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.