Ch 12: Fluid Mechanics

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 12: Fluid Mechanics

Problem 22

Chapter 12, Problem 22

Hydraulic Lift II.The piston of a hydraulic automobile lift is 0.30 m in diameter. What gauge pressure, in pascals, is required to lift a car with a mass of 1200 kg? Also express this pressure in atmospheres.

Verified step by step guidance

First, calculate the area of the piston using the formula for the area of a circle: \( A = \pi r^2 \), where \( r \) is the radius of the piston. Given the diameter is 0.30 m, the radius \( r = 0.30 / 2 \) m.

Next, determine the force required to lift the car. This force is equal to the weight of the car, which can be calculated using \( F = mg \), where \( m = 1200 \) kg is the mass of the car and \( g = 9.81 \) m/s² is the acceleration due to gravity.

Calculate the gauge pressure required using the formula \( P = \frac{F}{A} \), where \( F \) is the force calculated in the previous step and \( A \) is the area of the piston.

Convert the pressure from pascals to atmospheres. Use the conversion factor: 1 atmosphere = 101325 pascals.

Finally, express the gauge pressure in both pascals and atmospheres, ensuring to clearly distinguish between the two units.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Pascal's Principle

Pascal's Principle states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of its container. This principle is fundamental in hydraulic systems, where a small force applied at one point is transmitted to exert a larger force at another point, allowing for the lifting of heavy objects like cars.

Pressure Calculation

Pressure is defined as the force applied per unit area. In the context of a hydraulic lift, the pressure required to lift an object can be calculated using the formula P = F/A, where P is the pressure, F is the force (equal to the weight of the car, which is mass times gravity), and A is the area of the piston. This calculation is crucial for determining the gauge pressure needed to lift the car.

Unit Conversion

Unit conversion is essential for expressing physical quantities in different units. In this problem, after calculating the pressure in pascals, it is necessary to convert it to atmospheres for a comprehensive understanding. The conversion factor between pascals and atmospheres is 1 atm = 101,325 Pa, which allows for the expression of pressure in a more commonly used unit.

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