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A two-dimensional view of a dam with dimensions L and h is shown. Force F at h is shown by a horizontal arrow. The force F exerted by water on the dam is F equals average pressure p bar into area A and pressure in turn is average height h bar into density rho into acceleration due to gravity g.
The dam must withstand the force exerted against it by the water it retains. This force is small compared with the weight of the water behind the dam.

Atmospheric pressure is another example of pressure due to the weight of a fluid, in this case due to the weight of air above a given height. The atmospheric pressure at the Earth’s surface varies a little due to the large-scale flow of the atmosphere induced by the Earth’s rotation (this creates weather “highs” and “lows”). However, the average pressure at sea level is given by the standard atmospheric pressure P atm size 12{P rSub { size 8{"atm"} } } {} , measured to be

1 atmosphere (atm) = P atm = 1.01 × 10 5 N/m 2 = 101 kPa . size 12{1`"atmosphere"` \( "atm" \) =P rSub { size 8{"atm"} } =1 "." "01" times "10" rSup { size 8{5} } `"N/m" rSup { size 8{2} } ="101"`"kPa"} {}

This relationship means that, on average, at sea level, a column of air above 1.00 m 2 of the Earth’s surface has a weight of 1.01 × 10 5 N size 12{1 "." "01" times "10" rSup { size 8{5} } `N} {} , equivalent to 1 atm . (See [link] .)

Figure shows a column of air exerting a weight of one point zero one times ten to the power five newtons on a rectangular patch of ground of one square meter cross section.
Atmospheric pressure at sea level averages 1 . 01 × 10 5 Pa size 12{1 "." "01" times "10" rSup { size 8{5} } `"Pa"} {} (equivalent to 1 atm), since the column of air over this 1 m 2 size 12{1`m rSup { size 8{2} } } {} , extending to the top of the atmosphere, weighs 1 . 01 × 10 5 N size 12{1 "." "01" times "10" rSup { size 8{5} } " N"} {} .

Calculating average density: how dense is the air?

Calculate the average density of the atmosphere, given that it extends to an altitude of 120 km. Compare this density with that of air listed in [link] .

Strategy

If we solve P = hρg size 12{P=hρg} {} for density, we see that

ρ ¯ = P hg . size 12{ { bar {ρ}}= { {P} over { ital "hg"} } } {}

We then take P size 12{P} {} to be atmospheric pressure, h size 12{h} {} is given, and g size 12{g} {} is known, and so we can use this to calculate ρ ¯ size 12{ { bar {ρ}}} {} .

Solution

Entering known values into the expression for ρ ¯ size 12{ { bar {ρ}}} {} yields

ρ ¯ = 1 . 01 × 10 5 N/m 2 ( 120 × 10 3 m ) ( 9 . 80 m/s 2 ) = 8 . 59 × 10 2 kg/m 3 . size 12{ { bar {ρ}}= { {1 "." "01" times "10" rSup { size 8{5} } `"N/m" rSup { size 8{2} } } over { \( "120" times "10" rSup { size 8{3} } `m \) \( 9 "." "80"`"m/s" rSup { size 8{2} } \) } } =8 "." "59" times "10" rSup { size 8{ - 2} } `"kg/m" rSup { size 8{3} } } {}

Discussion

This result is the average density of air between the Earth’s surface and the top of the Earth’s atmosphere, which essentially ends at 120 km. The density of air at sea level is given in [link] as 1 . 29 kg/m 3 size 12{1 "." "29"`"kg/m" rSup { size 8{3} } } {} —about 15 times its average value. Because air is so compressible, its density has its highest value near the Earth’s surface and declines rapidly with altitude.

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Calculating depth below the surface of water: what depth of water creates the same pressure as the entire atmosphere?

Calculate the depth below the surface of water at which the pressure due to the weight of the water equals 1.00 atm.

Strategy

We begin by solving the equation P = hρg size 12{P=hρg} {} for depth h size 12{h} {} :

h = P ρg . size 12{h= { {P} over {ρg} } } {}

Then we take P size 12{P} {} to be 1.00 atm and ρ size 12{ρ} {} to be the density of the water that creates the pressure.

Solution

Entering the known values into the expression for h size 12{h} {} gives

h = 1 . 01 × 10 5 N/m 2 ( 1 . 00 × 10 3 kg/m 3 ) ( 9 . 80 m/s 2 ) = 10 . 3 m . size 12{h= { {1 "." "01" times "10" rSup { size 8{5} } `"N/m" rSup { size 8{2} } } over { \( 1 "." "00" times "10" rSup { size 8{3} } `"kg/m" rSup { size 8{3} } \) \( 9 "." "80"`"m/s" rSup { size 8{2} } \) } } ="10" "." 3`m} {}

Discussion

Just 10.3 m of water creates the same pressure as 120 km of air. Since water is nearly incompressible, we can neglect any change in its density over this depth.

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What do you suppose is the total pressure at a depth of 10.3 m in a swimming pool? Does the atmospheric pressure on the water’s surface affect the pressure below? The answer is yes. This seems only logical, since both the water’s weight and the atmosphere’s weight must be supported. So the total pressure at a depth of 10.3 m is 2 atm—half from the water above and half from the air above. We shall see in Pascal’s Principle that fluid pressures always add in this way.

Section summary

  • Pressure is the weight of the fluid mg size 12{ ital "mg"} {} divided by the area A size 12{A} {} supporting it (the area of the bottom of the container):
    P = mg A . size 12{P= { { ital "mg"} over {A} } } {}
  • Pressure due to the weight of a liquid is given by
    P = hρg , size 12{P=hρg} {}

    where P size 12{P} {} is the pressure, h size 12{h} {} is the height of the liquid, ρ size 12{ρ} {} is the density of the liquid, and g size 12{g} {} is the acceleration due to gravity.

Questions & Answers

A 20MH coil has a resistance of 50 ohms and us connected in series with a capacitor to a 520MV supply
Musa Reply
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Caya Reply
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Sujitha
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Junior
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AMIT
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Heat is transfered by thermal contact but if it is transfered by conduction or radiation, is it possible to reach in thermal equilibrium?
Eden Reply
Yes, It is possible by conduction if Surface is Adiabatic
Astronomy
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Magret Reply
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Kalilu
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Kalilu
Physics? Is a branch of science dealing with matter in relation to energy.
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Moses
are you asking for qualities or quantities?
Noman
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Ekwunazor Reply
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Universe
Noman
Yes the Universe itself
Astronomy
Examine different types of shoes, including sports shoes and thongs. In terms of physics, why are the bottom surfaces designed as they are? What differences will dry and wet conditions make for these surfaces?
Lathan Reply
sports shoes are designed in such a way they are gripped well with your feet and their bases have and high friction surfaces, Thong shoes are for comfort, these are easily removed and light weight. these are usually low friction surfaces but in wet conditions they offer greater friction.
Noman
thong sleepers are usually used in restrooms.
Noman
what is wave
Ochigbo Reply
The phenomenon of transfer of energy
Noman
how does time flow in one dimension
Lord Reply
you mean in three dimensions......numbnut
yeah that was a mistake
Lord
if it flows in three dimensions does it mean if an object theoretically moves beyond the speed of light it won't experience time
Lord
time seems to flow in one direction...but I the past present and future happen every moment time flies regardless.
but if an object moves beyond the speed of light time stops right for it
Lord
yes but at light speed it ceases
Lord
yes it always flow from past to future.
Noman
if v=ktx Ly Mz find the value of x,y and z
Emmanuel Reply
x=v=ktx Ly Mz find the value of x,y and z
y=v=ktx Ly Mz find the value of x,y and z
z=v=ktx Ly Mz find the value of x,y and z
now get your lazy arse up and clean the kitchen 😁
I want to join the conversation
Subaba Reply
😂
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Stephen
what conversation you talking about? .....numbnut
how do i calculate for period of the oscillation
Bridget Reply
T=2π√(m÷k).K is spring constance
Ambe
T=2π√m/k
Lord
does the force in a system result in the energy transfer?
Lebatam Reply
full meaning of GPS system
Anaele Reply
global positioning system
Noman
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Matthew
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Practice Key Terms 1

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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