# 11.4 Variation of pressure with depth in a fluid  (Page 2/4)

 Page 2 / 4 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 ${P}_{\text{atm}}$ , measured to be

$\text{1 atmosphere (atm)}={P}_{\text{atm}}=1.01×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}=\text{101 kPa}.$

This relationship means that, on average, at sea level, a column of air above $1.00\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}$ of the Earth’s surface has a weight of $1.01×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{N}$ , equivalent to $\text{1 atm}$ . (See [link] .) 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{1m 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 $P=\mathrm{h\rho g}$ for density, we see that

$\overline{\rho }=\frac{P}{\text{hg}}.$

We then take $P$ to be atmospheric pressure, $h$ is given, and $g$ is known, and so we can use this to calculate $\overline{\rho }$ .

Solution

Entering known values into the expression for $\overline{\rho }$ yields

$\overline{\rho }=\frac{1\text{.}\text{01}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}}{\left(\text{120}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m}\right)\left(9\text{.}\text{80}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\right)}=8\text{.}\text{59}×{\text{10}}^{-2}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}.$

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 $1\text{.}\text{29}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}$ —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.

## 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 $P=\mathrm{h\rho g}$ for depth $h$ :

$h=\frac{P}{\mathrm{\rho g}}.$

Then we take $P$ to be 1.00 atm and $\rho$ to be the density of the water that creates the pressure.

Solution

Entering the known values into the expression for $h$ gives

$h=\frac{1\text{.}\text{01}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}}{\left(1\text{.}\text{00}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}\right)\left(9\text{.}\text{80}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\right)}=\text{10}\text{.}3\phantom{\rule{0.25em}{0ex}}\text{m}.$

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.

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 $\text{mg}$ divided by the area $A$ supporting it (the area of the bottom of the container):
$P=\frac{\text{mg}}{A}.$
• Pressure due to the weight of a liquid is given by
$P=\mathrm{h\rho g},$

where $P$ is the pressure, $h$ is the height of the liquid, $\rho$ is the density of the liquid, and $g$ is the acceleration due to gravity.

A 20MH coil has a resistance of 50 ohms and us connected in series with a capacitor to a 520MV supply
what is physics
it is the science which we used in our daily life
Sujitha
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Junior
it is branch of science which deals with study of happening in the human life
AMIT
it is when you get up of your arse and do some real work 😁
Heat is transfered by thermal contact but if it is transfered by conduction or radiation, is it possible to reach in thermal equilibrium?
Yes, It is possible by conduction if Surface is Adiabatic
Astronomy
what are the fundamentals qualities
what is physic3
Kalilu
what is physic
Kalilu
Physics? Is a branch of science dealing with matter in relation to energy.
Moses
Physic... Is a purging medicine, which stimulates evacuation of the bowels.
Moses
are you asking for qualities or quantities?
Noman
give examples of three dimensional frame of reference
your fat arse sitting all day is a good reference of three dimensional numbnut
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?
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
The phenomenon of transfer of energy
Noman
how does time flow in one dimension
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
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
😂
hmm
Stephen
what conversation you talking about? .....numbnut
how do i calculate for period of the oscillation
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?
full meaning of GPS system
global positioning system
Noman
what's the use of the GPS
Matthew
how to prove that Newton's law of universal gravitation F = GmM ______ R²
sir dose it apply to the human system By By By Abby Sharp By OpenStax By OpenStax By By OpenStax By Laurence Bailen By OpenStax By Eddie Unverzagt By Richley Crapo By