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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.


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 .


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.


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

At time to = 0 the current to the DC motor is reverse, resulting in angular displacement of the motor shafts given by angle = (198rad/s)t - (24rad/s^2)t^2 - (2rad/s^3)t^3 At what time is the angular velocity of the motor shaft zero
Princston Reply
what is angular velocity
In three experiments, three different horizontal forces are ap- plied to the same block lying on the same countertop. The force magnitudes are F1 " 12 N, F2 " 8 N, and F3 " 4 N. In each experi- ment, the block remains stationary in spite of the applied force. Rank the forces according to (a) the
state Hooke's law of elasticity
Aarti Reply
Hooke's law states that the extension produced is directly proportional to the applied force provided that the elastic limit is not exceeded. F=ke;
You are welcome
what is drag force
A backward acting force that tends to resist thrust
solve:A person who weighs 720N in air is lowered in to tank of water to about chin level .He sits in a harness of negligible mass suspended from a scale that reads his apparent weight .He then dumps himself under water submerging his body .If his weight while submerged is 34.3N. find his density
Ian Reply
please help me solve this 👆👆👆
The weight inside the tank is lesser due to the buoyancy force by the water displaced. Weight of water displaced = His weight outside - his weight inside tank = 720 - 34.3 = 685.7N Now, the density of water = 997kg/m³ (this is a known value) Volume of water displaced = Mass/Density (next com)
density or relative density
Upthrust =720-34.3=685.7N mass of water displayed = 685.7/g vol of water displayed = 685.7/g/997 hence, density of man = 720/g / (685.7/g/997) =1046.6 kg/m3
R.d=weight in air/upthrust in water =720/34.3=20.99 R.d=density of substance/density of water 20.99=x/1 x=20.99g/cm^3
Kg /cubic meters
how please
Upthrust = 720-34.3=685.7N vol of water = 685.7/g/density of water = 685.7/g/997 so density of man = 720/g /(685.7/g/997) =1046.8 kg/m3
is there anyway i can see your calculations
Upthrust =720-34.3=685.7
Upthrust 720-34.3
Vol of water = 685.7/g/997
Hence density of man = 720/g / (685.7/g/997)
=1046.8 kg/m3
so the density of water is 997
Okay, thanks
try finding the volume then
Vol of man = vol of water displayed
I've done that; I got 0.0687m^3
okay i got it thanks
u welcome
HELLO kindly assist me on this...(MATHS) show that the function f(x)=[0 for xor=0]is continuous from the right of x->0 but not from the left of x->0
Duncan Reply
I do not get the question can you make it clearer
Same here, the function looks very ambiguous. please restate the question properly.
please help me solve this problem.a hiker begins a trip by first walking 25kmSE from her car.she stops and sets her tent for the night . on the second day, she walks 40km in a direction 60°NorthofEast,at which she discovers a forest ranger's tower.find components of hiker's displacement for each day
Liteboho Reply
Take a paper. put a point (name is A), now draw a line in the South east direction from A. Assume the line is 25 km long. that is the first stop (name the second point B) From B, turn 60 degrees to the north of East and draw another line, name that C. that line is 40 km long. (contd.)
Now, you know how to calculate displacements, I hope? the displacement between two points is the shortest distance between the two points. go ahead and do the calculations necessary. Good luck!
thank you so much Sharath Kumar
thank you, have also learned alot
No issues at all. I love the subject and teaching it is fun. Cheers!
cheers too
hii too
you mean
solution problems
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matthew Reply
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prove using vector algebra that the diagonals of a rhombus perpendicular to each other.
Baijnath Reply
A projectile is thrown with a speed of v at an angle of theta has a range of R on the surface of the earth. For same v and theta,it's range on the surface of moon will be
Roshani Reply
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Using some kinematics, time taken for the projectile to reach ground is (2*v*g*Sin (∆)) (here, g is gravity on Earth and ∆ is theta) therefore, on Earth, R = 2*v²*g*Sin(∆)*Cos(∆) on moon, the only difference is the gravity. Gravity on moon = 0.166*g substituting that value in R, we get the new R
Some corrections to my old post. Time taken to reach ground = 2*v*Sin (∆)/g R = (2*v²*Sin(∆)*Cos(∆))/g I put the g in the numerator by mistake in my old post. apologies for that. R on moon = (R on Earth)/(0.166)
state Newton's first law of motion
Awal Reply
Every body will continue in it's state of rest or of uniform motion in a straight line, unless it is compelled to change that state by an external force.
if you want this to become intuitive to you then you should state it
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what is a vector
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Emmanuel Reply
The result is a simple vector addition. The angle between the vectors is 90 degrees, so we can use Pythagoras theorem to get the result. V magnitude = sqrt(100*100 + 25*25) = 103.077 km/hr. the direction of the resultant vector can be found using trigonometry. Tan (theta) = 25/100.
state Newton's first law of motion
Kansiime Reply
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Grace Reply
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Umesh Reply
I want to join the conversation
Kumaga Reply
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