Basic Hydraulics Pressure and Force

1
Basic Hydraulics Pressure and Force

• Math for Water Technology
• MTH 082
• Lecture 5
• Hydraulics Chapter 2
• (pgs. 213-224)

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) 0.433 lb/in2 0.433
psi

0.433 lb of water
1 ft
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.

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

1. Static
2. Dynamic
3. Theoretical
4. Practical

6
A pound of water weighs ______lbs.

1. 1
2. 7.48
3. 8.34
4. 62.4

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

1. 1.0 lb
2. 2.31 lbs
3. 0.433 lbs
4. 62.4 lbs

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

0.433 lb of water
1 ft
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
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
30.5 psi
50 psi
12
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 ofeach 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

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
Gauge Pressure
Condition
Absolute Pressure
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
Total line vacuum
0 psia
-14.7 psig
15
Pressure Conversions
1 psig 2.31 ft head 1 ft head 0.433
psig 1kPa 0.0109 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?
0.1019 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
B? psi
A ? psi
19
Pressure Problems
Example 4. Psi gauges are used in this water
system, What is the pressure in feet at each
point?
h2
h3
h4
h1
56 psig
32 psig
20 psig
44 psig
A
B
C
D
20
Force
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
in2) F 30 lb of force
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

1. 24.2 psi
2. 14 psi
3. 2 psi
4. 100 psi
5. 56 psi

22
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?

1. 11.8 ft
2. 25.0 ft
3. 34.6 ft
4. 38.9 ft

23
Force
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
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 FP 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
Todays objective to become proficient with the
concept of pressure and force has been met.

1. Strongly Agree
2. Agree
3. Neutral
4. Disagree
5. Strongly Disagree