Solving problem related to absolute, atmospheric, gage pressures and The U-tube manometer.
Summary
TLDRThis educational video script explains how to determine the absolute pressure inside a tank and the column length of a mercury manometer. It covers the calculation using the given data, including atmospheric pressure, density of mercury, and gravity. The script walks through the process of finding the absolute pressure in Tank B using the pressure gauge reading in Tank A and then uses the pressure equation to calculate the column length in the U-tube manometer, ensuring consistent units throughout the explanation.
Takeaways
- 🔍 The video discusses a physics problem involving two tanks, A and B, with Tank A inside Tank B, both containing air.
- 📏 Tank A's absolute pressure is given as 267.7 kPa, while the pressure gauge inside Tank B reads 140 kPa.
- 🌡️ A U-tube manometer filled with mercury is connected to Tank B to measure pressure differences.
- 🌎 The atmospheric pressure surrounding Tank B is 101 kPa, and the acceleration due to gravity is 9.8 m/s².
- 🧮 The pressure gauge in Tank B measures the difference between the absolute pressure inside Tank A and Tank B.
- 🔄 By rearranging the pressure equation, the absolute pressure inside Tank B is calculated to be 127.7 kPa.
- 💧 The U-tube manometer is used to determine the pressure exerted by Tank B on the mercury, considering atmospheric pressure.
- 📐 The formula ρgl is used to calculate the column length 'l' in the U-tube manometer, where ρ is the density of mercury, g is gravity, and l is the length.
- 🔢 The calculation involves unit conversion, ensuring that the final unit for length 'l' is in meters, and then converting it to centimeters for the final answer.
- 📉 The final calculation results in a column length 'l' of 0.2 meters, which is then converted to 20 centimeters as per the problem's requirement.
Q & A
What is the absolute pressure inside Tank A?
-The absolute pressure inside Tank A is 267.7 kilo pascals.
What does the pressure gauge A connected to Tank A read?
-The pressure gauge A connected to Tank A reads 140 kilo pascals.
What is the atmospheric pressure surrounding Tank B?
-The atmospheric pressure surrounding Tank B is 101 kilo pascals.
What is the role of the U-tube manometer in this scenario?
-The U-tube manometer is used to measure the pressure difference between Tank B and the atmospheric pressure.
What is the density of mercury used in the U-tube manometer?
-The density of mercury is not explicitly stated in the script, but it is a known value, approximately 13,600 kilograms per cubic meter.
What is the acceleration due to gravity used in the calculations?
-The acceleration due to gravity used in the calculations is 9.8 meters per second squared.
How is the absolute pressure inside Tank B calculated?
-The absolute pressure inside Tank B is calculated by subtracting the pressure gauge reading of Tank A from the absolute pressure of Tank A.
What is the absolute pressure inside Tank B after calculations?
-The absolute pressure inside Tank B is 127.7 kilo pascals.
How is the column length 'l' in the U-tube manometer determined?
-The column length 'l' in the U-tube manometer is determined using the equation rho * g * l, where rho is the density of mercury, g is the acceleration due to gravity, and l is the column length.
What is the final calculated column length 'l' in the U-tube manometer in meters?
-The final calculated column length 'l' in the U-tube manometer is 0.2 meters.
How is the unit conversion from meters to centimeters squared done for the column length 'l'?
-The unit conversion from meters to centimeters squared is done by multiplying the length in meters by 100 (since 1 meter equals 100 centimeters) and then squaring the result.
Outlines
🔬 Pressure Calculation in a Nested Tank System
This paragraph discusses a physics problem involving two nested tanks, Tank A and Tank B, both containing air. Tank A has an absolute pressure of 267.7 kPa, and a pressure gauge inside Tank B reads 140 kPa. The goal is to determine the absolute pressure inside Tank B and the column length 'l' of a U-tube manometer connected to Tank B, which contains mercury. The atmospheric pressure is given as 101 kPa, and the acceleration due to gravity is 9.8 m/s^2. The process involves calculating the difference in pressure between the tanks and using the manometer to find the pressure exerted by Tank B on the mercury. The final calculation for the absolute pressure inside Tank B is 127.7 kPa.
📏 Determining Column Length in a U-Tube Manometer
The second paragraph elaborates on the process of calculating the column length 'l' in the U-tube manometer connected to Tank B. It explains the need to maintain consistent units and the conversion of units where necessary. The calculation involves using the density of mercury, the gravitational acceleration, and the pressure difference between the absolute pressure inside Tank B and the atmospheric pressure. The paragraph walks through the unit conversion and the mathematical steps to solve for 'l', including the manipulation of the pressure equation (ρgh) and the unit analysis leading to the final result of the column length being 0.2 meters, which is then converted to 20 centimeters for the final answer.
Mindmap
Keywords
💡Absolute Pressure
💡Pressure Gauge
💡U-tube Manometer
💡Mercury
💡Atmospheric Pressure
💡Acceleration of Gravity
💡Density
💡Column Length (l)
💡Pascal
💡Conservation of Pressure
Highlights
The absolute pressure in Tank A is 267.7 kilo pascal.
Pressure Gauge A reads 140 kilopascal and is located inside Tank B.
U-tube manometer connected to Tank B contains mercury.
Atmospheric pressure surrounding Tank B is 101 kilo pascal.
Acceleration of gravity is 9.8 meters per second squared.
Pressure Gauge A represents the difference between the absolute pressure and atmospheric pressure.
Absolute pressure of Tank B is calculated to be 127.7 kilo pascal.
The pressure in the U-tube manometer is a result of the force exerted by Tank B's pressure on the mercury fluid.
Pressure equation used is rho g l, where rho is the density, g is gravity, and l is the column length.
The units must be consistent; pascal is newton per meter squared, and newton is mass times acceleration.
To find the pressure in the manometer, atmospheric pressure and the pressure exerted by the mercury fluid are considered.
The length l in the U-tube manometer is solved using the pressure equation and given values.
The calculation involves converting kilo pascal to pascal and ensuring the correct unit of meters for length.
The final calculated length of the mercury column is 0.2 meters, which converts to 20 centimeters.
The video provides a detailed explanation of how to handle units and perform calculations in fluid mechanics.
The video concludes with a summary of the calculated values and a thank you note to the viewers.
Transcripts
hi in this figure
it shows us a tank within a tank each
containing air
the absolute pressure in tank a is 267.7
kilo pascal
pressure gauge a is located inside tank
b
and reads 140 kilopascal
the u-tube manometer connected to tank b
contains mercury
using data on the diagram determine the
absolute pressure
inside tank b and kilo pascal and the
column length
l in centimeter the atmospheric pressure
surrounding tank b
is 101 kilo pascal
the acceleration of gravity is 9.8 meter
per second
squared
what is given to us is tank a
inside tank b both contain air the
absolute pressure of tank a
the pressure gauge reads 140 kilo pascal
tank b is connected to a youtube mono
youtube manometer
the fluid of it is mercury it's very
important to keep consistent
uh units so we are dealing with meter
per second squared we're meeting with
pascal
which is newton per meter per second
squared
so that's why we had to convert the gram
per centimeters
per cubic centimeter by using these two
factors
to give us kilogram per cubic meter
we are giving the atmospheric pressure
as 101 kilopascal and the
acceleration due to gravity so we have
here the pressure gauge
connected to tank a and the u-tube
manometer
connected to tank b
this figure will help us determine the
absolute pressure
inside tank b as you can see
here we have the pressure gauge the
pressure gauge
is the difference between the absolute
pressure and the atmospheric pressure
now in our case the atmospheric pressure
is the outside temperature
which represent tank
b and the b absolute here
represent tank a
so to find so that so so that means
the pressure gauge a equals to
absolute pressure of tank a minus the
absolute pressure of tank
b the
pressure gauge that is connected to tank
a
inside tank b is reads 140 kilo pascal
the absolute pressure of tank a is given
as 267.7 kilo pascal and we need to find
the absolute pressure
of tank b we move the 267.7 to the other
side of the equation and we
change the sign we add these two numbers
both sides of the equation have negative
so we can cancel it
so we end up with uh without with the
absolute pressure
inside tank b is 127.7 kilo pascal
uh in this equation so since we are
giving given
the since we have found the absolute
pressure inside tank b
that means that the absolute pressure
inside
tank b
exert a force on the mercury fluid
in the u-tube manometer so as the
pressure of tank b
increases the length will
definitely increase
uh in fluids
at this fluids at the same depth
we have the same pressure so if we
so if we know the pressure in this
in this side that mean we know the
pressure
on this side and vice versa so
to find the pressure in this side
we can we need to add the atmospheric
pressure
which is exerting force pressure
on the mercury fluid and the
mercury
and the mercury fluid is exerting
that pressure on this point by using the
pressure equation
rho g l
so we need to determine the column
length
l in youtube manometer we use this
equation
we already know the absolute
pressure of tank b to be 127.7 kilo
pascal
we're giving the atmospheric pressure we
are giving the
density and the gravity we multiply the
density
times the gravity and we combine the
units
as you can see the kilogram sorry the
meter cancel with one of the three
meters in here so we are left with
meters squared
so we have kilogram meter squared second
squared
as a side note here pascal is a unit of
of newton per meter
squared newton is uh mass times
acceleration so kilogram times meter
square
divided by uh meter per second square
divided by
meter squared
so we ex so we replace the pascal with
this unit
uh and we remove the kilo pascal
by multiplying it by multiplying
by 1000 so instead of one thousand
one twenty seven point seven it become
one twenty seven
thousand seven hundred
we move the 101 thousand to the other
side of the equation and change the sign
we add these two numbers
and we solve now for length
l so
here we are solving for length l but we
need to make sure
that we have the correct units so
what we did is the kilogram times meter
per second square
the meter square since it's it was in
division it will go to the top
and it will be in by multiplication and
the sign
on the exponent will change from
positive to negative as we can see here
and similarly since this was uh
in division it will go to the top
multiplication
and since it was in division it it will
flip
whatever is in denominator will be in
the no in the numerator and then
whatever is in denominator will be in
the denominator
so we did the multiplication
we flipped and now we make sure that
we end up with meter uh so
what happened the kilogram cancel with
kilogram
second square will cancel with the
second squared exponents
uh in multiplication we add them so one
plus
minus two will end up with m minus one
and and we have m2 as we said the
kilogram cancel the second square
cancel so we're left with
meter so the exponent minus one plus one
will give us
meter to the power one so we will be
given the
so our units are correct so
the length will so the length of the
mercury is 0.2 meter
we use the conversion factor because we
are asked we are asked to find
uh in centimeters squared so it will be
20
centimeters square i hope you find this
helpful
thank you very much for watching and
have a good day
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