The maximum gauge pressure in a hydraulic lift

수연 조

수연 조

Answered question

2022-09-11

The maximum gauge pressure in a hydraulic lift is 17 atm. What is the largest size vehicle (kg) it can lift a diameter output line is 28.0 cm.

Answer & Explanation

user_27qwe

user_27qwe

Skilled2023-05-24Added 375 answers

To determine the largest size vehicle that a hydraulic lift can lift, we need to consider the maximum gauge pressure and the diameter of the output line.
Given information:
- Maximum gauge pressure: 17 atm
- Diameter of the output line: 28.0 cm
Let's proceed with the solution:
1. Convert the pressure to SI units:
Since the pressure is given in atmospheres (atm), we need to convert it to pascals (Pa) in order to use it in calculations. The conversion factor is 1 atm = 1.013×105 Pa.
Therefore, the maximum gauge pressure in pascals is:
P=17×1.013×105Pa
2. Calculate the cross-sectional area of the output line:
The cross-sectional area of a circle can be calculated using the formula:
A=πd24
where:
- A is the cross-sectional area
- π is a mathematical constant approximately equal to 3.14159
- d is the diameter
Substituting the given diameter of the output line (28.0 cm) into the formula, we can calculate the cross-sectional area in square meters.
3. Determine the force exerted by the hydraulic lift:
The force exerted by the hydraulic lift can be calculated using the formula:
F=P·A
where:
- F is the force
- P is the pressure
- A is the cross-sectional area
Substituting the calculated pressure and the cross-sectional area into the formula, we can determine the force exerted by the hydraulic lift.
4. Calculate the weight of the largest size vehicle:
The force exerted by the hydraulic lift is equal to the weight of the vehicle it can lift. Therefore, the weight of the largest size vehicle is equal to the force.

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