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bulk strain = Δ V V 0 .
Figure is a schematic drawing of forces experienced by an object under the bulk stress. Equal forces perpendicular to the surface act from all directions and reduce the volume by the amount delta V compared to the original volume, V0.
An object under increasing bulk stress always undergoes a decrease in its volume. Equal forces perpendicular to the surface act from all directions. The effect of these forces is to decrease the volume by the amount Δ V compared to the original volume, V 0 .

The bulk strain results from the bulk stress, which is a force F normal to a surface that presses on the unit surface area A of a submerged object. This kind of physical quantity, or pressure p , is defined as

pressure = p F A .

We will study pressure in fluids in greater detail in Fluid Mechanics . An important characteristic of pressure is that it is a scalar quantity and does not have any particular direction; that is, pressure acts equally in all possible directions. When you submerge your hand in water, you sense the same amount of pressure acting on the top surface of your hand as on the bottom surface, or on the side surface, or on the surface of the skin between your fingers. What you are perceiving in this case is an increase in pressure Δ p over what you are used to feeling when your hand is not submerged in water. What you feel when your hand is not submerged in the water is the normal pressure     p 0 of one atmosphere, which serves as a reference point. The bulk stress is this increase in pressure, or Δ p , over the normal level, p 0 .

When the bulk stress increases, the bulk strain increases in response, in accordance with [link] . The proportionality constant in this relation is called the bulk modulus, B , or

B = bulk stress bulk strain = Δ p Δ V / V 0 = Δ p V 0 Δ V .

The minus sign that appears in [link] is for consistency, to ensure that B is a positive quantity. Note that the minus sign ( ) is necessary because an increase Δ p in pressure (a positive quantity) always causes a decrease Δ V in volume, and decrease in volume is a negative quantity. The reciprocal of the bulk modulus is called compressibility     k , or

k = 1 B = Δ V / V 0 Δ p .

The term ‘compressibility’ is used in relation to fluids (gases and liquids). Compressibility describes the change in the volume of a fluid per unit increase in pressure. Fluids characterized by a large compressibility are relatively easy to compress. For example, the compressibility of water is 4.64 × 10 −5 /atm and the compressibility of acetone is 1.45 × 10 −4 /atm . This means that under a 1.0-atm increase in pressure, the relative decrease in volume is approximately three times as large for acetone as it is for water.

Hydraulic press

In a hydraulic press [link] , a 250-liter volume of oil is subjected to a 2300-psi pressure increase. If the compressibility of oil is 2.0 × 10 −5 / atm , find the bulk strain and the absolute decrease in the volume of oil when the press is operating.

Figure is a schematic drawing of a hydraulic press. A small piston is displaced downward and causes the large piston holding object to move upward.
In a hydraulic press, when a small piston is displaced downward, the pressure in the oil is transmitted throughout the oil to the large piston, causing the large piston to move upward. A small force applied to a small piston causes a large pressing force, which the large piston exerts on an object that is either lifted or squeezed. The device acts as a mechanical lever.

Strategy

We must invert [link] to find the bulk strain. First, we convert the pressure increase from psi to atm, Δ p = 2300 psi = 2300 / 14.7 atm 160 atm , and identify V 0 = 250 L .

Solution

Substituting values into the equation, we have

bulk strain = Δ V V 0 = Δ p B = k Δ p = ( 2.0 × 10 −5 /atm ) ( 160 atm ) = 0.0032 answer: Δ V = 0.0032 V 0 = 0.0032 ( 250 L ) = 0.78 L.

Significance

Notice that since the compressibility of water is 2.32 times larger than that of oil, if the working substance in the hydraulic press of this problem were changed to water, the bulk strain as well as the volume change would be 2.32 times larger.

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Questions & Answers

state the properties of a base
Muhammad Reply
state 3 properties of a base
Muhammad
State three properties of a base
mubarak
a stone is projected from the top of the tower 24.5m high with velocity of 39.2m/s at an angle of 30° with horizontal compute time taken to hit he ground
Sarah Reply
it took a car driver 30mins to travel a distance of 50km.what is the average speed
Isiguzo Reply
Suppose the master cylinder in a hydraulic system is at a greater height than the cylinder it is controlling. Explain how this will affect the force produced at the cylinder that is being controlled.
Louise Reply
Why is popo less than atmospheric? Why is popo greater than pipi?
Louise
The old rubber boot shown below has two leaks. To what maximum height can the water squirt from Leak 1? How does the velocity of water emerging from Leak 2 differ from that of Leak 1? Explain your responses in terms of energy.
Louise
David rolled down the window on his car while driving on the freeway. An empty plastic bag on the floor promptly flew out the window. Explain why.
Louise Reply
the pressure differential exerted a force on the bag greater than the gravitational force holding it on the floor.
gtitboi
what is angular velocity
Sthandazile Reply
The rate of change in angular displacement is defined as angular velocity.
Manorama
a length of copper wire was measured to be 50m with an uncertainty of 1cm, the thickness of the wire was measured to be 1mm with an uncertainty of 0.01mm, using a micrometer screw gauge, calculate the of copper wire used
Nicole Reply
What is the answer please
Mustapha
it took a car driver 30 mins to travel a distance of 50km what is the average speed .
Isiguzo
If centripetal force is directed towards the center,why do you feel that you're thrown away from the center as a car goes around a curve? Explain
Maira Reply
if there is a centripetal force it means that there's also a centripetal acceleration, getting back to your question, just imagine what happens if you pull out of a car when it's quickly moving or when you try to stop when you are running fast, anyway, we notice that there's always a certain force..
Lindomar
... that tends to fight for its previous direction when you try to attribute to it an opposite one ou try to stop it.The same thing also happens whe a car goes around a curve, the car it self is designed to a"straight line"(look at the position of its tyres, mainly the back side ones), so...
Lindomar
... whenever it goes around a curve, it tends to throw away its the occupiers, it's given to the fact that it must interrupt its initial direction and take a new one.
Lindomar
Which kind of wave does wind form
Matthias Reply
calculate the distance you will travel if you mantain an average speed of 10N m/s for 40 second
Abdulai Reply
400m/s
Feng
hw to calculate the momentum of the 2000.0 elephant change hunter at a speed of 7.50 m/s
Kingsley Reply
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Hassan Reply
2.5
omwoyo
2.54cm=1inche
omwoyo
how do we convert from m/s to km/hr
Toni Reply
When paddling a canoe upstream, it is wisest to travel as near to the shore as possible. When canoeing downstream, it may be best to stay near the middle. Explain why?
SANA Reply
Explain why polarization does not occur in sound
Nuradeen
one ship sailing east with a speed of 7.5m/s passes a certain point at 8am and a second ship sailing north at the same speed passed the same point at 9.30am at what distance are they closet together and what is the distance between them then
Kuber Reply

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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