Which of the following is the correct formula for pressure?
P = F / A
P = F × A
P = F + A
P = F - A
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Pressure Formula – Formula, Applications, Example Problems
Pressure Formula – Formula, Applications, Example Problems
What is Pressure Formula?
The pressure formula, crucial in physics, quantifies the force per unit area applied to a surface and is expressed as
- 𝑃 represents pressure.
- 𝐹 the applied force.
- 𝐴 the area involved.
Developed by figures like Blaise Pascal, this formula is vital for studying phenomena in physics, engineering, and meteorology. Additionally, the hydrostatic pressure formula calculates the pressure exerted by a fluid at equilibrium due to gravity.
- 𝜌 is the fluid’s density
- 𝑔 the acceleration due to gravity
- ℎ the height of the fluid column.
Both formulas are foundational for predicting and understanding the behavior of gases and liquids under various conditions, enhancing our grasp of natural and engineered systems.
Applications of Pressure Formula
- Weather Forecasting: Meteorologists use the pressure formula to predict weather changes by analyzing atmospheric pressure variations.
- Designing Hydraulic Systems: Engineers apply the formula to design systems like brakes and hydraulic lifts, ensuring they operate safely under the right pressure.
- Calculating Force in Pistons: The formula helps in calculating the force exerted by pistons in engines and pumps, critical for their efficiency and functionality.
- Understanding Deep-Sea Conditions: Scientists calculate the pressure exerted on submarines and underwater equipment to ensure structural integrity at great depths.
- Medical Applications: The formula is used to monitor blood pressure and design medical devices that rely on precise pressure measurements, such as ventilators and IV drips.
Example Problems on Pressure Formula
Example 1: Calculating Pressure Inside a Tire
Problem: A force of 1500 Newtons is exerted over an area of 0.035 square meters in a car tire. What is the pressure inside the tire?
Solution: Use the pressure formula 𝑃=𝐹 / 𝐴.
- 𝐹= 1500 Newtons
- 𝐴=0.035 square meters
𝑃=1500 / 0.035=42857.14 Pascals
Example 2: Force Exerted by a Hydraulic Press
Problem: A hydraulic press exerts a pressure of 200,000 Pascals. If the contact area between the press and the block is 0.1 square meters, calculate the force exerted by the press.
Solution: Rearrange the formula to solve for F : 𝐹 = 𝑃 × 𝐴.
- 𝑃=200,000 Pascals
- 𝐴=0.1 square meters
𝐹=200,000 × 0.1=20,000 Newtons
Example 3: Height of Water in a Tank
Problem: The hydrostatic pressure at the bottom of a tank filled with water is 500 Pascals. Given the density of water is 1000 kg/m³, calculate the height of the water column.
Solution: Use the hydrostatic pressure formula 𝑃 = 𝜌 x 𝑔 x ℎ and rearrange to solve for ℎ:
- 𝑃=500 Pascals
- 𝜌=1000 kg/m³
- 𝑔=9.81 m/s² (acceleration due to gravity)
ℎ = 𝑃 x 𝜌 x 𝑔 = 500 x 1000×9.81 = 0.051 meters
FAQs
What is Pressure Formula and Its Unit?
The pressure formula is 𝑃=𝐹𝐴, where P represents pressure, measured in Pascals (Pa).
What Are the 3 Units of Pressure?
Pressure is commonly measured in Pascals (Pa), atmospheres (atm), and pounds per square inch (psi).
What is the g in Pressure Formula?
In the pressure formula, g represents the acceleration due to gravity, typically 9.81 m/s² on Earth.
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Practice Test
If the force is 50 N and the area is 2 m², what is the pressure?
25 Pa
100 Pa
50 Pa
2 Pa
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The pressure exerted by a 100 N force on an area of 4 m² is:
25 Pa
400 Pa
100 Pa
4 Pa
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If the pressure is 200 Pa and the area is 4 m², what is the force?
800 N
50 N
200 N
400 N
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Which of the following does not affect pressure directly?
Force
Area
Volume
Both force and area
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What is the unit of pressure in the SI system?
Newton
Pascal
Joule
Watt
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A force of 500 N acts over an area of 0.5 m². What is the pressure?
1000 Pa
500 Pa
250 Pa
2000 Pa
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Calculate the pressure if a 10 N force is applied on a 0.1 m² area.
100 Pa
10 Pa
0.1 Pa
1000 Pa
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A block exerts a force of 300 N on a surface area of 2 m². What is the pressure?
150 Pa
300 Pa
600 Pa
100 Pa
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If the pressure is 500 Pa and the force is 1000 N, what is the area?
2 m²
0.5 m²
5 m²
2000 m²
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