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

2. Pressure

3. What is Pressure and Force?
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

4. Pressure =Water Height
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/ft2
Convert = 62.4 lb/ft2 = 62.4 lb/ (1 ft) (1 ft)
= 62.4 lb/(12 in) (12 in)
= 62.4 lb/(144 in2)
= lb/in2
= psi
1 ft
0.433 lb
of water
A foot high column of water over a square inch surface area weighs lb which equals psi.
***Thus, converts pressure from feet of water to pressure in pounds per square inch. *****

5. The pressure exerted by a column of water one inch square when at rest, is the _________ pressure. It is usually measured in psi.
Static
Dynamic
Theoretical
Practical

6. A pound of water weighs ______lbs.1
7.48
8.34
62.4

7. A column of water 12" high and 1 square inch in surface area will produce a pressure of _______ lbs.

8. Pressure = Water Height
Can use a ratio to determine feet of water are equivalent to 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

9. Pressure Rule
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

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

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

12. A. 3.8 psi; 38.0 psi B. 8.8 psi; 8.0 psi C. 20.3 psi; 20.3 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 psi; 20.3 psi
D psi; 38.0 psi

13. Pressure Types 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.

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

15. 1 psig = 2.31 ft head 1 ft head = 0.433 psig 1kPa = 0.0109 m of head
Pressure Conversions
1 psig = ft head
1 ft head = psig
1kPa = m of head

16. Pressure Problems
Example 1. Convert gauge pressure of 14 ft to pounds per square inch gauge.
2.31 ft of head
1 psig
Example 2. A head of 250 ft of water is equivalent to what pressure in pounds per square inch?
2.31 ft of head
1 psig

17. Pressure Problems
Example 3. A pressure of 210 kPa (gauge) is equivalent to how many meters of head? m
of head
1 kPa

18. Pressure Problems
Example 3. What would be the psi gauge readings at point A and B?
200 ft
80 ft
A ? psi
B? psi

19. Pressure Problems
Example 4. Psi gauges are used in this water system, What is the pressure in feet at each point? h1 h2 h3 h4
56 psig
32 psig
20 psig
44 psig A B C D

20. Force Force = Pressure X Area F= P X A 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 in2)
F= 30 lb of force
2 in
3 in
5 lb

21. 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
24.2 psi
14 psi
2 psi
100 psi
56 psi

22. The pressure gauge on the bottom of a water holding tank reads 15 psi
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?
11.8 ft
25.0 ft
34.6 ft
38.9 ft

23. Force F= P X A F= (12 psig) (120 in2) F= 1440 lb of force F= P X A
Example 6. The pressure on a surface is 12 psig. If the surface is 120 in2. What is the force?
F= P X A
F= (12 psig) (120 in2)
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 in2)
F= 11,520 lb
A= (1 ft) (2ft)
A=(2 ft2)
A =(2 ft2) ( 12 in/1ft)2
A= 288 in2

24. Force Force = Pressure X Area
The jack has an operating piston with a surface area of 5 in2 and a lifting piston with a surface area of 100 in2. 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 Operating Cylinder
F=P X A F= P X A
150 lb= (x psig) (5in2) F= (30 psig)(100 in2)
150lb/5in2 = x F= 3000 lb
30 psig =x

25. Strongly Agree Agree Neutral Disagree Strongly Disagree
Today’s objective: to become proficient with the concept of pressure and force has been met.
Strongly Agree
Agree
Neutral
Disagree
Strongly Disagree