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**Basic Hydraulics Pressure and Force**

Math for Water Technology MTH 082 Lecture 5 Hydraulics Chapter 2 (pgs )

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Pressure

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**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

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**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. *****

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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

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**A pound of water weighs ______lbs.**

1 7.48 8.34 62.4

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

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**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

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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

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**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

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**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

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**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

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**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.

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**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

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**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

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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

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

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

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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

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**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

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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

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**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

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**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

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**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

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**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

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