The maximum gauge pressure in a hydraulic lift is 18 atm. What is the largest size vehicle (kg) it can lift if the diameter of the output line is 22 cm?
pressure*area=lift
101.3kPa*PI*.11^2= max lift in newtons
To calculate the largest size vehicle the hydraulic lift can lift, we need to consider the maximum force that the lift can generate.
First, let's calculate the maximum force using the formula:
Force = Pressure × Area
The pressure is given as the gauge pressure, which means it already includes atmospheric pressure. Therefore, we can use it directly in our calculation.
To find the area, we need to calculate the cross-sectional area of the output line, which is a circle.
The formula for the area of a circle is:
Area = π × (radius)^2
Given that the diameter of the output line is 22 cm, we can calculate the radius:
Radius = diameter / 2 = 22 cm / 2 = 11 cm = 0.11 m
Now, we can calculate the area:
Area = π × (0.11 m)^2
Next, we can substitute the given values into the force equation:
Force = 18 atm × Area
Finally, with the maximum force calculated, we can determine the largest size vehicle it can lift. Keep in mind that this depends on the specific design and capabilities of the hydraulic lift.
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.
First, let's convert the given diameter from centimeters to meters. Since 1 meter is equal to 100 centimeters, the diameter of the output line is 0.22 meters.
Next, we need to calculate the cross-sectional area of the output line. The formula to calculate the area of a circle is:
Area = π * (radius)^2
Since the diameter is given, we can find the radius by dividing the diameter by 2:
Radius = 0.22 / 2 = 0.11 meters
Now, we can calculate the cross-sectional area using the formula mentioned above:
Area = π * (0.11)^2 = 0.0381 square meters (approx.)
To determine the force that the hydraulic lift can exert, we multiply the pressure by the area:
Force = Pressure * Area
Given that the maximum gauge pressure is 18 atm (atmospheres) and 1 atm is approximately equal to 101325 pascals (Pa), we can convert the pressure to pascals:
Pressure = 18 atm * 101325 Pa/atm = 1823850 Pa
Now, we can calculate the force:
Force = 1823850 Pa * 0.0381 square meters = 69569.335 N (Newtons) (approx.)
Finally, we need to convert the force to weight (in kg) using the acceleration due to gravity. The standard value for acceleration due to gravity is approximately 9.8 m/s^2:
Weight = Force / Acceleration due to gravity
Weight = 69569.335 N / 9.8 m/s^2 = 7094.51 kg (approx.)
Therefore, the largest size vehicle that the hydraulic lift can lift is approximately 7094.51 kg.