# Calculating Pressure for a Hydraulic Lift: A Scientific Approach

• sghaussi
In summary, given a hydraulic lift with a diameter of X meters, a pressure of pascals is required to lift a car with a mass of Y kg. The pressure is calculated in Pascals, and is wrong.
sghaussi
Hello! I was wondering if you could help me with a homework problem:

The piston of a hydraulic automobile lift is X meters in diameter.

What gauge pressure, in pascals, is required to lift a car with a mass of Y kg?

I know that a piston is a cylindrical shaped apparatus - however I believe that does not affect my calculations.

I also know this about pressure: p = F/A

F = mass x a so in my case that would be: Y kg x 9.8m/s

A (of a circle) = 2 x pi x r^2 r being half my diameter so X/2

From using this formula, the pressure is calculated in Pascals. The answer I get however is wrong. Am i using the wrong formula? should find the volume of the piston? I'm not sure how that would help... hope someone can give me some hints! =)

If you are considering the pressure on just the bottom of the piston (or top) then you only need to consider the area of one circle, not two.

that's right, i should only consider the area of one circle. that "2" in front of pi r squared was a typo... =) I've been trying to calculate it assuming it's one circle but I'm doing something wrong. =/

Is your final result

$$\frac{4(Y kg)(9.8 m/s^2)}{\pi x^2}$$?

Why is the equation being multiplied by 4?

The 4 comes from the denominator, since you are squaring X/2, you get x^2/4, and instead of having stacked fractions, you can multiply top and bottom by 4 to get what I gave.

My final equation looks like this:

(Y kg)*(9.8 m/s^2) / (pi)*(r^2) = p (pascals)

regarding the equation that I am using (p = F/A), does that even look like the correct equation I need to solve this type of problem?

Express it in terms of x and y, I think that's what you need to do. Is this online homework? Is that the complete problem?

sghaussi said:
regarding the equation that I am using (p = F/A), does that even look like the correct equation I need to solve this type of problem?

Yes it is the right equation. Your first calculation of area was wrong. If you get the area right, I think you will have it.

yes, it is online homework and that is the complete problem except "x" and "y" there are real numbers. so instead of multiplying by 4 i just divided x by two before I plugged it into the equation.

Last edited:
Did you divide correctly? ;)
Lets see the numbers.

got it.. i WAS getting the area wrong.. i was imputing it incorrectly into the calc. thanks so much for your time and patience!

## 1. How do I find the volume of the piston?

To find the volume of a piston, you will need to measure the diameter and height of the piston. Then, use the formula V = πr²h, where r is the radius (half of the diameter) and h is the height of the piston. This will give you the volume in cubic units.

## 2. Why is it important to know the volume of a piston?

The volume of a piston is important because it determines the amount of space available for the air or fluid inside. This can affect the performance of the engine or machine the piston is a part of.

## 3. Can I use the same formula to find the volume of any piston?

Yes, the formula V = πr²h can be used to find the volume of any piston, as long as you have accurate measurements for the diameter and height.

## 4. What units should I use for the measurements when finding the volume of a piston?

The units used for the measurements should be consistent. If the diameter and height are measured in inches, then the volume will be in cubic inches. If they are measured in centimeters, then the volume will be in cubic centimeters.

## 5. Is there a more accurate way to find the volume of a piston?

There are other methods that can be used to find the volume of a piston, such as using a displacement method where the piston is placed in a container of water and the change in water level is measured. However, using the formula V = πr²h is a commonly used and accurate method for finding the volume of a piston.

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