXI, No. 3 
The velocity head is based on the net cross sectional area of dis¬ 
charge and suction pipes, respectively. The velocity of water in 
each instance was determined by this formula: 
in which v = velocity in feet per second, 0 = flow in cubic feet per 
second, and A = net sectional area in square feet. 
Velocity head was obtained from the formula: 
in which h = velocity head in feet, v = velocity in feet per second, 
and g = acceleration of gravity = 32.2. 
The velocity-head difference is therefore equal to — 2g^ J * n 
which v is the velocity of water in the discharge pipe, and v t is 
the velocity in the suction pipe. If the net area of the suction pipe 
at' the point where the pipe is tapped for the measurement of the 
vacuum, is greater than that of the discharge pipe where it is tapped 
for the measurement of pressures, h is positive and is therefore additive 
to the total head composed of pressure, vacuum, and static heads. 
In the case of the pumps tested, the net area at the point of vacuum 
tap was less than tne net area at the point of pressure tap, and hence 
the velocity of the water in the suction pipe was greater for a given 
volume than that in the discharge pipe. The velocity-head differ¬ 
ence between discharge and suction pipes was therefore subtractive. 
Diagrams based on the formula h= ■■■■■■ 1 have been prepared 
t7 
for each pump, as shown in Figures 3 to 8, inclusive, for the purpose 
of determining in the tests the amount of head to be added or sub¬ 
tracted due to the velocity of flow in the suction and discharge pipes. 
In studying the diagrams, it is interesting to note the recovery of 
head due to velocity. Referring to Tables I and IV, comparing 
pumps Nos. 1 and 4, respectively, the recovery of head in pump No. 1 
is shown to be 2.3 feet for a maximum flow of 1,321 gallons per 
minute, or 2.94 second-feet; while in pump No. 4 the recovery was 
0.99 foot with a maximum flow of 1,466 gallons per minute, or 3.26 
second-feet. Both pumps are 24 inches in diameter; No. 1 is 3-stage 
and No. 4 is 2-stage. They are of different makes, however, and the 
difference is due to the design, which gives a greater difference in 
area between discharge and suction in the case of No. 4 than No. 1. 
The recovery of head appears to be greater in the pumps of smaller 
diameter than in the larger pumps. For example, in pump No. 5, 
Table *V, the velocity-head difference is 6.36 feet for a maximum 
flow of 1,092 gallons per minute, or 2.43 second-feet. This quantity 
is subtractive, indicating that there was no head recovered, but 
rather a loss of head, because the net area of discharge pipe at 
pressure tap was larger than the net area of the suction pipe at 
vacuum tap. 
