A training manual in conducting a workshop in the design, construction, operation, maintenance and repair of hydrams 
Session 6: Hydram theory (23 hour) 

Attachment 6B
Atmospheric pressure  the pressure at sea level caused by the weight of air; atmospheric pressure = 14.7 psia, and 0 psig
Force  (delivery to drive head ratio) the ratio of lift to fall. The inverse of this ratio times the efficiency of the hydram will determine the percentage of water that the hydram will pump. The higher the h:H ratio, the lower the hydram efficiency (n). The usual range of the h:H ratio is from 2:1 to 20:1, but h:H ratios have been measured up to 60:1.
Hydram capacity  the maximum amount of water that a hydram can use. This is determined by the drive pipe size and length, the drive head, and the impulse valve size and design.
Impulse valve stroke  the distance the impulse valve travels during a cycle.
Impulse valve weight  the total weight or downward force of the impulse valve and its springs or weights.
Kinetic energy  active energy, ½ the mass times the velocity squared
E_{k} = ½ mv²
Pressure  force applied over a surface measured as force per unit of area such as pounds per square inch (psi) (a head of 28" of water develops a pressure of 1 psi) or a pascal (Pa) which is equal to 1 newton per square meter (a head of 1 cm = 98 Pa) 28" of water equals 71.1 cm of water equals 1 psi = 6895 Pa.
psia  (pounds per square inch absolute) the total real pressure as if the atmospheric pressure is not present. Atmospheric pressure at sea level is 14.7 psi, so if a pressure gauge reads 100 psi (psig) the absolute pressure is 114.7 psia.
psig  (pounds per square inch gauge) the pressure that a gauge reads, actually the pressure above atmospheric.
Static head  a column of water without motion. The static drive head of a hydram can be measured with a pressure gauge but only when the ram is stopped and the drive pipe is full of water.
Time of cycle  (t) the time it takes for a hydram to complete one cycle, such as the time lapse between the impulse valve closing twice.
Velocity  speed usually measured in feet per second or meters per second.
Water used  (Q.) the amount of water that flows through the drive pipe during a unit of time (as in gallons per minute or liters per second) which is equal to the water pumped (q) plus the water wasted (Q_{w})
The flow rate range of hydrams are as follows:
Drive pipe diameterFlow rate 

mm 
in 
U.S. 
gal/min 
Imperial 
gal/min 
liters/min 

19 
¾ 
0.8 
2 
0.6 
1.7 
2.8 
7.6 

25 
1 
1.5 
4 
1.3 
3.3 
5.7 
15.0 

32 
1¼ 
1.5 
7 
1.3 
5.8 
5.7 
26.0 

38 
1½ 
2.5 
13 
2.0 
10.8 
9.4 
49.0 

50 
2 
6.0 
20 
5.0 
17.0 
23.0 
76.0 

63 
2½ 
10.0 
45 
8.0 
38.0 
38.0 
170.0 

75 
3 
15.0 
50 
13.0 
42.0 
57.0 
189.0 

100 
4 
30.0 
125 
25.0 
104.0 
113.0 
473.0 

125 
5 
40.0 
150 
33.0 
125.0 
151.0 
567.0 
Determining Drive Pipe Length, L:
1. Consider drive head, H
L:H ratio  drive pipe length to head ratio, when H is less than 15 ft. (4.5m) L:H should equal 6.
When H is greater than 15 ft (4.5m), but less than 25' (8m) L:H should equal 4.
When H is greater than 28 ft. (8m), but less than 50' (16m) L:H should equal 3.
When H is greater than 50 ft. (16m) L:H ratio should equal 2.
2. Consider drive pipe diameter, D
L:D ratio  drive pipe length to diameter ratio, should be kept between 150 and 1000.
A rule of thumb: maximum number of pipe lengths = 4D
(based on chart below, and 21' pipe length)
Optimal number of pipe lenghts = 2D
D 
L = 150D 
L = 500D 
L = 1000D 
No of pipes 
½" 
6.25 
20.8 
41.6 
2 
3/4" 
9.3 
31.25 
62.5 
3 
1" 
12.5 
41.6 
83.2 
4 
1½" 
15.6 
52.0 
104.0 
5 
1½" 
18.6 
62.5 
125.0 
6 
2 
25.0 
83.2 
166.4 
8 
IMPORTANT NUMBERS TO REMEMBER
1440 minutes in a day
0.433 psi per foot (measured vertically) of water column
28 inches of a water column produces 1 psi
14.7 psi atmospheric pressure
7.48 gallons per cubic toot