Pressure in liquids (hydrostatic pressure)
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PART I: INTRODUCTION : swimming under pressure.
Do the following experiment at home. make 3 holes in a container (like a 1 gallon
milk bottle) and watch the water coming out. (see below). Where does the water squirt fastest ? where is the pressure greater ? at the top hole or at the bottom hole? why?
Pressure increases with depth. While you are swimming you feel the pressure of the water on your ear drums. (inside the ear, the pressure is the same as it is at sea level.
That's why the ears pop in altitude. the pressure inside becomes greater than the one outside). This pressure called the hydrostatic pressure is created by the weight of all that water above the diver.
1) Let's compute the pressure inside a liquid at a given depth. (let's forget about the weight of the air pushing also on the liquid)
The pressure of a fluid is the weight per unit area (A) of the fluid above you.
Suppose the water above you has a mass of m and a volume of V and a density of d.
Suppose you are swimming at a depth of h.
Show that the pressure at that given depth is: P = g x h x d (g = 9.8 m/s/s)
or Pressure (N/m2) = 9.8 x depth (m) x density (kg/m3)
hint: Use pressure = weight/ area and volume = area x h and weight = mass x g
The pressure of a liquid does not depend on the shape of the reservoir you are swimming in ! you will feel the same pressure at a depth of 1 foot in Lake Erie or in your bathtub. This is not intuitive. The shape of the bathtub does not matter either.. This can be shown by the well-known Pascal's vases.
The level is the same because the pressure is the same at the bottom of the vase.
Using this idea, you can siphon out a big aquarium.
Try these experiments. 1 the 1st experiment, the water will rise and the levels in the 2 containers will try to match.
The excess of pressure (excess of weight per unit area) will push the water our of the hose. Explain the others.
extra credits experiment:
This is used as a pump. the hydraustatic pressure in the bottle pushes the water up.
This principle is used to build a well that does not need any pump. The water will squirt outside "by itself ".
2) Consider the equation P = h g d. Suppose the density of water is 1000 kg/m3
We are used to atmospheric pressure due to the weight of the atmosphere above us.
At sea level: P = 1 atmosphere or 105 N/m2 or 1000kg per m2 or 15lbs per in2.
But when we dive the pressure on our body (or a submarine) dangerously increases. Let's find out by how much.
A) Suppose you dive 10 meters down. Find the pressure at that depth.
Suppose g=10m/s/s. P = ______ Pa or P ______ atmosphere.
(hint: 1 atmosphere = 105 Pa).
So a diver should know that each 10 meters of descent increases the pressure on the body by about 1 atmosphere.
(like 15pounds more pressing on any part of your body).
A healthy diver can tolerate pressure of 10 atmospheres, but must me extremely careful to come up slowly. A sudden reduction in pressure can be fatal, as it causes nitrogen dissolved in the blood to form bubbles that block the circulation.
LAb: watch these videos and write an essay about it.
watch the video segments called deep sea diving and then gas and pressure.
here is a website to learn more about deep sea diving and the Physics/biology
going 300 feet is going about 100m
the excess pressure is about 10 atm. (10 ATA)
The force pushing on a diver body is 10 times
larger than on the surface. A diver needs to
increase the pressure in his lungs to balance the force.
This way, his body will not be crushed !
A submarine has to be strong enough not to break under
that much of pressure. Inside the submarine
the pressure is 1 atm.
More pressure in lungs means more gas dissolved in blood and tissue.
Ask your Biology teacher to learn more.
effect pressure on human body on EArth, below sea level, in space.
In space, there is no air to press on us. If you take off your suit, you explode ! sweet!
(pressure inside your body will push hard enough outwards to blow off your thorax! )
If you climb a high mountain, you can feel your ears pop out. why ?
When you are considering a reservoir of water on earth (lake, ocean, bathtub, bottle,
any container) you need to add the atmospheric pressure (weight of the atmosphere per unit area)
to the hydrostatic pressure to find the absolute pressure.
We should write:
P (at depth h ) = Po (usually about 105 Pa at sea level) + h g d
But we will only compute the excess pressure above atmospheric pressure in this class:
P (at depth h )excess = h g d
Our human body is sensitive to the excess of pressure (in water) or the lack of pressure (in space)
Here is a demonstration to measure the increase of pressure with the height of a liquid:
Measure pressure in liquids with a U-tube
Half fill a U-tube with colored water. Stretch a piece of thin rubber loosely over the mouth of a filter funnel and tie it securely. Attach the stem of the filter funnel to one arm of the U-tube with rubber tubing. Hold the mouth of the filter funnel at different depths in a container of water. Record the depths of the mouth of the funnel in the water corresponding to the differences in heights of the colored water in the U-tube. This U-tube is being used as a pressure gauger.
1) Cut one end off a tall plastic drink bottle to make a tall container. Use the pressure manometer from the previous experiment. Place the funnel at different depths to measure the pressure. 2) Repeat the experiment with a container of methylated spirit, pure water and salt water. Hold the mouth of the filter funnel at the same depths in the three liquids and note the corresponding differences in the heights of the colored water in the U-tube. At the same depth, the less dense methylated spirit exerts less pressure than pure water and the more dense salt water exerts more pressure than pure water. 3) Repeat the experiment using a large container of water and a small container of water. Hold the mouth of the filter funnel at the same depths as before. The corresponding differences in height of the colored water in the U-tube are the same. (source)
Do it and get some extra credits ! Will be added on your next test. Ask me for advices.
3) A
If you are a scuba diver you are instructed not to hold your breath while you come up.
Why ?
hint:if you hold your breath, you are in your lungs compressed air, whereas, at the surface the pressure is less. Something really bad happens to you lungs.
Think of tires in hot Summer.
3) What is the (excess) pressure at a depth of 23 m in water in Pa ?
hint: P = 105 + hgd with d = 1000 kg/m3 and g=10m/s/s
4) A large tank holds salad oil, density 0.9 103 kg/m3, to a depth of 6m.
A) What is the (excess) pressure at the bottom of the tank ? P = ____ Pa (use g = 10m/s/s)
hint: P = 105 + hgd with d = 900 kg/m3 and g=10m/s/s
B) convert to atmospheres P = ____ atm
hint: use 1 atm = 105 Pa
C) you now know that 1 atmosphere is like 15 pounds per in2. (about) pressing at a given depth. so the pressure in the tank, as computed in B) = _______ pounds/in2
hint: it is a conversion 1 atm = 15lbs/in2
4) What is the(excess) pressure in atmospheres, on the ears of a diver, who is 65m deep in the water ? use g=10m/s/s and d = 1000 kg/m3
hint: P = h g d . The unit will be N/m2 or Pa. convert to atm. 1 atm = 105 Pa
5) A dam is to be made to hold black an artificial lake 110m deep.
A)Find the pressure that the bottom of the dam must withstand, in pascals (Pa).
hint: P = h g d
Why do you think the wall of the dam needs to be thicker at the base of a dam ?
B) you dive 1m below surface in the dam. Do you feel less, same or more pressure
than in your bathtub (same depth) . (suppose your bathtub is at least 1m deep).
C) The larger dam in the world will be done in 2009 in china.
Three Gorges Dam, in Hubei Province, China, will be the world's largest dam and largest concrete structure and create the largest lake. The dam will be built across the 3 Gorges section of the Yangtze River. It will be a 610-foot high wall running about 1.3 miles from bank to bank. Requiring 12 years and tens of thousands of workers to complete, the dam will cost $29 billion, and will create a 370 mile long lake, a distance equal to nearly half the length of California, that will be visible from Earth orbit.
Let's try to find out the excess pressure at the bottom of the wall.
convert feet to meters. (1 foot = 0.3048 m). Use the formula to find the pressure in Pa (kg/m3).
Then convert in atm. (1atm = 105 Pa ) . 1 atm is a force of 15 lbs per in2 so at the bottom of that dam, the excess force is _____ lbs per in2.
click here
6) Steel submarines can stand about 4000,000 Pa and Titanium subs can stand about 10, 000, 000 Pa.
Write these number in scientific notation then convert to atm. (105 Pa = 1 atm)
complete: every 33 feet adds another 15 pounds of pressure (called another atmosphere of pressure). At 100 feet deep, the pressure is 4 times the pressure at sea level, or approximately_________ pounds per square inch. Few vessels could survive this pressure unless they were designed to be very strong.
6) the density of mercury is 13.6 103 kg/m3
A beaker filled with mercury to a height of 0.20m is placed inside a vacuum chamber in a laboratory. (this means we don't have to worry about the air pressure). What is the pressure at the bottom of the beaker?
hint: P = h d g easy
7) Two fish swim in a freshwater lake, one at a depth of 14.0 m and the other at a depth of 98.0 m.
What is th difference in pressure on the two fish ?
8) Challenger Deep in the Mariana Trench is the deepest point in Earth's oceans. The bottom there is 10,924 meters (35,840 feet) below sea level. If Mount Everest, the highest mountain on Earth, were placed at this location it would be covered by over one mile of water. The Challenger Deep is named after the British survey ship Challenger II, which discovered this deepest location in 1951.
Let's round the depth to 11 km. A)What is the excess pressure would a submarine need to be able to withstand to reach this depth i ? P = ______ Pa hint: convert km to meters first
B) convert the pressure to atm. (105 Pa = 1 atm)
C) 1 atm is for 15 pounds / in2 so the submarine has to withstand ___________ / in2
D) Let's say the submarine has a circular window with a diameter of 20 in. Calculate the total force (pounds) exerted at this depth on this window. Use C)
hint: first find the area of the window in in2. Area = pi x (radius)2 and radius = diameter /2. Then use C) . force = pressure x area.
9) A column of water in a vertical pipe has a cross-sectional area of 0.2 m2 and a weight of 450N. What is the increase in pressure (in Pa) from the top to the bottom of the pipe ?
hint: pressure = force / area = weight / area
10) Water has a density of d= 1000 kg/m2. The depth of a swimming pool at the deep end is about 3m.
A) what is the volume V of a column of water h = 3m deep and A= 0.5m2 in cross-sectional area?
hint: volume = height x area
B) What is the mass of this column of water ?
hint: density = mass/volume or d = m/V. solve for mass m.
Ç) What is the weight of this column of water in newtons ? g= 10m/s/s
hint: weight = mass x g
D) What is the excess of pressure exerted by this column of water on the bottom of the pool ?
hint: pressure = weight /area
E) How does this value compare to atmospheric pressure? ( atmospheric pressure is about 105PA or 105 N/m2)
PART I: INTRODUCTION : swimming under pressure.
Do the following experiment at home. make 3 holes in a container (like a 1 gallon
milk bottle) and watch the water coming out. (see below). Where does the water squirt fastest ? where is the pressure greater ? at the top hole or at the bottom hole? why?
Pressure increases with depth. While you are swimming you feel the pressure of the water on your ear drums. (inside the ear, the pressure is the same as it is at sea level.
That's why the ears pop in altitude. the pressure inside becomes greater than the one outside). This pressure called the hydrostatic pressure is created by the weight of all that water above the diver.
1) Let's compute the pressure inside a liquid at a given depth. (let's forget about the weight of the air pushing also on the liquid)
The pressure of a fluid is the weight per unit area (A) of the fluid above you.
Suppose the water above you has a mass of m and a volume of V and a density of d.
Suppose you are swimming at a depth of h.
Show that the pressure at that given depth is: P = g x h x d (g = 9.8 m/s/s)
or Pressure (N/m2) = 9.8 x depth (m) x density (kg/m3)
hint: Use pressure = weight/ area and volume = area x h and weight = mass x g
The pressure of a liquid does not depend on the shape of the reservoir you are swimming in ! you will feel the same pressure at a depth of 1 foot in Lake Erie or in your bathtub. This is not intuitive. The shape of the bathtub does not matter either.. This can be shown by the well-known Pascal's vases.
The level is the same because the pressure is the same at the bottom of the vase.
Using this idea, you can siphon out a big aquarium.
Try these experiments. 1 the 1st experiment, the water will rise and the levels in the 2 containers will try to match.
The excess of pressure (excess of weight per unit area) will push the water our of the hose. Explain the others.
extra credits experiment:
This is used as a pump. the hydraustatic pressure in the bottle pushes the water up.
This principle is used to build a well that does not need any pump. The water will squirt outside "by itself ".
2) Consider the equation P = h g d. Suppose the density of water is 1000 kg/m3
We are used to atmospheric pressure due to the weight of the atmosphere above us.
At sea level: P = 1 atmosphere or 105 N/m2 or 1000kg per m2 or 15lbs per in2.
But when we dive the pressure on our body (or a submarine) dangerously increases. Let's find out by how much.
A) Suppose you dive 10 meters down. Find the pressure at that depth.
Suppose g=10m/s/s. P = ______ Pa or P ______ atmosphere.
(hint: 1 atmosphere = 105 Pa).
So a diver should know that each 10 meters of descent increases the pressure on the body by about 1 atmosphere.
(like 15pounds more pressing on any part of your body).
A healthy diver can tolerate pressure of 10 atmospheres, but must me extremely careful to come up slowly. A sudden reduction in pressure can be fatal, as it causes nitrogen dissolved in the blood to form bubbles that block the circulation.
LAb: watch these videos and write an essay about it.
watch the video segments called deep sea diving and then gas and pressure.
here is a website to learn more about deep sea diving and the Physics/biology
going 300 feet is going about 100m
the excess pressure is about 10 atm. (10 ATA)
The force pushing on a diver body is 10 times
larger than on the surface. A diver needs to
increase the pressure in his lungs to balance the force.
This way, his body will not be crushed !
A submarine has to be strong enough not to break under
that much of pressure. Inside the submarine
the pressure is 1 atm.
More pressure in lungs means more gas dissolved in blood and tissue.Ask your Biology teacher to learn more.
effect pressure on human body on EArth, below sea level, in space.
In space, there is no air to press on us. If you take off your suit, you explode ! sweet!
(pressure inside your body will push hard enough outwards to blow off your thorax! )
If you climb a high mountain, you can feel your ears pop out. why ?
When you are considering a reservoir of water on earth (lake, ocean, bathtub, bottle,
any container) you need to add the atmospheric pressure (weight of the atmosphere per unit area)
to the hydrostatic pressure to find the absolute pressure.
We should write:
P (at depth h ) = Po (usually about 105 Pa at sea level) + h g d
But we will only compute the excess pressure above atmospheric pressure in this class:
P (at depth h )excess = h g d
Our human body is sensitive to the excess of pressure (in water) or the lack of pressure (in space)
Here is a demonstration to measure the increase of pressure with the height of a liquid:
Measure pressure in liquids with a U-tube
Half fill a U-tube with colored water. Stretch a piece of thin rubber loosely over the mouth of a filter funnel and tie it securely. Attach the stem of the filter funnel to one arm of the U-tube with rubber tubing. Hold the mouth of the filter funnel at different depths in a container of water. Record the depths of the mouth of the funnel in the water corresponding to the differences in heights of the colored water in the U-tube. This U-tube is being used as a pressure gauger.
1) Cut one end off a tall plastic drink bottle to make a tall container. Use the pressure manometer from the previous experiment. Place the funnel at different depths to measure the pressure. 2) Repeat the experiment with a container of methylated spirit, pure water and salt water. Hold the mouth of the filter funnel at the same depths in the three liquids and note the corresponding differences in the heights of the colored water in the U-tube. At the same depth, the less dense methylated spirit exerts less pressure than pure water and the more dense salt water exerts more pressure than pure water. 3) Repeat the experiment using a large container of water and a small container of water. Hold the mouth of the filter funnel at the same depths as before. The corresponding differences in height of the colored water in the U-tube are the same. (source)
Do it and get some extra credits ! Will be added on your next test. Ask me for advices.
3) A
If you are a scuba diver you are instructed not to hold your breath while you come up.
Why ?
hint:if you hold your breath, you are in your lungs compressed air, whereas, at the surface the pressure is less. Something really bad happens to you lungs.
Think of tires in hot Summer.
3) What is the (excess) pressure at a depth of 23 m in water in Pa ?
hint: P = 105 + hgd with d = 1000 kg/m3 and g=10m/s/s
4) A large tank holds salad oil, density 0.9 103 kg/m3, to a depth of 6m.
A) What is the (excess) pressure at the bottom of the tank ? P = ____ Pa (use g = 10m/s/s)
hint: P = 105 + hgd with d = 900 kg/m3 and g=10m/s/s
B) convert to atmospheres P = ____ atm
hint: use 1 atm = 105 Pa
C) you now know that 1 atmosphere is like 15 pounds per in2. (about) pressing at a given depth. so the pressure in the tank, as computed in B) = _______ pounds/in2
hint: it is a conversion 1 atm = 15lbs/in2
4) What is the(excess) pressure in atmospheres, on the ears of a diver, who is 65m deep in the water ? use g=10m/s/s and d = 1000 kg/m3
hint: P = h g d . The unit will be N/m2 or Pa. convert to atm. 1 atm = 105 Pa
5) A dam is to be made to hold black an artificial lake 110m deep.
A)Find the pressure that the bottom of the dam must withstand, in pascals (Pa).
hint: P = h g d
Why do you think the wall of the dam needs to be thicker at the base of a dam ?
B) you dive 1m below surface in the dam. Do you feel less, same or more pressure
than in your bathtub (same depth) . (suppose your bathtub is at least 1m deep).
C) The larger dam in the world will be done in 2009 in china.
Three Gorges Dam, in Hubei Province, China, will be the world's largest dam and largest concrete structure and create the largest lake. The dam will be built across the 3 Gorges section of the Yangtze River. It will be a 610-foot high wall running about 1.3 miles from bank to bank. Requiring 12 years and tens of thousands of workers to complete, the dam will cost $29 billion, and will create a 370 mile long lake, a distance equal to nearly half the length of California, that will be visible from Earth orbit.
Let's try to find out the excess pressure at the bottom of the wall.
convert feet to meters. (1 foot = 0.3048 m). Use the formula to find the pressure in Pa (kg/m3).
Then convert in atm. (1atm = 105 Pa ) . 1 atm is a force of 15 lbs per in2 so at the bottom of that dam, the excess force is _____ lbs per in2.
click here
6) Steel submarines can stand about 4000,000 Pa and Titanium subs can stand about 10, 000, 000 Pa.
Write these number in scientific notation then convert to atm. (105 Pa = 1 atm)
complete: every 33 feet adds another 15 pounds of pressure (called another atmosphere of pressure). At 100 feet deep, the pressure is 4 times the pressure at sea level, or approximately_________ pounds per square inch. Few vessels could survive this pressure unless they were designed to be very strong.
Submarines must be able to stand up to the crushing pressures of the depths. Submarines are commonly made of strong _______ and very thick _________ or Plexiglass for viewing portals. It takes clever engineers to design a craft that has the best combination of strength without becoming too heavy or bulky to move efficiently through the water.
source: learn more about the Physics of submarines
6) the density of mercury is 13.6 103 kg/m3
A beaker filled with mercury to a height of 0.20m is placed inside a vacuum chamber in a laboratory. (this means we don't have to worry about the air pressure). What is the pressure at the bottom of the beaker?
hint: P = h d g easy
7) Two fish swim in a freshwater lake, one at a depth of 14.0 m and the other at a depth of 98.0 m.
What is th difference in pressure on the two fish ?
8) Challenger Deep in the Mariana Trench is the deepest point in Earth's oceans. The bottom there is 10,924 meters (35,840 feet) below sea level. If Mount Everest, the highest mountain on Earth, were placed at this location it would be covered by over one mile of water. The Challenger Deep is named after the British survey ship Challenger II, which discovered this deepest location in 1951.
Let's round the depth to 11 km. A)What is the excess pressure would a submarine need to be able to withstand to reach this depth i ? P = ______ Pa hint: convert km to meters first
B) convert the pressure to atm. (105 Pa = 1 atm)
C) 1 atm is for 15 pounds / in2 so the submarine has to withstand ___________ / in2
D) Let's say the submarine has a circular window with a diameter of 20 in. Calculate the total force (pounds) exerted at this depth on this window. Use C)
hint: first find the area of the window in in2. Area = pi x (radius)2 and radius = diameter /2. Then use C) . force = pressure x area.
9) A column of water in a vertical pipe has a cross-sectional area of 0.2 m2 and a weight of 450N. What is the increase in pressure (in Pa) from the top to the bottom of the pipe ?
hint: pressure = force / area = weight / area
10) Water has a density of d= 1000 kg/m2. The depth of a swimming pool at the deep end is about 3m.
A) what is the volume V of a column of water h = 3m deep and A= 0.5m2 in cross-sectional area?
hint: volume = height x area
B) What is the mass of this column of water ?
hint: density = mass/volume or d = m/V. solve for mass m.
Ç) What is the weight of this column of water in newtons ? g= 10m/s/s
hint: weight = mass x g
D) What is the excess of pressure exerted by this column of water on the bottom of the pool ?
hint: pressure = weight /area
E) How does this value compare to atmospheric pressure? ( atmospheric pressure is about 105PA or 105 N/m2)