Solving problem related to absolute, atmospheric, gage pressures and The U-tube manometer.

Summary

This 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

00:00

🔬 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.

05:01

📏 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.

Keywords

💡Absolute Pressure

Absolute pressure is the total pressure exerted by a fluid, including the atmospheric pressure. In the video, it is crucial for determining the pressure inside Tank B. The script mentions that the absolute pressure inside Tank A is 267.7 kilopascals, and the pressure gauge inside Tank B reads 140 kilopascals. The difference between these values, considering the atmospheric pressure, is used to calculate the absolute pressure inside Tank B.

💡Pressure Gauge

A pressure gauge is an instrument used to measure the pressure relative to the atmospheric pressure. In the context of the video, the pressure gauge inside Tank B reads 140 kilopascals, which is used to calculate the absolute pressure inside Tank B. The script explains that the pressure gauge's reading is the difference between the absolute pressure of Tank A and Tank B.

💡U-tube Manometer

A U-tube manometer is a device used to measure pressure differences by observing the height difference of a fluid in a U-shaped tube. The video script describes using a U-tube manometer connected to Tank B, filled with mercury, to determine the absolute pressure inside Tank B by observing the column length of mercury.

💡Mercury

Mercury is a dense, silvery metal used in the U-tube manometer due to its high density, which allows for precise measurement of pressure differences. In the video, the height of the mercury column in the U-tube manometer is used to calculate the pressure inside Tank B, as explained by the script.

💡Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of air molecules in the Earth's atmosphere. The script states that the atmospheric pressure surrounding Tank B is 101 kilopascals, which is a standard value used in the calculations to find the absolute pressure inside Tank B.

💡Acceleration of Gravity

The acceleration of gravity is the rate at which objects fall towards the Earth due to gravity. In the script, it is given as 9.8 meters per second squared and is used in the formula to calculate the column length of mercury in the U-tube manometer, which is essential for determining the pressure inside Tank B.

💡Density

Density is the mass per unit volume of a substance. The script mentions the density of mercury, which is necessary for the calculation of the pressure exerted by the mercury column in the U-tube manometer. The density of mercury is used in conjunction with the acceleration of gravity to find the height of the mercury column.

💡Column Length (l)

The column length refers to the height of the mercury column in the U-tube manometer. The script explains that by knowing the absolute pressure inside Tank B and using the formula involving density, gravity, and atmospheric pressure, one can calculate the column length in meters, which is then converted to centimeters for the final answer.

💡Pascal

The pascal is the SI unit of pressure, defined as one newton per square meter. The script discusses converting the pressure readings from kilopascals to pascals for the calculations, emphasizing the importance of consistent units in scientific calculations.

💡Conservation of Pressure

Conservation of pressure, as implied in the script, refers to the principle that at the same depth in a fluid, the pressure is the same. This principle is applied when calculating the pressure exerted by the mercury column in the U-tube manometer, which is equal to the pressure inside Tank B.

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