Basic Hydraulics Pressure and
Force
Math for Water Technology
MTH 082
Lecture 5
Hydraulics Chapter 2
(pgs. 213-224)

• Flow of water in a system is dependant on the amount of force causing the water to move.
Force= pressure X area
• Pressure is the amount of force acting (pushing) on a unit area.
• Units of pressure = psi (pounds per square inch)
• Units of pressure = kPa (kilopascals)
In the water industry we deal with pressure exerted by water or the height of water

A container that is 1 ft by 1 ft by 1 ft (a cubic foot container) is filled with water. What is the pressure on the square foot bottom of the container.
Water density = 62.4 lb/ft 2
Convert = 62.4 lb/ft 2 = 62.4 lb/ (1 ft) (1 ft)
= 62.4 lb/(12 in) (12 in)
= 62.4 lb/(144 in 2 )
= 0.433 lb/in 2
1 ft 0.433 lb of water
=
0.433 psi
A foot high column of water over a square inch surface area weighs 0.433 lb which equals 0.433 psi.
***Thus, 0.433 converts pressure from feet of water to pressure in pounds per square inch. *****

The pressure exerted by a column of water one inch square when at rest, is the _________ pressure. It is usually measured in psi.
100%
1. Static
2. Dynamic
3. Theoretical
4. Practical
0% 0% 0%
S ta tic
D yn am ic
T he or et ic al
P ra ct ic al

1. 1
2. 7.48
3. 8.34
4. 62.4
A pound of water weighs
______lbs.
57%
43%
1
7.
48
0%
8.
34
0%
62
.4

A column of water 12" high and
1 square inch in surface area will produce a pressure of _______ lbs.
75% 1. 1.0 lb
2. 2.31 lbs
3. 0.433 lbs
4. 62.4 lbs 13%
0%
1
.0
lb
2
.3
1 lb s
0
.4
33
lb s
13%
6
2.
4 lb s

Can use a ratio to determine feet of water are equivalent to psi
1 ft ( x ) ft

0 .
433 psi 1 psi
( 1 ft )( 1 ft )
 x
0 .
433 psi
1 ft 0.433 lb of water
2.31 ft = x
1 psi is equivalent to the pressure created by a column of water 2.31 ft high

• Rule 1- The height of water determines pressure over square inch area. This is termed head which is measured in feet.
• Rule 2- As long as the height of water stays the same, changing the shape of the container does not change the pressure at the bottom of an object
Same hydrostatic pressure in a circle or a square pool, 15 feet below water surface

Same Pressures/Different Containers
7 ft
3 psi
6 psi
14 ft
7 ft
3 psi
6 psi
14 ft
7 ft
3 psi
6 psi
14 ft

Water Tank Pressure
Same pressure at bottom
50,000 gallons of water
Different pressure at bottom
25,000 gallons of water
140 ft
61 psi
140 ft
130 ft
61 psi 50 psi
70 ft
30.5 psi

Two columns of water are filled completely at sea level to a height of 88 feet. Column A is 0.5 inches in diameter. Column B is 5 inches in diameter. What will two pressure gauges, one attached to the bottom of each column, read?
A. 3.8 psi; 38.0 psi
B. 8.8 psi; 8.0 psi
C. 20.3 psi; 20.3 psi
D. 38.0 psi; 38.0 psi
82%
9% 9%
0%
A
. 3
.8
p si
; 3
8.
..
B
. 8
.8
p si
; 8
...
.
C
. 2
0.
3 ps i;
2.
..
D
. 3
8.
0 ps i;
3.
..

• Atmospheric pressure is 14.7 psi at sea level.
exerted everywhere so oftentimes its neglected
• Gauge pressure is water pressure in a main or container that is measured by a gauge.
• The absolute pressure pounds per square inch absolute (psia) is obtained by adding the gauge and atmospheric pressure. height of water determines pressure over square inch area.
This is termed head which is measured in feet.

Absolute Pressure
Gauge Pressure Condition
64.7 psia 50 psig 116 ft of head
14.7 psia
12.7 psia
0 psia
0 psig
-2 psig
-14.7 psig
Empty line
Atmosph. press
Partial line vacuum
Total line vacuum

1 psig = 2.31 ft head
1 ft head = 0.433 psig
1kPa = 0.0109 m of head

Example 1. Convert gauge pressure of 14 ft to pounds per square inch gauge.
1 psig 2.31 ft of head
14
1 ft
(
1 psig
2 .
31 ft
)

6 .
06 psig
Example 2. A head of 250 ft of water is equivalent to what pressure in pounds per square inch?
1 psig 2.31 ft of head
250 ft
1
(
1 psig
2 .
31 ft
)

108 .
23 psig

Example 3. A pressure of 210 kPa (gauge) is equivalent to how many meters of head?
1 kPa
0.1019 m of head
210 kPa
1
(
0 .
1019 m
)
1 kPa

21 .
4 m

Example 3. What would be the psi gauge readings at point A and B?
200 ft
A ? psi
Po int A
200 ft
1
1 psig
(
2 .
31 ft
)

86 .
58 psig
80 ft
B? psi
80 ft
1
(
1 psig
2 .
31 ft
)

34 .
63 psig

Example 4. Psi gauges are used in this water system, What is the pressure in feet at each point?
h
1 h
2 h
3 h
4
Po int A
56 psig
1
(
2
1
.
31 psig ft
)

129 .
36 ft of head
56 psig
A
32 psig
44 psig
B C
20 psig
D
Po int D
20 psig
1
(
2 .
31
1 psig ft
)

46 .
2 ft of head
Po int C
32 psig
1
(
2 .
31
1 psig ft
)

73 .
92 ft of head
Po int B
44 psig
1
(
2 .
31
1 psig ft
)

101 .
64 ft of head

Force = Pressure X Area
F= P X A
Example 5. If a pressure of 5 psig is exerted on a surface 2 in by 3 in, what is its force?
F= P X A
F= (5 psig) (2in) (3 in)
F= 5 psig (6 in 2 )
F= 30 lb of force
5 lb
5 lb
5 lb
5 lb
5 lb
5 lb
2 in
3 in

You have a water storage tank that is 90' tall and 45' in diameter, it currently has 56' of water in it, what is the pressure in the bottom of the tank
100%
1. 24.2 psi
2. 14 psi
3. 2 psi
4. 100 psi
5. 56 psi
2
4.
2 ps i
1
4 ps i
0% 0%
2
p si
0%
1
00
p si
0%
5
6 ps i

The pressure gauge on the bottom of a water holding tank reads 15 psi. The tank is 15 ft in diameter and 40 ft high. How many feet of water are in the tank?
80%
1. 11.8 ft
2. 25.0 ft
3. 34.6 ft
4. 38.9 ft
10%
0%
10%
1
1.
8 ft
2
5.
0 ft
3
4.
6 ft
3
8.
9 ft

Example 6. The pressure on a surface is 12 psig. If the surface is 120 in 2. What is the force?
F= P X A
F= (12 psig) (120 in 2 )
F= 1440 lb of force
Example 7. The pressure is 40 psig against a surface that is 1 ft by 2 ft . What is the force against the surface?
F= P X A
F= (40 psig) (288 in 2 )
F= 11,520 lb
A= (1 ft) (2ft)
A=(2 ft 2 )
A =(2 ft 2 ) ( 12 in/1ft) 2
A= 288 in 2

The jack has an operating piston with a surface area of 5 in 2 and a lifting piston with a surface area of 100 in 2 . A force of 150 lb is applied to the operating piston. What pressure is created within the hydraulic system of the jack?
Force = Pressure X Area
Force on operating system= Pressure on jack X Area of operating piston
Operating System
F=P X A
150 lb= (x psig) (5in 2 )
150lb/5in 2 = x
30 psig =x
Operating Cylinder
F= P X A
F= (30 psig)( 100 in 2 )
F= 3000 lb

Today’s objective: to become proficient with the concept of pressure and force has been met.
20% 20% 20% 20% 20%
1. Strongly Agree
2. Agree
3. Neutral
4. Disagree
5. Strongly Disagree
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